Journal of Theoretical and Applied Computer Science

Transcription

1 Journal of Theoretical and Applied Computer Science Vol. 6, No. 3, 2012 QCA & CQCA: QUAD COUNTRIES ALGORITHM AND CHAOTIC QUAD COUNTRIES ALGORITHM M. A. Soltani-Sarvestani, Shahriar Lotfi EFFECTIVENESS OF MINI-MODELS METHOD WHEN DATA MODELLING WITHIN A 2D-SPACE IN AN INFORMATION DEFICIENCY SITUATION Marcin Pietrzykowski SMARTMONITOR: RECENT PROGRESS IN THE DEVELOPMENT OF AN INNOVATIVE VISUAL SURVEILLANCE SYSTEM Dariusz Frejlichowski, Katarzyna Gościewska, Paweł Forczmański, Adam Nowosielski, Radosław Hofman NONLINEARITY OF HUMAN MULTI-CRITERIA IN DECISION-MAKING Andrzej Piegat, Wojciech Sałabun METHOD OF NON-FUNCTIONAL REQUIREMENTS BALANCING DURING SERVICE DEVELOPMENT Larisa Globa, Tatiana Kot, Andrei Reverchuk, Alexander Schill DONOR LIMITED HOT DECK IMPUTATION: EFFECTS ON PARAMETER ESTIMATION Dieter William Joenssen, Udo Bankhofer

2 Journal of Theoretical and Applied Computer Science Scientific quarterly of the Polish Academy of Sciences, The Gdańsk Branch, Computer Science Commission Scientific advisory board: Chairman: Prof. Henryk Krawczyk, Corresponding Member of Polish Academy of Sciences, Gdansk University of Technology, Poland Members: Prof. Michał Białko, Member of Polish Academy of Sciences, Koszalin University of Technology, Poland Prof. Aurélio Campilho, University of Porto, Portugal Prof. Ran Canetti, School of Computer Science, Tel Aviv University, Israel Prof. Gisella Facchinetti, Università del Salento, Italy Prof. André Gagalowicz, The National Institute for Research in Computer Science and Control (INRIA), France Prof. Constantin Gaindric, Corresponding Member of Academy of Sciences of Moldova, Institute of Mathematics and Computer Science, Republic of Moldova Prof. Georg Gottlob, University of Oxford, United Kingdom Prof. Edwin R. Hancock, University of York, United Kingdom Prof. Jan Helmke, Hochschule Wismar, University of Applied Sciences, Technology, Business and Design, Wismar, Germany Prof. Janusz Kacprzyk, Member of Polish Academy of Sciences, Systems Research Institute, Polish Academy of Sciences, Poland Prof. Mohamed Kamel, University of Waterloo, Canada Prof. Marc van Kreveld, Utrecht University, The Netherlands Prof. Richard J. Lipton, Georgia Institute of Technology, USA Prof. Jan Madey, University of Warsaw, Poland Prof. Kirk Pruhs, University of Pittsburgh, USA Prof. Elisabeth Rakus-Andersson, Blekinge Institute of Technology, Karlskrona, Sweden Prof. Leszek Rutkowski, Corresponding Member of Polish Academy of Sciences, Czestochowa University of Technology, Poland Prof. Ali Selamat, Universiti Teknologi Malaysia (UTM), Malaysia Prof. Stergios Stergiopoulos, University of Toronto, Canada Prof. Colin Stirling, University of Edinburgh, United Kingdom Prof. Maciej M. Sysło, University of Wrocław, Poland Prof. Jan Węglarz, Member of Polish Academy of Sciences, Poznan University of Technology, Poland Prof. Antoni Wiliński, West Pomeranian University of Technology, Szczecin, Poland Prof. Michal Zábovský, University of Zilina, Slovakia Prof. Quan Min Zhu, University of the West of England (UWE), Bristol, United Kingdom Editorial board: Editor-in-chief: Dariusz Frejlichowski, West Pomeranian University of Technology, Szczecin, Poland Managing editor: Piotr Czapiewski, West Pomeranian University of Technology, Szczecin, Poland Section editors: Michaela Chocholata, University of Economics in Bratislava, Slovakia Piotr Dziurzański, West Pomeranian University of Technology, Szczecin, Poland Paweł Forczmański, West Pomeranian University of Technology, Szczecin, Poland Przemysław Klęsk, West Pomeranian University of Technology, Szczecin, Poland Radosław Mantiuk, West Pomeranian University of Technology, Szczecin, Poland Jerzy Pejaś, West Pomeranian University of Technology, Szczecin, Poland Izabela Rejer, West Pomeranian University of Technology, Szczecin, Poland ISSN The on-line edition of JTACS can be found at: The printed edition is to be considered the primary one. Publisher: Polish Academy of Sciences, The Gdańsk Branch, Computer Science Commission Address: Waryńskiego 17, Szczecin, Poland

3 Journal of Theoretical and Applied Computer Science Vol. 6, No. 3, 2012, pp ISSN QCA & CQCA: Quad Countries Algorithm and Chaotic Quad Countries Algorithm M. A. Soltani-Sarvestani 1, Shahriar Lotfi 2 1 Computer Engineering Department, University College of Nabi Akram, Tabriz, Iran 2 Computer Science Department, University of Tabriz, Tabriz, Iran soltani_mohammadamin@yahoo.com, shahriar_lotfi@tabrizu.ac.ir Abstract: Keywords: This paper introduces an improved evolutionary algorithm based on the Imperialist Competitive Algorithm (ICA), called Quad Countries Algorithm (QCA) and with a little change called Chaotic Quad Countries Algorithm (CQCA). The Imperialist Competitive Algorithm is inspired by socio-political process of imperialistic competition in the real world and has shown its reliable performance in optimization problems. This algorithm converges quickly, but is easily stuck into a local optimum while solving high-dimensional optimization problems. In the ICA, the countries are classified into two groups: Imperialists and Colonies which Imperialists absorb Colonies, while in the proposed algorithm two other kinds of countries, namely Independent and Seeking Independence countries, are added to the countries collection which helps to more exploration. In the suggested algorithm, Seeking Independence countries move in a contrary direction to the Imperialists and Independent countries move arbitrarily that in this paper two different movements are considered for this group; random movement (QCA) and Chaotic movement (CQCA). On the other hand, in the ICA the Imperialists positions are fixed, while in the proposed algorithm, Imperialists will move if they can reach a better position compared to the previous position. The proposed algorithm was tested by famous benchmarks and the compared results of the QCA and CQCA with results of ICA, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Particle Swarm inspired Evolutionary Algorithm (PS-EA) and Artificial Bee Colony (ABC) show that the QCA has better performance than all mentioned algorithms. Between all cases, the QCA, ABC and PSO have better performance respectively about 50%, 41.66% and 8.33% of cases. Optimization, Imperialist Competitive Algorithm (ICA), Independent country, Seeking Independent country, Quad Countries Algorithm (QCA) and Chaotic Quad Countries Algorithm (CQCA). 1. Introduction Evolutionary algorithms (EA) [1, 2] are algorithms that are inspired by nature and have many applications to solving NP problems in various fields of science. Some of the famous Evolutionary Algorithms proposed for optimization problems are: the Genetic Algorithm (GA) [2, 3, 4], at first proposed by Holland, in 1962 [3], Particle Swarm Optimization algorithm (PSO) [5] first proposed by Kennedy and Eberhart [5], in In 2007, Atashpaz and Lucas proposed an algorithm known as Imperialist Competitive Algorithm (ICA) [6,7], that was inspired by a socio-human phenomenon. Since 2007 attempts were performed to in-

4 4 M. A. Soltani-Sarvestani, Shahriar Lotfi crease the efficiency of the ICA. Zhang, Wang and Peng proposed the approach based on the concept of small probability perturbation to enhance the movement of colonies to imperialist, in 2009 [8]. Faez, Bahrami and Abdechiri, in 2010, proposed a new method using the chaos theory to adjust the angle of colonies movement toward the Imperialist s positions (CICA: Imperialist Competitive Algorithm using Chaos Theory for Optimization) [9], and in another paper in the same year, they proposed another algorithm that applies the probability density function to adapt the angle of colonies movement towards imperialist s position dynamically, during iterations (AICA: Adaptive Imperialist Competitive Algorithm) [10]. In the Imperialist Competitive Algorithm (ICA), there are only two different types of countries, Imperialists and Colonies that Imperialists absorb. While, in the real world, there are some Independent Countries which are neither Imperialists nor Colonies. Some of the Independent Countries are at peace with Imperialists and the others have challenge with Imperialists to stable their independence. In the ICA, only the Colonies movements toward Imperialists are considered while in the real world each Imperialist moves in order to promote its political and cultural position. In the Quad Countries Algorithm (QCA) and Chaotic Quad Countries Algorithm (CQCA), countries are divided into four categories: Imperialist, Colony, Seeking Independent and Independent as each category has its special movement compared to the others. In the QCA and CQCA, as in the real world, an Imperialist will move if it brings advancement to a better position than its current position. The rest of this paper is arranged as follows. Section two explains about related works. Section three presents a brief description of Imperialist Competitive Algorithm. Section four will explain the proposed algorithm. In section five, the result will be analyzed and the performance of algorithms will be evaluated. In the section six, a conclusion will be presented. 2. Related Works In 2009 Zhang, Wang and Peng [8] mentioned that the original approach in the Imperialist Competitive Algorithm has difficulty in practical implementation with the increase of the dimension of the search spaces, as the ambiguous definition of the random angle in the process of optimization. Compared to the original algorithm, their approach based on the concept of small probability perturbation has more simplicity to be implemented, especially in solving high-dimensional optimization problems. Furthermore, their algorithm has been extended to constrained optimization problem, using a classical penalty technique to handle constraints. In 2010, Faez, Bahrami and Abdechiri [9] introduced a new Imperialist Competitive Algorithm using chaotic maps (CICA). In their algorithm, the chaotic maps were used to adapt the angle of colonies movement towards imperialist s position to enhance the escaping capability from a local optima trap. In the same year Faez, Bahrami and Abdechiri [10] introduced an algorithm that the Absorption Policy changed dynamically to adapt the angle of colonies movement towards imperialist s position. They mentioned that The ICA is easily stuck into a local optimum when solving high-dimensional multi-model numerical optimization problems. To overcome this shortcoming, they used probabilistic model that utilize the information of colonies positions to balance the exploration and exploitation abilities of the imperialistic competitive algorithm. Using this mechanism, ICA exploration capability enhanced.

5 QCA & CQCA: Quad Countries Algorithm and Chaotic Quad Countries Algorithm 5 3. The Imperialist Competitive Algorithm (ICA) Imperialist Competitive Algorithm (ICA) was proposed for the first time by Atashpaz and Lucas in 2007 [6]. ICA is a new evolutionary algorithm in the Evolutionary Computation (EC) field based on the human socio-political evolution. The algorithm starts with an initial random population called countries, then some of the best countries in the population are selected to be the imperialists and the rest of them form the colonies of these imperialists. The colonies are divided between them according to imperial power. In an N var - dimensional optimization problem, a country is a 1 N var array. This array defined as below: country p1 p2 p N = [,,..., ]. (1) The cost of a country is found by evaluating the cost function f at the variables ( p, p,..., p ). Then 1 2 Nvar i i 1 2 N var c = f ( country ) = f ( p, p,..., p ). (2) The algorithm starts with N pop initial countries and the N imp of the most powerful countries is chosen as imperialists. The remaining countries are colonies belong into imperialists in convenience with their powers. To distribute the colonies among imperialist proportionally, the normalized cost of an imperialist is defined as follow { } var C n = max i ci cn, (3) where, c n is the cost of n th imperialist and C n is its normalized cost. Each imperialist with more cost value will have less normalized cost value. Having the normalized cost, the normalized power of each imperialist is calculated as below and based on this, the colonies are distributed among the imperialist countries: P n = C n N imp C i i = i, (4) where P n is the normalized power of an imperialist. On the other hand, the normalized power of an imperialist is assessed by its colonies. Then, the initial number of colonies of an empire will be NC n {.( N col) } = rand p n, (5) where NC n is initial number of colonies of n th empire and N col is the number of all colonies. To distribute the colonies among imperialist, NC n of the colonies is selected randomly and assigned to their imperialist. The imperialist countries absorb the colonies towards themselves using the absorption policy. The absorption policy makes the main core of this algorithm and causes the countries move towards their minimum optima; this policy is shown in Fig.1. In the absorption policy, the colony moves towards the imperialist by x unit. The direction of movement is the vector from colony to imperialist, as shown in Fig.1. In this figure, the distance between the imperialist and colony is shown by d and x is a random variable with uniform distribution: (, β d ) x U 0, (6)

6 6 M. A. Soltani-Sarvestani, Shahriar Lotfi where β is greater than 1 and is near to 2. So, in [6] is mentioned that a proper choice can be β=2. In ICA algorithm, to search different points around the imperialist, a random amount of deviation is added to the direction of colony movement towards the imperialist. In Fig.1, this deflection angle is shown as Ө, which is chosen randomly and with a uniform distribution: ( γ, γ ) θ U. (7) While moving toward the imperialist countries, a colony may reach a better position, so the colony position changes according to the position of the imperialist. d Ө x Figure 1. Moving colonies toward their imperialist [6] The imperialists absorb these colonies towards themselves with respect to their power that is described in (8). The total power of each imperialist is determined by the power of its both parts, the empire power plus the percent of its average colonies power: TC { } ( imperialist ) ξ ( empire ) = cost + mean cost colonies of, (8) n n n where TC n is the total cost of the n th empire and ξ is a positive number which is considered to be less than one. In the ICA, the imperialistic competition has an important role. During the imperialistic competition, the weak empire will lose their power and their colonies. To model this competition, first the probability of possessing all the colonies is calculated for each empire, considering the total cost of such an empire: NTC n i { TCi } TC = max, (9) where TC n is the total cost of n th empire and NTC n is the normalized total cost of n th empire. Having the normalized total cost, the possession probability of each empire is calculated as below: n p p = n NTC n N imp NTC i i = 1. (10) After a while all the empires except the most powerful one will collapse and all the colonies will be under the control of this unique empire.

7 QCA & CQCA: Quad Countries Algorithm and Chaotic Quad Countries Algorithm 7 4. Quad Countries Algorithm (QCA) In this paper, a new Imperialist Competitive Algorithm is proposed which is called Quad Countries Algorithm where two new categories of countries are added to the collection of countries; Independent and Seeking Independence countries. In addition, in the new algorithm Imperialists can also move like the other countries. In the main ICA, there are only two categories of countries, Imperialist and Colony, and the only movement that exists there is the Colonies movement towards Imperialists, while in the proposed algorithm, there are four categories of countries with different movements. Therefore, the primary ICA may fall into local minimum trap during the search process and it is possible to get far from the global optimum. With changes that were performed in ICA a new algorithm called QCA was made whose power of exploration in the search space will substantially increase and prevent it from sticking in the local traps Independent Country In the real world, permanently there are countries which have been neither Colonies, nor Imperialist. These Countries may perform any movements in order to take their advantage and try to improve their current situation. In the proposed algorithm, some countries are defined as Independent countries which explore search space randomly. As an illustration in Fig. 2, if during the search process an Independent country reaches a better position compared to an Imperialist, they definitely exchange their positions. The Independent country changes to a new Imperialist and will be the owner of old Imperialist s Colonies, and the Imperialist changes to an Independent Country and will start to explore the search space like these kinds of countries. As mentioned, the Independent countries can perform any movements in the algorithm and their movements are arbitrary. In this paper, two different kinds of movements are considered for the Independent countries. One is a completely random movement. With this kind of movement, the Independent countries move completely randomly in different directions, and also independently from each other, which is named QCA. In the second kind of movement, these countries move based on Chaos Theory which is named CQCA which is explained in the next part Definition of Chaotic movement for Independent Countries (CQCA) In this approach, the Independent countries move according to Chaos Theory. In this kind of movement, the angle of movement is changed in a Chaotic way during the search process.

8 8 M. A. Soltani-Sarvestani, Shahriar Lotfi Independent Colonies Imperialists One step of movement Replacing an Empire with an Independent Figure 2. Replacing an Empire with an Independent This Chaotic action in the Independent countries movements in the CQCA makes the proper condition for the algorithm to more exploration and escape from local peaks and we introduce this approach as Chaotic Quad countries algorithm (CQCA). Chaos variables are usually generated by the some well-known Chaotic maps [11, 12]. Table 1 shows some of the Chaotic maps for adjusting Ө parameter (Angle of Independent countries movement). CM1 CM2 CM3 Table 1. Chaotic maps Chaotic maps θ = 1 αθ (1 + θ ) n n n θ αθ πθ = 2 n+ 1 n sin( n ) θ = n 1 θ + n b ( α + )sin(2 πθ ) mod(1) 2π n In Table 1, α is a control parameter and Ө is a chaotic variable in k th iteration which belongs to interval (0, 1). During the search process, no value of Ө is repeated.

9 QCA & CQCA: Quad Countries Algorithm and Chaotic Quad Countries Algorithm Seeking Independence Countries Seeking Independence Countries are countries which have challenges with the Imperialists and try to be away from them. In the main ICA, the only movement is the Colonies movements toward Imperialists and in fact, there is only Absorption policy. While by defining the Seeking Independence Countries in proposed algorithm, there is also Repulsion policy versus Absorption policy. Fig.3 illustrates the Repulsion Policy. Empire1 Empire2 Empire3 Colony1 Colony2 Colony3 Global Optimum a) Absorption policy Independent Global Optimum b) Absorption and Repulsion policy Figure 3. Different movement policy As can be seen in Fig.3.a, there is only Absorption policy that matches with the ICA. As it shows, the only use of applying Absorption policy causes that countries positions to get closer to each other and their surrounded space to decrease gradually, and the global optima might be lost. In Fig.3.a the algorithm is converging to a local optimum. Fig.3.b illustrates the process of the proposed algorithm. The black squares represent the Seeking Independence Countries, and as can be seen, these countries can steer the search process to a direction which the other countries don t cover. It shows that using Absorption and Repulsion policies together leads to a better coverage of search space. To apply the Repulsion policy in the QCA, first the sum of differences between the Seeking Independent Countries and the Imperialists positions is calculated as a vector like (11) named Center, that is a 1 N vector. Center = ( a p ), i = 1, 2,..., N, (11) N imp i j= 1 i ji where Center i is sum of i th component of all Imperialists, p ji is i th component of j th Imperialist, a i is i th component of Seeking Independence Country and N indicates the problem dimensions. Then the Seeking Independence Countries will move in the direction of obtained vector as (12). D = δ Center, δ (0,1), (12)

10 10 M. A. Soltani-Sarvestani, Shahriar Lotfi where δ is relocation factor and D is relocation vector that its components sum peer to peer with the Seeking Independence Country s components and obtain new position of the Seeking Independence Country Imperialists Movement In the real world, all countries including Imperialists perform ongoing efforts to improve their current situation. While in the main ICA, Imperialists never move and this fixed situation sometimes leads to the loss of global optima or prevents to reach up better solutions. Fig.4 illustrates this problem clearly. Fig.4 could be a final state of running the ICA, when only one Imperialist has remained. Since in the ICA Imperialists have no motion, solution 1 is the answer that the ICA returns. In the proposed approach, a random movement is assumed for Imperialists in each iteration and the cost of this hypothetical position will be calculated. If the cost of the new position is less than the cost of the previous one, the Imperialist will move to the new position, otherwise the Imperialist will not move. As can be seen in Fig.4, using this method leads to solution 2 which is a better solution than solution 1. Figure 4. A final state of ICA and QCA To applying this policy in the QCA, first of all, equals to the number of problem dimensions, the random values are generated like (13). α i = Rand I, (13) where I is an arbitrary value that is dependent on the problem size. Then the new position of Imperialist is obtained like (14). ( P1,..., PN ) = ( P var 1 + α1,..., PN + α ) var Nvar if f ( P1 + α1,..., PN + α ) ( var N < f P var 1,..., PN ), (14) var ( P1,..., PN ) = ( P var 1,..., PN ) Otherwise var where the α i are numbers which were obtained in Equation (13) and P i shows the value of i th dimension of a country. In fact, equation (14) states that if the new position of Imperialist is better than its current position, the Imperialists will be transferred to the new position, otherwise, they remain in their current position. According to the explained part about countries Seeking Independence and Independent countries, now their actions in the algorithm are specific. By adding these policies and ac-

11 QCA & CQCA: Quad Countries Algorithm and Chaotic Quad Countries Algorithm 11 tions, a new algorithm is generated, called Quad Countries Algorithm (QCA), and through defining Chaotic movement for Independent Countries another algorithm is generated, which is named Chaotic Quad Countries Algorithm (CQCA), both of which have better performance compared to ICA. 5. Evaluation and Experimental Results In this paper, two new algorithms based on the Imperialist Competitive Algorithm (ICA), called Quad Countries Algorithm (QCA) and Chaotic Quad Countries Algorithm (CQCA) are introduced and were applied to some well-known benchmarks in order to verify their performance and compare to ICA. These benchmark functions are presented in Table 2. The simulation was made to evaluate the rate of convergence and the quality of the proposed algorithm optima results, in comparison to ICA with all the benchmarks tested for minimization. Both algorithms are applied in identical conditions in 2, 10, 30, 50 dimensions. The number of countries in both algorithms were 125, including 10 Imperialists and 115 Colonies in the ICA, and 10 Imperialists, 80 Colonies, 18 countries Seeking Independence and 17 Independent countries in the QCA and CQCA. Both algorithms are run 100 times and 1000 generations in each iteration and average of these iterations are recorded in Table 3. Table 2. Benchmarks for simulation Benchmark Mathematical Representation Range Ackley = 1 D 1 D f x 2 ( ) 20 exp 0.2 x i x = i exp cos 2π 1 i = 1 i n n D 1 D Griewank 2 x ( ) = i f x x cos i= 1 i i = 1 i D 2 Rastrigin f ( x) xi cos( π x ) ( ) Sphere = D 2 f ( x) ( x ) + 20 e [ , ] [-600,600] = D [-15,15] i = 1 i i = 1 D Rosenbrock f ( x) = 100 ( x ) + ( x ) Symmetric Griewank Symmetric i= 1 i 2 ( i 1 i i 1 ) D 1 D 2 f ( x) = x cos 4000 i= 1 i i = 1 [-600,600] x [-15,15] x i i + 1 D 2 f ( x) = ( x ( x ) + ) Rastrigin i 10 cos 2 10 Symmetric i = 1 D 2 f ( x) = ( x ) Sphere i i = 1 i [-600,600] π [-600,600] [-600,600] Experiments started with Griewank Inverse function. Griewank Inverse is a hill-like function and its global optima are located in the corner of search space. Both algorithms were applied 100 times in identical conditions and the entrances are selected randomly. Fig.5 averagely, illustrates the graph of the results of 100 iterations in different dimensions with 1000 generations in each iteration of Griewank Inverse.

12 12 M. A. Soltani-Sarvestani, Shahriar Lotfi In Figures 5.a, 6.a, 7.a and 8.a the horizontal axis indicates the number of iterations. These graphs show the obtained results in each iteration for each algorithm. And in Figures 5.b, 6.b, 7.b and 8.b the horizontal axis indicates the number of generation. These graphs illustrate the convergence of algorithms. As mentioned, two different kinds of motions are defined for Independent countries: Chaotic and random motions which are named CQCA and QCA respectively. So there are three curves in all graphs in these Figures, ICA, QCA and CQCA. Figure 5.a illustrates the results of 100 iterations of applying algorithms on Griewank Inverse with two dimensions. In 100 iterations, 79 times the QCA and CQCA achieve better results than ICA. As can be seen in Figures 6.a, 7.a and 8.a by increasing the function s dimensions respectively to 10, 30 and 50, the QCA and CQCA achieve better results compared to the ICA in every 100 iterations. Figures 5.b, 6.b, 7.b and 8.b illustrate the average of the convergence of both algorithms and as can be seen, in addition to the quality of the results the convergences of the QCA and CQCA are also faster than the ICA. By increasing the problem s dimensions, the performance of ICA will decrease, while the QCA and CQCA still maintain their performances. It is worth consideration that the results of applying two kinds of Independent countries movement are so close to each other that their curves are the same. The observed results of applying the algorithms on the rest of the benchmarks in Table 2 were approximately similar to Griewank Inverse and the results are shown in Table 3. The Table 3 includes 14 columns; from left to right: the 1 st column indicates the benchmark s name, the 2 nd one is the range of the function s parameters, the 3 rd indicates the function s dimensions and the 4 th column indicates the optimum of benchmark. The 5 th column indicates the best results obtained by the QCA and the 8 th and 11 th columns are respectively the best results of the CQCA and the ICA. The 6 th,9 th and 12 th columns respectively indicate the average of the results in 100 iterations of the QCA, CQCA and the ICA. And 7 th, 10 th and 13 th columns indicate standard deviation (SD) of the QCA, CQCA and the ICA. And the 14 th column indicates the rate of improvement of QCA in comparison to the ICA. As can be seen, the QCA and CQCA results are better than the ICA in all cases except the Schwefel, where all algorithms achieve the same results. The recorded results in Table 3 show that, as the problem dimensions increase, the performance of the QCA and CQCA increases versus the ICA. The results of the QCA and CQCA are closely the same considerably. Each function in Table 3 performs 100 times and up to 1000 generation in each iteration by the same entrances with 2, 10, 30 and 50 dimensions. In the other comparison, the results are compared to Genetic Algorithm (GA), Particle Swarm Optimization (PSO), PS-EA and Artificial Bee Colony (ABC) in Table 4. As can be seen, the results of the proposed algorithm are better than GA and PS-EA in 100 percent of cases. But in the comparison with the QCA, the ABC and PSO the conditions are different. Also, in 50 percent of cases the QCA has better performance in compared to ABC and PSO and the best results are highlight in Table 4. The ABC and PSO have better performance respectively and 8.33 percent of cases. But there is a doubt about the ABC. As can be observed in all results, by increasing the problem dimensions, the performance of the algorithm will decrease. Naturally, the obtained results for a function with higher dimensions should be equal or bigger than the function with lower dimensions. By considering the Greiwank in Table 4, observed that the ABC acted inversely in this case and the result of applying the algorithm on function with 30 dimensions is smaller than 10 dimensions one and it seems that it is a mistake. So if this paradox is considered as a mistake, performance of QCA, PSO and ABC will change to 58.33, and 25 percent.

13 QCA & CQCA: Quad Countries Algorithm and Chaotic Quad Countries Algorithm 13 cost Run number 5.a. Stability of ICA, QCA and CQCA cost Generation 5.b. Convergence of ICA, QCA and CQCA Figure 5. The result of applying the ICA, QCA and CQCA on Griewank Inverse with 2 Dimensions

14 14 M. A. Soltani-Sarvestani, Shahriar Lotfi cost Run number 6.a. Stability of ICA, QCA and CQCA cost Generation 6.b. Convergence of ICA, QCA and CQCA Figure 6. The result of applying the ICA, QCA and CQCA on Griewank Inverse with 10 Dimensions

15 QCA & CQCA: Quad Countries Algorithm and Chaotic Quad Countries Algorithm 15 cost Run number 7.a. Stability of ICA, QCA and CQCA cost Generation 7.b. Convergence of ICA, QCA and CQCA Figure 7. The result of applying the ICA, QCA and CQCA on Griewank Inverse with 30 Dimensions

16 16 M. A. Soltani-Sarvestani, Shahriar Lotfi cost Run number 8.a. Stability of ICA, QCA and CQCA cost Generation 8.b. Convergence of ICA, QCA and CQCA Figure 8. The result of applying the ICA, QCA and CQCA on Griewank Inverse with 50 Dimensions

17 Table 3. The results of applying benchmarks on the QCA, CQCA and the ICA with 2, 10, 30 and 50 dimensions Benchmark Range Dim Optimum QCA CQCA ICA Imp. Best Result Mean SD Best Result Mean SD Best Result Mean SD E E E E E E E E E-9 100% Sphere [-600, E E E E E E E E E % 600] E E E E E E E E E % E E E E E E E % E E E E E E E % Sphere Inv. [-600, E E E E E E E E % 600] E E E E E E E E E E % E E E E E E E E E E % E E % Rastrigin [-15,15] E E E E E E E % E E E E E E E % Rastrigin Inv. Griewank Griewank Inv. Ackley Schewefel [-600, 600] [-600, 600] [-600, 600] [ , ] [-500, 500] E E % E E+5-7.2E E+5-7.2E E E % E E E E E E E E % E E E E e E E E E E % E E E E E E E E E E % E E % E E E E E E E E E % E E % % % % E E E E E E E % E E E E E E % E E E E E E E E E % E E E E E E E E E % E E E E E E E E E % E E E E E E E E %

18 Benchmark D Table 4. The result of GA, PSO, PS-EA, ABC, ICA, QCA GA [14] PSO [14] PS-EA [14] ABC [13] ICA QCA CQCA Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD Mean SD E E E E E E-8 Griewank E E E E E E E E E E E E E E-14 Rastrigin E E E E E E E E E-8 1.5E E E E E E E E E E E E-8 Ackley E E E E E E E E E E E E E-12 5E E E E E E E E-09 4E Schwefel

19 QCA & CQCA: Quad Countries Algorithm and Chaotic Quad Countries Algorithm Conclusions In this paper, two improved imperialist algorithms are introduced which are called respectively the Quad Countries Algorithm (QCA) and the Chaotic Quad Countries Algorithm (CQCA). In the QCA and CQCA, we define four categories of countries including Imperialist, Colony, Independent, and Seeking Independent country so that each group of countries has special motion and moves differently compared to the others. The difference between QCA and CQCA is related to the Independent countries movement. In the QCA Independent countries move completely randomly, but in the CQCA they move with chaotic maps. In the primary ICA there are only two categories, Colony and Imperialist, and the only motion is the Colonies movement toward Imperialists which is applied through Absorption policy. Whereas by adding Independent countries in the QCA, a new policy which is called Repulsion policy is also added. The empirical results were found by applying the proposed algorithm to some famous benchmarks, indicating that the quality of global optima solutions and the convergence speeds towards the optima have remarkably increased in the proposed algorithms, in comparison to the primary ICA. In experiments it can be clearly seen that, when the ICA sticks into a local optimum trap the QCA and CQCA find global optima. In cases when the ICA found a solution near to the global optima, the QCA and CQCA discovered an equal or better solution than the ICA s solution. Through the increase of the problem dimensions, the performance of the QCA and CQCA increase considerably when compared to the ICA. In comparison with the QCA, CQCA, GA, PSO, PS-EA and ABC, it was observed that in 100 percent of cases the proposed algorithms has better performance than GA and PS-EA, but in comparison with ABC and PSO, in 50 percent of cases the QCA has better performance than ABC and PSO. ABC and PSO have better performance about and 8.33percent of cases. Overall, the performed experiments showed that the QCA and CQCA have considerably better performance in comparison with the primary ICA and also the other evolutionary algorithms such as GA, PSO, PS-EA and ABC. The Quad Countries Algorithm (QCA) has a proper performance to solve optimization problems, but by changing the countries movements and defining new movement policies its performance will increase. In fact, by defining new movement policies both the ability of exploration and algorithm performance will increase. References [1] Sarimveis H., Nikolakopoulos A.: A Life Up Evolutionary Algorithm for Solving Nonlinear Constrained Optimization Problems. Computer & Operation Research, 32(6):pp (2005) [2] Mühlenbein H., Schomisch M., Born J.: The Parallel Genetic Algorithm as Function Optimizer. Proceedings of The Forth International Conference on Genetic Algorithms, University of California, San Diego, pp (1991) [3] Holland J. H.: ECHO: Explorations of Evolution in a Miniature World. In: Farmer J. D., Doyne J., editors, Proceedings of the Second Conference on Artificial Life (1990) [4] Melanie M.: An Introduction to Genetic Algorithms. Massachusett's: MIT Press (1999) [5] Kennedy J., Eberhart R.C.: Particle Swarm Optimization. In: Proceedings of IEEE, pp (1995) [6] Atashpaz-Gargari E., Lucas C.: Imperialist Competitive Algorithm: An Algorithm for Optimization Inspired by Imperialistic Competition. IEEE Congress on Evolutionary Computation (CEC 2007), pp (2007)

20 20 M. A. Soltani-Sarvestani, Shahriar Lotfi [7] Atashpaz-Gargari E., Hashemzadeh F., Rajabioun R., Lucas C.: Colonial Competitive Algorithm: A novel approach for PID controller design in MIMO distillation column process. International Journal of Intelligent Computing and cybernetics (IJICC), Vol. 1 No. 3, pp (2008) [8] Zhang Y., Wang Y., Peng C.: Improved Imperialist Competitive Algorithm for Constrained Optimization. International Forum on Computer Science-Technology and Applications (2009) [9] Bahrami H., Feaz K., Abdechiri M.: Imperialist Competitive Algorithm using Chaos Theory for Optimization (CICA). Proceedings of the 12 th International Conference on Computer Modelling and Simulation (2010) [10] Bahrami H., Feaz K., Abdechiri M.: Adaptive Imperialist Competitive Algorithm (AI- CA). Proceedings of The 9 th IEEE international Conference on Cognitive Informatics (ICCI'10) (2010) [11] Karaboga D., Basturk B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization, vol. 39, Issue.3, pp (2007) [12] Srinivasan D., Seow T.H.: Evolutionary Computation. CEC 03, Dec. 2003, 4, Canberra, Australia, pp (2003) [13] Schuster H.G.: Deterministic Chaos: An Introduction. 2 nd reviseded, Weinheim, Federal Republic of Germany: Physick-Verlag GmnH (1988) [14] Zheng W.M.: Kneading plane of the circle map. Chaos, Solitons & Fractals, 4:1221 (1994) [15] Soltani-Sarvestani M.A., Lotfi S., Ramezani F.: Quad Countries Algorithm (QCA). In: Proc. of the 4th Asian Conference on Intelligent Information and Database Systems (ACIIDS 2012), Part III, LNAI, pp (2012)

21 Journal of Theoretical and Applied Computer Science Vol. 6, No. 3, 2012, pp ISSN Effectiveness of mini-models method when data modelling within a 2D-space in an information deficiency situation Marcin Pietrzykowski Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland mpietrzykowski@wi.zut.edu.pl Abstract: This paper examines mini-models method and its effectiveness when data modelling in an information deficiency situation. It also compares the effectiveness of mini-models with various methods of modelling such as neural networks, the KNN-method and polynomials. The algorithm concentrates only on local query data and does not construct a global model during the learning process when it is not necessary. It is characterized by a high efficacy and a short calculation time. The article briefly describes the method by means of four variants: linear heuristic, nonlinear heuristic, mini-models based on linear regression, and minimodels based on polynomial approximation. The paper presents the results of experiments that compare the effectiveness of mini-models with selected methods of modelling in an information deficiency situation. Keywords: mini-models, modelling, parameter of minimum number of samples, leave one out error, information gap 1. Introduction The concept of mini-models method was developed by Piegat [1], [2]. In contrast to most well-known methods of modelling such as neural networks, neuro-fuzzy networks and polynomial approximation, the method does not create a global model when it is not necessary [3]. Mini-models method, similarly to the method of k-nearest neighbours, operates only on data from the local neighbourhood of a query [4], [5]. This is a consequence of the fact that in the modelling process we are generally only interested in an answer to a specific query, such as: What does the compressive strength of 28-day concrete amount to when that of cement amounts to 163 kg/m 3, water to 180 kg/m 3, coarse aggregate to 843 kg/m 3 and fine aggregate to 746 kg/m 3? The answer to the first question requires only the data, cement amounts to about 163 kg/m 3, water to 180 kg/m 3, etc. This approach frees us from the time consuming process of creating a global model. Moreover, when a new sample is acquired the global model becomes outdated and re-learning is required. Mini-model methods calculate the answer to the query point ad-hocly, which allows them to work in situations where new data points are continuously being received. It is also possible to build a global model in order to learn the value of a modelled variable across an entire domain. This can be done very simply by adding together mini-models for subsequent query points. The main aim of this paper is to compare the effectiveness of mini-models with selected methods of modelling in information deficiency situations. The article only briefly describes

22 22 Marcin Pietrzykowski the methods. Results of experiments on datasets that don't contain information gaps and the details of mini-models method have been described more comprehensively in previous works by the author [6], [7]. Mini-models in 2D-space form the basis for mini-models operating in spaces with a greater number of dimensions. In 2D-space mini-models can take the form of a line segment for linear models, or either a polynomial curve or an arc of a circle for nonlinear minimodels. In 3D-space mini-models take the form of a polygon. In 4D-space mini-models take the form of a polyhedron [1]. However, regardless of the dimensionality of the space in which mini-models operate it is necessary to define the query point and the mini-model's local neighbourhood. The query point is a set consisting of some independent variables with known values and a dependent variable with an unknown value. For example, for the simple query in a 2D-space: What does the compressive strength of 28-day concrete amount to when that of cement amounts to 163 kg/m 3, the dependent variable is the compressive strength and the independent variable is the quantity of cement. Query points will therefore take the following form: = 163, =?; or simply =163. For proper operation of a mini-models method the query point and its local neighbourhood must first be defined. The local neighbourhood may take various forms that depend on: the shape of the modelled data, the type of mini-model it is, and the location of the query point. The main parameter in defining the local neighbourhood is that of the minimum number of samples (). This parameter is closely related to the mini-model's limit points. In 2D-space they form graphical representations of the end points of a line or curve segment. It is assumed that the parameter is defined by the formula: +1, (1) where is the number of dimensions of the modelled space. In 2D-space, 3. The parameter can be defined globally for the entire domain or locally for either a selected range or a selected group of learning points. Unfortunately, there is no simple rule for choosing the optimal value of the parameter for a particular problem. Finding the optimal value instead requires an extensive search through all possible values. Thus, the solution may locally adapt to the modelled data. A test method based on leave-one-out cross-validation is used in the process of testing the effectiveness of mini-models for selected values of the parameter. 2. Details of the method A mini-models method works on a training dataset which consists of some points and is sorted in ascending order with respect to the variable, : =,, (2) =,,,,h +1. (3) The local neighbourhood of the query point is defined by boundaries or limit points: i.e. the lower limit and the upper limit : We call the set of points on which the mini-models operate &:, ", (4) ;. (5) & = ;, (6)

23 Effectiveness of mini-models method when data modelling 23 ()&. (7) There are two basic variants of the method: linear and nonlinear. As the name suggests linear mini-models form the shape of a line segment in response to query point data, and nonlinear mini-models take the shape of a curve segment after the learning process has completed Linear mini-models The simplest linear mini-models are based on linear regression. The learning algorithm for these is as follows: 1. choose a set of points & * that satisfy properties: (4), (5), (6) and (7), 2. calculate the function + * of the local mini-model using linear regression and a set & *, 3. calculate the error * committed by the model + *. The error * is calculated using following formula: * = / / - /9:, (8) ;<=> 2 4. repeat steps 1 3 until all combinations have been checked, 5. select the unique model + whichthat caused the minimal value of the error. In order to gain a valid solution, an extensive search through all possible combinations is first required to define the local neighbourhood, while satisfying the properties above: (4), (5), (6) and (7). Note that the error (8) is also the estimated value of the error that can be committed by the model during the process of calculating the answer to a query point. For example, for the error = 0.09 and the answer = 0.43 it is assumed that = 0.43 ± Estimation of the value of the error also applies to other versions of mini-models presented later in this article. The second type of linear mini-model is trained heuristically. Unlike linear regression mini-models, there is no problem in defining the local neighbourhood of a query point. The neighbourhood is instead created ad-hoc during the training of the mini-model. Heuristic learning is done by cyclic movement of the limits and along the x- and y-axis. When a change in the location of one limit point does not show any improvement in results, we change the location of the second point. We then repeat the whole operation again with the first limit point and so on. This whole operation is repeated until the stop condition has been reached. Searching along the y-axis is done by moving the limit point by a value of in the desired direction. Searching along the x-axis is done in a similar way, but the limit point must take the value of of the nearest point in the desired direction. The variable does not have to take any intermediate values, since this would not affect the number of points included in a mini-model and thus the error committed by that mini-model. We should remember that limit points after each operation along the x-axis have to satisfy the above properties: (4), (5), (6) and (7). After each shift of limit points we calculate the equation of a mini-model based on equations of a straight line passing through two points on a plane: =. D D , (9)

24 24 Marcin Pietrzykowski we then calculate the error committed by a mini-model (8). The mini-model having the smallest error value will become the output value for the next cycle of operations. In the end, we select the best model with the smallest value of the error Nonlinear mini-models The first variant of nonlinear mini-models is based on polynomial approximation. This type of mini-model works in a similar way to the linear equivalent. The only difference is that a polynomial approximation of the second order is used instead of linear regression. There is no need to use polynomial approximation of the higher order, and this would only increase the complexity of the algorithm. Mini-models are able to model the complex shape of a function of a few mini-models so long as they have relatively simple shape. The second variant of nonlinear mini-models is the heuristic mini-models. The initial stage of these mini-models' learning process is the same as the learning process of heuristic linear mini-models. After finding the best solution, the model takes the form of a circular arc when represented graphically. This can curve either up or down depending on the type of the modelled data. The results of numerical experiments have shown that those minimodels which were curved in the process of determining the locations of the limit points achieve worse results than the mini-models presented above. Training of mini-models with a higher number of degrees of freedom is more difficult and such models often reach local minima. 3. Experiments and results In order to test the effectiveness of mini-models in an information deficiency situation and to compare them with other commonly used methods of modelling, experiments were performed on the following specially prepared data sets: a dataset containing an information hole with a width of 10% of the interval, a dataset containing an information hole with a width of 20% of the interval, a dataset with 30% random sample removal. These experiments were performed with optimal values for all parameters, for all tested methods. Two types of tests were made. Firstly, the algorithms were tested using a test method based on leave-one-out cross validation using datasets with information loss. Secondly, the tested methods were trained with datasets with information loss and their effectiveness was checked against data sets consisting of lost data. For example, methods were tested with data from information holes that were not involved in the learning process. The experiments were conducted on 11 different data sets: Compressive Strength of 28-day Concrete, Concrete Slump Test, Unemployment Rate in Poland, Housing Value Concerns in the Suburbs of Boston, Computer Hardware Performance, Concentration of NO 2 Measured at Alnabru in Oslo, Sold Production of Industry with Inflation in Poland, Sleep in Mammals, Air Pollution to Mortality, Fuel Consumption in Miles per Gallon, and Determinants of Wages. It should be noted that the learning datasets are multi-dimensional and presented as mini-models operating within 2D-space. It was possible to perform 37 different numerical experiments for each type of modification of the learning datasets. A summary comparison of these tested methods is shown in Table 1.

25 Effectiveness of mini-models method when data modelling 25 Table 1. The total number of experiments in which the tested methods achieved the best results (i.e. achieved a better result than the other tested method) method heuristic linear minimodel mini-model based on linear regression heuristic nonlinear minimodel mini-model based on polynomial approximation heuristic linear minimodel mini-model based on linear regression heuristic nonlinear minimodel mini-model based on polynomial approximation count of exper. 10% gap 20% gap 30% random loss % of experiments count of exper. LOO 1 TT 2 LOO TT LOO TT % of experiments LO O mini-model with global parameter of minimal numbers of points count of exper. % of experiments TT LOO TT LOO TT 0 4 0,0 10, ,0 5, ,0 7, ,0 7, ,0 7, ,0 15, ,00 5, ,0 15, ,0 7, ,6 2, ,0 2, ,0 5,3 mini-model with local parameter of minimal numbers of points ,4 7, ,4 5, ,1 7, ,00 7, ,6 7, ,6 13, ,6 13, ,6 2, ,2 7, ,8 10, ,8 2, ,5 2,6 other methods k-nearest neighbours 1 3 2,6 7, ,6 21, ,0 5,2 polynomial approximation of degree n feed forward neural network General Regression Neural Network [8] mini-model with global parameter mini-model with local parameter 0 4 0,0 10, ,0 13, ,0 7, ,0 13, ,0 15, ,6 10, ,0 2, ,0 0, ,0 7,9 summary comparison ,6 26, ,00 31, ,00 36, ,7 39, ,4 18, ,4 31,6 other methods ,6 34, ,6 50, ,6 31,6 all mini-models ,4 65, ,4 50, ,4 68,4 1 Test method based on leave-one-out cross validation 2 Testing using lost data for example form information hole

26 26 Marcin Pietrzykowski 4. Discussion of results It should be noted that the information gap does not significantly affect the results of experiments using test methods based on leave-one-out cross validation. Mini-models method was the most effective and the effectiveness of different types of mini-models only varied slightly. Mini-models were less efficient in the tests with datasets than those with information gaps, but their advantage is still significant. In the tests with datasets containing a hole with a width of 10%, mini-models were the most efficient and achieved best results in 65% of the tests. For datasets containing an information hole with a width of 20%, mini-models achieved best results in 50% of the tests. The KNN method also achieved good results with these datasets. The KNN method is considered as the main competitor to the mini-models method. It should be remembered that the KNN method in an information hole situation is effective only for datasets where samples are not evenly distributed (Figure 1c). The method does not work very well with datasets that have a clearly visible trend line. The graph shows clearly the steps behaviour of the method shown in Figure 2c. For the datasets with 30% of the random loss of samples, the mini-models achieved the best results in 68% of tests. It should be noted that other methods (except KNN mentioned above) gained no more than several percent across all tests. Mini-models with a global value of the parameter performed as well across the entire range as mini-models with a local value of this parameter. a) b) c) Figure 1. a) Original data of compressive strength of 28-day concrete depending on fine aggregate. b) Global model build with heuristic linear mini-models with global value of the parameter (best minimodel MAE=0,1599) for a dataset with a hole in the interval [0.5; 0.7]. c) Global model build with the k-nearest neighbours method (best result MAE=0,1598) for a dataset with a hole in the interval [0.5; 0.7] a) b) c) Figure 2. a) Original data of unemployment rate in Poland depending on the money supply. b) Global model build with heuristic linear mini-models with a global value of the parameter (best result MAE=0,0374) for a dataset with a hole in the interval [0.3; 0.5]. c) Global model build with the k-nearest neighbours method (worst result MAE=0,1611) for a dataset with a hole in the interval [0.3; 0.5]

27 Effectiveness of mini-models method when data modelling Conclusions The results of the experiments have shown advantages of mini-models over other methods of modelling information deficiency situations. Their advantage is not as great as in the situation of testing with leave-one-out cross validation method for original data, but still remains significant. The irregularity of the global models created by mini-models method and their high efficiency raises the question of the validity of the theory of regularization. Authors in future research should move towards the use of mini-models in spaces with a higher number of dimensions and their relevance to the theory of regularization. References [1] Piegat A., Wąsikowska B., Korzeń M.: Differences between the method of mini-models and of the k-nearest neighbors on example of modeling of unemployment rate in Poland in Information Systems in Management IX. Bussines Inteligence and Knowledge Management, Warsaw, 2011, pp [2] Piegat A., Wąsikowska B., Korzeń M.: Zastosowanie samouczącego się trzypunktowego minimodelu do modelowania stopy bezrobocia w Polsce, Studia Informatica, no. 27, pp , [3] Rutkowski L.: Metody i techniki sztucznej inteligencji. Warszawa: PWN, [4] Fix E., Hodges J. L.: Discriminatory analysis, nonparametric discrimination: Consistency properties, Randolph Field, Texas, [5] Kordos M., Blachnik M., Strzempa D.: Do We Need Whatever More than k-nn?, in Proceedings of 10-th International Conference on Artificial Inteligence and Soft Computing, Zakopane, [6] Pietrzykowski M.: Comparison of effectiveness of linear mini-models with some methods of modelling, in Młodzi naukowcy dla Polskiej Nauki, Kraków, [7] Pietrzykowski M.: The use of linear and nonlinear mini-models in process of data modelling in a 2D-space, in Nowe trendy w naukach inżynieryjnych., [8] Specht D. F.: A General Regression Neural Network, IEEE Transactions on Neural Networks, pp , [9] Witten I. A., Frank E.: Data mining. San Francisco: Morgan Kaufmann Publishers, [10] Pluciński M.: Nonlinear ellipsoidal mini-models application for the function approximation task, paper accepted for ACS Conference, 2012 [11] Pluciński M.: Application of the information-gap theory for evaluation of nearest neighbours method robustness to data uncertainty, paper accepted for ACS Conference, 2012

28 Journal of Theoretical and Applied Computer Science Vol. 6, No. 3, 2012, pp ISSN SmartMonitor: recent progress in the development of an innovative visual surveillance system Dariusz Frejlichowski 1, Katarzyna Gościewska 1,2, Paweł Forczmański 1, Adam Nowosielski 1, Radosław Hofman 2 1 Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland 2 Smart Monitor sp. z o.o., Szczecin, Poland {dfrejlichowski,pforczmanski,anowosielski}@wi.zut.edu.pl, {katarzyna.gosciewska,radekh}@smartmonitor.pl Abstract: Keywords: This paper describes recent improvements in developing SmartMonitor an innovative security system based on existing traditional surveillance systems and video content analysis algorithms. The system is being developed to ensure the safety of people and assets within small areas. It is intended to work without the need for user supervision and to be widely customizable to meet an individual s requirements. In this paper, the fundamental characteristics of the system are presented including a simplified representation of its modules. Methods and algorithms that have been investigated so far alongside those that could be employed in the future are described. In order to show the effectiveness of the methods and algorithms described, some experimental results are provided together with a concise explanation. SmartMonitor, visual surveillance system, video content analysis 1. Introduction Existing monitoring systems usually require supervision by responsible person whose role it is to observe multiple monitors and report any suspicious behaviour. The existing intelligent surveillance systems that have been built to perform additional video content analysis tend to be very specific, narrowly targeted and expensive. For example, the Bosch IVA 4.0 [1], an advanced surveillance system with VCA functionality, is designed to help operators of CCTV monitoring and is applied primarily for the monitoring of public buildings or larger areas, hence making it unaffordable for personal use. In turn, SmartMonitor is being designed for individual customers and home use, and user interaction will only be necessary during system calibration. SmartMonitor s aim is to satisfy the needs of a large number of people who want to ensure the safety of both themselves and their possessions. It will allow for the monitoring of buildings (e.g. houses, apartments, small enterprises, etc.) and their surroundings (e.g. yards, gardens, etc.), where only a small number of objects need to be tracked. Moreover, it will utilize only commonly available and inexpensive hardware such as a personal computer and digital cameras. Another intelligent monitoring system, described in [2], analyses human location, motion trajectory and velocity in an attempt to classify the type of behaviour. It requires both the participation of a qualified employee and the preparation of a large database during the learning process. These steps are unnecessary with the SmartMonitor system due to a simple calibration mechanism and feature-based methods. Moreover, a precise calibra-

29 SmartMonitor: recent progress tion can improve a system s effectiveness and allow the system s sensitivity to be adjusted to situations that do not require any system reaction. The customization ability offered by SmartMonitor is very advantageous. In [3], the problem of automatic monitoring systems with object classification was described. It was assumed that the background model used for foreground subtraction does not change with time. This is a crucial limitation caused by the background variability of real videos. Therefore, and due to planned system scenarios, the model that best adapts to changes in the scene will be utilized. SmartMonitor will be able to operate in four independent modes (scenarios) that will provide home/surroundings protection against unauthorized intrusion, allow for supervision of people who are ill, detect suspicious behaviours and sudden changes in object trajectory and shape, and detect smoke or fire. Each scenario is characterized by a group of performed actions and conditions, such as movement detection, object tracking, object classification, region limitation, object size limitation, object feature change, weather conditions and work time (with artificial lighting required at night). A more detailed explanation of system scenarios and parameters is provided in [4]. The rest of the paper is organised as follows: Section 2 contains the description of the main system modules; algorithms and methods that are utilised in each module are briefly described in Section 3; Section 4 contains selected experimental results; and Section 5 concludes the paper. 2. System Modules SmartMonitor will be composed of six main modules: background modelling, object tracking, artefacts removal, object classification, event detection and system response. Some of these are common to the intelligent surveillance systems that were reviewed in [5]. A simplified representation of these system modules is displayed in Fig. 1. Figure 1. Simplified representation of system modules Background modelling detects movement through use of background subtraction methods. Foreground objects that are larger than a specified size and coherent are extracted as objects of interest (OOI). The second module, object tracking, tracks object locations across consecutive video frames. When multiple objects are tracked, each object is labelled accordingly. Every object moves along a specified path called a trajectory. Trajectories can be compared and analysed in order to detect suspicious behaviours. The third module, artefacts removal, is an important step preceding classification and should be performed correctly. In this, all

30 30 Dariusz Frejlichowski, et al. artefacts, such as shadows, reflections or false detection results, enlarge the foreground region and usually move with the actual OOI. The fourth module, object classification, will allow for simple classification using object parameters and object templates. The template base will be customizable so that new objects can be added. A more detailed classification will also be possible using more sophisticated methods. The key issue of the fifth, i.e. the event detection module, is to detect changes in object features. The system will react to both sudden changes (mainly in shape) and a lack of movement. The final module defines how the system responds to detected events. By eliminating the human factor it is important to determine which situations should set off alarms or cause information to be sent to the appropriate services. 3. Employed Methods and Algorithm For each module we investigated the existing approaches, and modified them to apply the best solution for the system. Below we present a brief description and explanation of this. Background modelling includes models that utilize static background images [3], background images averaged in time [6] and background images built adaptively, e.g. using Gaussian Mixture Models (GMM) [7, 8]. Since the backgrounds of real videos tend to be extremely variable in time, we decided to use a model based on GMM. This builds per-pixel background image that is updated with every frame, and is also sensitive to sudden changes in lighting which can cause false detections, mainly by shadows. It was stated in [9] that shadows only affects the image brightness and not the hue. By comparing foreground images constructed using both the Y component of the YIQ colour scheme and the H component of the HSV colour scheme, it is possible to exclude false detections that are caused by shadows. Following this, morphological operations are applied to the resulting binary mask. Erosion allows for the elimination of small objects composed of one or few pixels (such as noise) and the reduction of the region. Later the dilation process fills in the gaps. For the object tracking stage we investigated three possible implementations, namely the Kalman filter [10], Mean Shift and Camshift [11, 12] algorithms. The Mean Shift algorithm is simple and appearance-based. It requires one or more feature, such as colour or edge data to be selected for tracking purposes. This can cause several problems with object localization when particular features change. The Camshift algorithm is simply a version of the Mean Shift algorithm that continuously adapts to the variable size of tracked objects. Unfortunately, the described solution is not optimal since it increases the number of computations. Moreover, both methods are effective only when certain assumptions are met, such as that tracked objects will differ from the background (e.g. through variations in colour). The Kalman filter algorithm was therefore selected to overcome these drawbacks. This constitutes a set of mathematical equations that define a predictor-corrector type estimator. The main task was to estimate future values in two steps: prediction based on known values, and correction based on new measurements. It is assumed that objects can move uniformly and in any direction but will not change direction suddenly and unpredictably. After tracking the objects are classified (labelled) as either human or not human. A boosted cascade of Haar-like features [13] connected using the AdaBoost algorithm [14] can be utilized. However, at this stage, we replaced the AdaBoost classification with a simpler one. Objects can now be classified using their binary masks and the threshold values of two of their properties: area size and minimum bounding rectangle aspect ratio. A specific and detailed classification can be performed using a Histogram of Oriented Gradients (HOG) [15]. A HOG descriptor localises and extracts objects from static scenes

31 SmartMonitor: recent progress through use of specified patterns. Despite its high computational complexity, the HOG algorithm can be applied to a system under several conditions such as those with limited regions or time intervals. 4. Experimental Conditions and Results In this section we present some experimental results from employing the algorithms for object localization, extraction and tracking that have given the best results so far. In order to ensure the experiments were performed under realistic conditions, a set of test video sequences corresponding to certain system scenarios was prepared. These include scenes recorded both inside and outside the buildings, with different types of moving objects. A database also had to be created due to the lack of free, universal video databases that matched the planned scenarios. The results of employing both the GMM algorithm and the methods for removing false objects are presented in Fig. 2. The first row contains the sample frame and background images for the Y and H components. The second row shows the respective foreground images for the Y and H components alongside the foreground object s binary mask after false objects removal. It is noticeable that the foregrounds constructed using the different colour components strongly differ and that, by subtracting one image from another, we can eliminate false detections. Figure 2. Results of employing the GMM algorithm and false objects removal methods Specific objects can be localised and extracted using the HOG descriptor. This detects objects using a predefined patterns and extracted feature vectors. Below we present the results of the experiments utilizing HOG descriptor. The first experiment was performed using a fixed template size and two sample frames, the second one utilized various template sizes and one sample frame. The results of the first experiment are pictured in Fig. 3. The figure contains: a sample frame with a chosen template (left column) and two frames (middle column) from the same video sequence which were scanned horizontally in an attempt to identify the matching regions. The depth maps (right column) show the results of the HOG algorithm the darker the colour the more similar the region is. Black regions indicate a Euclidean distance between two feature vectors of zero.

32 32 Dariusz Frejlichowski, et al. Figure 3. Results of the experiment utilizing the HOG descriptor with a fixed template size In the next experiment, devoted to an investigation of the HOG descriptor, various template sizes were tested. The left column of Fig. 4 presents a frame with a chosen template marked by a white rectangle, the central column contains a frame that was scanned horizontally using two different template sizes (dark rectangles in the top left corners define the size of the rescaled template) and the right column provides the respective results of the HOG algorithm. Clearly, the closer the template size is to object size, the more accurate the depth map is. Figure 4. Results of the experiment utilizing the HOG descriptor with a variable template size As mentioned in the previous section, we investigated three tracking methods. The first one, the Mean Shift algorithm, uses part of an image to create a fixed template model. In this case we converted images to the HSV colour scheme. Fig. 5 presents three sample frames from the tracking process (first row) and their corresponding binary masks (second row). The white masked regions indicate those regions that are similar to the template, the dark rectangle determines the template and the light points within the rectangle create the object s trajectory. Camshift was the second tracking method investigated. This uses the HSV colour scheme and a variable template model. The first row in Fig. 6 presents sample frames from the tracking process: the starting frame with the chosen template, the central frame with an enlarged template and the finishing frame where the moving object leaves the scene. The second row in Fig. 6 shows corresponding binary masks for each frame. Both tracking methods, thanks

33 SmartMonitor: recent progress Figure 5. Results of the experiment utilizing the Mean Shift algorithm to their local application, were effective despite of the presence of many similar regions to the template. Figure 6. Results of the experiment utilizing the Camshift algorithm Fig. 7 shows a result of employing the third algorithm, the Kalman filter, to track a person walking in a garden. Light asterisks are obtained for object positions that were estimated using a moving object detection algorithm and dark circles are positions predicted by the Kalman filter. 5. Summary and Conclusions In this paper, recently achieved results from the SmartMonitor system during the development process were described. We provided basic information about system characteristics and properties, and system modules. Investigated methods and algorithms were briefly described. Selected experimental results on utilizing various solutions were presented. SmartMonitor will be an innovative surveillance system based on video content analysis and targeted at individual customers. It will operate in four independent modes which are fully customizable (and will also be combinable to make custom modes). This allows for individual safety rules to be set based on different system sensitivity degrees. Moreover, SmartMonitor will utilize only commonly available hardware. It will almost eliminate human involvement,

34 34 Dariusz Frejlichowski, et al. Figure 7. Results of the experiment utilizing the Kalman filter being only required for the calibration process. Our system will analyse a small number of moving objects over limited region which could additionally improve its effectiveness. Currently, there are no similar systems on the market. Modern surveillance systems are usually expensive, specific and need to be operated by a qualified employee. SmartMonitor will eliminate these factors by offering less expensive software, making it more affordable for personal use and requiring less effort to use. Acknowledgements The project Innovative security system based on image analysis SmartMonitor prototype construction (original title: Budowa prototypu innowacyjnego systemu bezpieczeństwa opartego o analize obrazu SmartMonitor) is the project co-founded by the European Union (project number PL: UDA-POIG /10-01, Value: PLN, EU contribution: PLN, realization period: ). European Funds for the development of innovative economy (Fundusze Europejskie dla rozwoju innowacyjnej gospodarki). References [1] Bosch IVA 4.0 Commercial Brochure, resource.boschsecurity.com/ documents/ Commercial Brochure enus pdf [2] Robertson N., Reid I.: A general method for human activity recognition in video. Computer Vision and Image Understanding 104, (2006) [3] Gurwicz Y., Yehezkel R., Lachover B.: Multiclass object classification for real-time video surveillance systems. Pattern Recognition Letters 32, (2011) [4] Frejlichowski D., Forczmański P., Nowosielski A., Gościewska K., Hofman R.: SmartMonitor: An Approach to Simple, Intelligent and Affordable Visual Surveillance System. In: Bolc, L. et al. (eds.) ICCVG LNCS, vol. 7594, pp Springer, Heidelberg (2012)

35 SmartMonitor: recent progress [5] Forczmański P., Frejlichowski D., Nowosielski A., Hofman R.: Current trends in the developement of intelligent visual monitoring systems (in Polish). Methods of Applied Computer Science 4/2011(29), (2011) [6] Frejlichowski D.: Automatic Localisation of Moving Vehicles in Image Sequences Using Morphological Operations. 1st IEEE International Conference on Information Technology, (2008) [7] Stauffer C., Grimson W. E. L.: Adaptive background mixture models for real-time tracking. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, (1999) [8] Zivkovic Z.: Improved adaptive Gaussian mixture model for background subtraction. Proceedings of the 17th International Conference on Pattern Recognition 2, (2004) [9] Forczmański P., Seweryn M.: Surveillance Video Stream Analysis Using Adaptive Background Model and Object Recognition. In: Bolc, L. et al. (eds.) ICCVG 2010, Part I. LNCS, vol. 6374, pp Springer, Heidelberg (2010) [10] Welch G., Bishop G.: An Introduction to the Kalman Filter. UNC-Chapel Hill, TR (24 July 2006) [11] Cheng Y.: Mean Shift, Mode Seeking, and Clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(8), (1995) [12] Comaniciu D., Meer P.: Mean Shift: A Robust Approach Toward Feature Space Analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(5), (2002) [13] Viola P., Jones M.: Rapid Object Detection Using a Boosted Cascade of Simple Features. IEEE Computer Society Conference on Computer Vision and Pattern Recognition 1, (2001) [14] Avidan S.: Ensemble Tracking. IEEE Transactions on Pattern Analysis and Machine Intelligence 29(2), (2007) [15] Dalal N., Triggs B.: Histograms of oriented gradients for human detection. IEEE Computer Society Conference on Computer Vision and Pattern Recognition 1, (2005)

36 Journal of Theoretical and Applied Computer Science Vol. 6, No. 3, 2012, pp ISSN Nonlinearity of human multi-criteria in decision-making Andrzej Piegat, Wojciech Sałabun Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland {apiegat, Abstract: In most cases, known methods of multi-criteria decision-making are used in order to make linear aggregation of human preferences. Authors of these methods seem not to take into account the fact that linear functional dependences rather rarely occur in real systems. Linear functions rather imply a global character of multi-criteria. This paper shows several examples of human nonlinear multi-criteria that are purely local. In these examples, the nonlinear approach is used based on fuzzy logic. It allows for better understanding of how important is the non-linear aggregation of human multi-criteria. The paper contains also proposal of an indicator of nonlinearity degree of the criteria. The presented results are based on investigations and experiments realized by authors. Keywords: Multi-criteria analysis, multi-criteria decision-analysis, non-linear multi-criteria, fuzzy multi-criteria, indicator of nonlinearity. 1. Introduction On a daily basis and in professional life we frequently have to make decisions. Then we use some criteria that depend on our individual preferences, or in case of group-decisions on preferences of the group. Further on, criteria represent preferences of a single person will be called individual criteria and criteria represent a group will be called group-criteria. Groupcriteria can be achieved by aggregation of individual ones. Therefore, further on, the nonlinearity problem of criteria will be analyzed on examples of individual criteria, because properties of individual criteria are transferred on the group-ones. Individual human multicriteria are programmed in our brains and special methods for their elicitation and mathematical formulation of them are necessary. Multi-criteria (for short M-Cr) of different persons are more or less different and therefore it would be not reasonable to assume one and the same type of a mathematical formula for certain criterion representing thousands of different people, e.g. for the individual criterion of car attractiveness. However, in case of M- Crs most frequently used criterion type is the linear M-Cr form (1). = , (1) where: w i weight coefficients of particular component criteria, = 1, K i - the component criteria aggregated by the M-Cr ( = ). 1: They are mostly used, also in this paper, in the form which is normalized to interval [0,1]. The linear criterion-function in the space 2D is represented by a straight line, in the space 3D by a plane, Fig.1, and in the space nd by a hyper-plane.

37 Nonlinearity of human, decisional multi-criteria 37 Figure 1. A linear criterion function in space 2D (Fig.1a) and in space 3D (Fig.1b) Let us notice that in the linear-criterion function K particular component-criteria K i influence the superior criterion in the mutually independent and uncorrelated way. Apart of this, the influence strength of particular component criteria K i is of the global, constant and unchanging character in the full criterion-domain. Both above features are great disadvantages of the linear M-Cr, because human M-Cr are in most cases nonlinear and significance of component criteria K i is not constant, is not independent from other criteria and varies in particular, local sub-domains of the global MCr. Unfortunately, linear multicriteria are used in many world-known methods of the multi-criteria decision-analysis. Following examples illustrating the above statement can be given: the method SAW (Simple Additive Weighting) [4,15], the very known and widely used AHP-method of Saaty (the Analytic Hierarchy Process) [11,15,18], the ANP-method (Analytic Network Process), [12,13]. Other known MCr-methods as TOPSIS [15,16], ELECTRE [2], PROMETHEE [1,2] are not strictly linear ones. However, they assume global weight-coefficients w i, constant for the full MCr-domain and in certain steps of their algorithms they also use the linear, weighted aggregation of alternatives. The next part will present the simplest examples of nonlinear criterion-functions in 2D-space. 2. Nonlinear human criterion-functions in 2D-space An example of a very simple human nonlinear criterion-function can be the dependence between the coffee taste (CT), CT [0,1], and the sugar quantity S, S [0,5] expressed in number of sugar spoons, Fig.2. Coffee taste represents inner human preference. The criterion function of the coffee taste can be identified by interviewing a given person or more exactly, experimentally, by giving the person coffees with different amount of sugar and asking he/she to evaluate the coffee taste or to compare tastes of pairs of coffees with different amount of sugar. The achieved taste evaluations can be processed with various MCr-methods previously cited or with the method of characteristic objects proposed by one of the paper authors. However, even without scientific investigations it is easy to understand that the criterion-function shown in Fig.2 is qualitatively correct. This function represents preferences of the author-ap. He does not like coffee with too great amount of sugar (more than 3 coffee-spoons) and evaluates its taste as CT 0. The taste of coffee without sugar (S=0) he also evaluates as a poor one. The best taste he feels when cup of coffee con-

38 38 Andrzej Piegat, Wojciech Sałabun tains 2 spoons of sugar (S opt =2). For other persons the optimal sugar amount will be different. Thus, this criterion-function is not an objective (what does it mean?) function of all people in the world but an individual criterion-function of the AP-author of the paper. It is very important to differentiate between individual criteria and group-criteria, which represent small or greater group of people. Similar in character as the function in Fig.2 is also other one-component human criterion function: e.g. dependence of the text-reading easiness from the light intensity. Figure 2. Criterion function representing dependence of the coffee taste CT from number of sugar spoons S (felt by an individual person, the paper author-ap) 3. Nonlinear, human, multi-criterion function in 3D-space and a method of its identification Already in 60-ties and 70-ties of the 20 th century American scientists D. Kahneman and A. Tversky, Nobel prize winners from 2002 have drawn the attention of the scientific community on the nonlinearity of human multi-criteria [5] by their investigation results on human decisions based on a MCr. In their experiment were aggregated some component criteria: value of a possible profit, probability of the possible profit value, value of a possible loss, probability of the possible loss-value. Further on, there will be presented a similar but a simplified problem of evaluation of the individual play acceptability-degree K in dependence of a possible winnings-value K 1 [$] and of a possible loss-value K 2 [$]. Both values are not great. The interviewed person has to make decisions in the problem described below. Among 25 plays shown in Table 1, with different winnings K 1 [$] and losses K 2 [$] (if you don t win you will have to pay a sum equal to the loss K 2 ) at first find all plays (K 1,K 2 ) which certainly are not accepted by you (K=0), and next all plays which are certainly accepted by you (K=1). For rest of the plays determine a rank with the method of pairtournament (pair comparisons). Probability of winnings and losses are the same and equal to 0.5.

39 Nonlinearity of human, decisional multi-criteria 39 Table 1 gives values of possible winnings and losses (K1,K2) in particular plays. It also informs for which plays the AP-author declares the full acceptation (full readiness to take up the game) that means K=1, and informs for which plays he does not accept at all (zero readiness to take up the game) that means K=0. The acceptability degree plays a role of the multi-criterion in the shown decision-problem. The acceptability degree of plays marked with question mark will be determined with the tournament-rank method. The investigated person chooses from each play-pair the more acceptable play (inserting the value 1 in the table for this play), which means the win. If the person is not able to decide which of two plays is better, then she/he inserts the value 0.5 for both plays of the pair, which means the draw. Summarized scores from Table 2 are shown in Table 3 for particular plays (K 1,K 2 ). Table 1. Winnings K 1 [$] and losses K 2 [$] in particular 25 plays and first decisions of the interviewed person : determining the unacceptable plays (acceptation degree K=0) and the fully acceptable plays (K=1) which certainly would be played by the person. Plays with question marks are plays of a partial (fractional) acceptation that is to be determined. The value of losses [$] The value of winning [$] ??? ?? ? Table 2. Tournament results of particular play-pairs. The value 1 means the win of a play, the value 0.5 means the draw. A single play is marked by (K 1,K 2 ). Points, [$], ) [$] Points Points, [$], ) [$] Points 0 (5.0, 2.5) (7.5, 2.5) 1 1 (7.5, 2.5) (10.0, 7.5) 0 0 (5.0, 2.5) (10.0, 2.5) 1 1 (10.0, 2.5) (7.5, 5.0) (5.0, 2.5) (7.5, 5.0) (10.0, 2.5) (10.0, 5.0) 0 0 (5.0, 2.5) (10.0, 5.0) 1 1 (10.0, 2.5) (10.0, 7.5) (5.0, 2.5) (10.0, 7.5) (7.5, 2.5) (10.0, 5.0) 1 0 (7.5, 2.5) (10.0, 2.5) (7.5, 2.5) (10.0, 7.5) (7.5, 2.5) (7.5, 5.0) 0 1 (10.0, 5.0) (10.0, 7.5) (7.5, 2.5) (10.0, 5.0) 0.5 Table 3. Scores of particular plays (K 1,K 2 ) and rank places assigned to particular plays with fractional acceptation degree K (multi-criterion) of the investigated person Play (K 1,K 2 ) (10.0, 2.5) (10.0, 5.0) (7.5, 2.5) (10.0, 7.5) (5.0, 2.5) (7.5, 5.0)!"#, Rank(K 1,K 2 ) I II II III III III Analysis of Table 3 shows that in the end we have 3 play types with differentiated values of the multi-criterion K. Apart from 6 plays with fractional acceptation given in Table 3 we also have 15 plays with the zero-acceptability K=0 and 4 plays with the full acceptability

40 40 Andrzej Piegat, Wojciech Sałabun K=1, see Table 1. Applying the indifference principle of Laplace [2], we can assume that the full difference of acceptation value relating to plays from Table 3, K max - K min = 1-0 = 1 should be partitioned in 4 equal differences K = ¼. The plays (5, 2.5), (7.5, 5), (10,7.5) achieve the M-Cr value K=1/4 (the third place in the rank). The plays (7.5, 2.5) and (10, 5) achieve K=2/4 (the second place in the rank). The play (10,2.5) achieves K=3/4 (the first place in the rank of fractional-acceptability of plays). Resulting values of the M-Cr K determined for particular plays with the tournament-rank method are given in Table 4. Table 4. Resulting values of the multi-criterion K= f(k 1,K 2 ), which represents the acceptability degree of particular plays (K 1,K 2 ) for the investigated person. The value of losses The value of winning [$] [$] On the basis of Table 4 a visualization of the investigated multi-criterion K of the play acceptability-degree can be realized, Fig. 3 and 4. Figure 3. Visualization of the 25 analyzed plays (K 1,K 2 ) as 25 characteristic objects regularly placed in the decisional domain K 1 K 2 of the problem Each of the 25 characteristic plays (decisional objects) can be interpreted as a crisp rule, e.g.: IF (K 1 = 7.5) AND (K 2 = 5) THEN (K = ¼) (2) However, if K 1 is not exactly equal to 7.5 and K 2 is not exactly equal to 5.0 then rule (2) can be transformed in a fuzzy rule (3) based on tautology Modus Ponens [8, 9]. IF (K 1 close to 7.5) AND (K 2 close 5.0) THEN (K close ¼) (3)

41 Nonlinearity of human, decisional multi-criteria 41 This way 25 fuzzy rules of type (4) were achieved on the basis of each characteristic object (play) given in Table 3. The rules enable calculating values of the nonlinear multicriterion K for any values of the component criteria K 1i and K 2j, i,j =1:5. IF (K 1 close to K 1i ) AND (K 2 close to K 2j ) THEN (K close to K ij ) (4) The complete rule base is given in Table 3. To enable calculation of the fuzzy M-Crfunction K it is necessary to define membership functions µ K1i ( close to K 1i ), µ K2j (close to K 2j ) and µ Kij (close to K ij ). These functions are shown in Fig.4. Figure 4. Membership functions µ K1i (close to K 1i ), µ K2j (close to K 2j ) of the component criteria and µ Kij (close to K ij ) of the aggregating multi-criterion K On the basis of the rule base (Table 3) and of membership functions from Fig.4 it is easy to visualize the function-surface K = f(k 1,K 2 ) of individual multi-criterion of the play acceptation. As visualization tool one also can use toolbox of fuzzy logic from MATLAB or own knowledge about fuzzy modeling [8, 9]. The functional surface is shown in Fig.5. As Fig.5 shows, the functional surface of the human multi-criterion K=f(K 1,K 2 ) is strongly nonlinear. This surface represents the M-Cr of one person. However, in case of other persons surfaces of this multi-criterion are qualitatively very similar (an investigation was realized on approximately 100 students of Faculty of Computer Science of West Pomeranian University of Technology in Szczecin and of Faculty of Management and Economy of University of Szczecin). Quantitative differences of the multi-criterion K between particular investigated persons were mostly not considerable. All identified surfaces were strongly nonlinear. The second co-author WS of the paper used the method of characteristic objects in investigation of the attractiveness degree of color. In the experiment two attributes occur: the degree of brightness green (in short G), the degree of brightness blue (in short B).

42 42 Andrzej Piegat, Wojciech Sałabun Figure 5. Functional surface of the individual multi-criterion K=f(K 1,K 2 ) of the play acceptability with possible winnings K 1 [$] and losses K 2 [$], probability of winnings and losses are identical and equal to 0.5. This particular surface represents the AP-author of the paper. The degree of red was fixed at constant brightness level 50%. The brightness level of each components was normalized to the range [0,1]. The first step was to define linguistic values for the G and B components, presented in Fig. 6. and 7. Figure 6. Definitions of linguistic values for the component G Figure 7. Definitions of linguistic values for the component B

43 Nonlinearity of human, decisional multi-criteria 43 Membership functions presented in Fig 6. are described by formula (5): ( ) =.+,-.+ (.) = -,.+ (./ =,-.+ ( 0 = -,.+.+, (5) where: L low, ML medium left, MR medium right, H height, G the level of brightness green. Membership functions presented in Fig. 7. are described by formula (6): ( ) =.+,1.+ (.) = 1,.+ (./ =,1.+ ( 0 = 1,.+.+, (6) where: L low, ML medium left, MR medium right, H height, B the level of brightness blue. Linguistic values of attributes generate 9 characteristic objects. Their distribution in the problem space is presented by Fig.8. Figure 8. Characteristic objects R i in the space of the problem Attribute values of the characteristic R i objects, their names and colors are given in Table 5. Table 5. Complex color and their rules Rule [R, G, B] Color R1 [0.5, 0.0, 0.0] R2 [0.5, 0.0, 0.5] R3 [0.5, 0.0, 1.0] R4 [0.5, 0.5, 0.0] R5 [0.5, 0.5, 0.5] R6 [0.5, 0.5, 1.0] R7 [0.5, 1.0, 0.0] R8 [0.5, 1.0, 0.5] R9 [0.5, 1.0, 1.0] The interviewed person has to make decisions described below. In the survey, please indicate, which color of the pair of colors is more attractive (please mark this color by X). If both colors have similar or identical level of attractiveness, please mark a draw. Attractiveness of color is telling you which color you prefer more from the pair of colors.

44 44 Andrzej Piegat, Wojciech Sałabun Evaluation of characteristic objects is determined with the tournament-rank method. If one color of a pair is preferred, then this color receives 1 point and second color receives 0 points. If the interviewed person marks a draw, both colors receive 0.5 point. Next, all the points assigned to each object are added. On the basis of the sums the ranking of objects is established. Applying the indifference principle of Laplace we can assume that the full difference value = = 1 should be partitioned in equal differences 89:;,89<=. ( m number of places in the ranking). Experimental identification of surfaces 2, of the multi-criterion showed, that for all interviewed people, this surfaces were strongly nonlinear. Fig. 9. shows the multi-criterion surface for a randomly chosen person. For comparison, Fig. 10 shows the multi-criterion surface for co-author WS of the article. Figure 9. Functional surface of the individual multi-criterion of the resulting color-attractiveness achieved by mixing 2 component colors with different proportion-rates. Figure 10. Functional surface of the individual multi-criterion of attractiveness of the resulting color achieved by mixing 2 component colors with different proportion-rates (WS)

45 Nonlinearity of human, decisional multi-criteria 45 The realized investigation also showed that functional surfaces of the multi-criterion of all persons were strongly nonlinear. Fig. 9 presents the functional, M-Cr-surface of one of the persons taking part in the investigation. For other interviewed people, these M-Crsurfaces were also highly nonlinear. (Identification of M-Cr-surfaces has been performed for a group of 307 selected people). 4. Nonlinearity indicator of the functional surface of a multi-criterion In case of the 2-component multi-criterion K = f(k 1,K 2 ) there exists visualization possibility of the functional surface of the M-Cr and possibility of an approximate, visual evaluation of its nonlinearity degree or, at least, of evaluation whether the surface is linear or nonlinear one. However, in case of higher-dimensional multi-criteria K = f(k 1,K 2,,K n ) visualization and visual evaluation of nonlinearity becomes more and more difficult, though it can be realized e.g. with method of lower-dimension cuts [7]. Therefore it would be very useful to construct a quantitative indicator of nonlinearity N-Ind K of a model of the multicriterion K. First, let us analyze, for better understanding of the problem, the most simple criterion-model K = f(k 1 ),the criterion of the lowest dimension identified with the method of characteristic objects (Ch-Ob-method). Let us assume that after realized investigations we have at disposal m objects, each of them is described by the pair (K 1,K) of coordinate values and can be interpreted as a measurement sample that can be used for identification of a functional dependence. Let us assume that the characteristic objects are distributed in the coordinate-system space as shown in Fig.11a. Figure 11. An example placement of characteristic objects (, ), =, 1:7 in the space >, Fig.11a, and a nonlinear, fuzzy model approximating the characteristic objects, Fig.11b Nonlinearity of the fuzzy model approximating the criterion-function K=f(K 1 ) will be the smaller, the smaller is the difference sum (K i K Li ) of corresponding points lying on the fuzzy and on the linear approximation of the criterion function. Information about this sum delivers the proposed indicator N-Ind K of nonlinearity, formula (7).? 8 = 9 <DE 8 <,8 C< = 9 <DE 8 <,F G HF E 8 E<.+28 9:;,8 9<=.+28 9:;,8 9<= (7)

46 46 Andrzej Piegat, Wojciech Sałabun The denominator 0.5m (K max -K min ) in formula (5) realizes normalization of the indicator to interval [0,1]. Fig. 12a presents distribution of characteristic objects for which the nonlinearity indicator equals zero. Fig.12b presents the inverse situation, when the indicator assumes value equal to 1. Figure 12. Distribution of characteristic objects (K 1i,K i ), I = 1-m, for which the nonlinearity indicator N-Ind K is equal to zero, Fig.12a, and distribution for which the indicator assumes the maximal value 1, Fig.12b If we use a multi-criterion K aggregating n component criteria K i, then the linear approximation K L of K has the form (8) and the nonlinearity indicator N-Ind K is expressed by formula (9). ) = (8)? 8 = 9 <DE 8 <,8 C<.+28 9:;,8 9<= (9) The linear approximation K L of a M-Cr can be determined e.g. with the method of the minimal sum of square errors for which many program-tools can be found, e.g. in MATLAB and STATISTICA. As an example, the nonlinearity indicator was determined for the multi-criterion K = f(k 1,K 2 ) aggregating winnings and losses of a play, see Fig.5 and Table 3. The achieved value of the indicator was? 8 = The obtained (with the least squares) linear model K L of multi-criterion K is presented in Fig. 13a, and in Fig. 13b, for comparison, the fuzzy model of this criterion, obtained with the characteristic objects method is shown. Another example of determining the nonlinearity indicator N-Ind K is given for the multicriterion of attractiveness of the resulting color achieved by mixing 2 component colors with different proportion-rates, which was presented in part 3. The indicator N-Ind K was calculated for the nonlinear models from Fig. 9 and Fig. 10.

47 Nonlinearity of human, decisional multi-criteria 47 Figure 13. Comparison of the linear model KL = w0 + w1k1 +w2k2, Fig.13a, and of the nonlinear model K = f(k1,k2) of the multi-criterion of acceptability of plays on the basis of their winnings K1($) and losses K2($). In Fig.13b the nonlinear model obtained with the method of characteristic objects with the nonlinearity indicator? A8 = The linear model in Fig. 14a was identified by method of least squares. For comparison the nonlinear model presented in Fig. 14b was determined. For this model the nonlinearity indicator is equal to This means a higher nonlinearity degree than in case of the playproblem presented in Fig. 13 where this value was equal to Figure 14. Comparison of the linear model KL = w0 + w1g +w2b, Fig.14a, and of the nonlinear model K = f(g, B) of the multi-criterion of attractiveness of the resulting color achieved by mixing 2 component colors with different proportion-rates, Fig.14b. The nonlinear model obtained with the method of characteristic objects is characterized by the nonlinearity indicator? A8 = Fig. 15a presents the linear model of this same multi-criterion for co-author WS of the article. This model was identified with method of least squares. After comparing the linear model with the fuzzy model presented in Fig. 15b the nonlinearity indicator 0.54 was achieved. This means the highest degree of the multi-criterion nonlinearity in all presented cases.

48 48 Andrzej Piegat, Wojciech Sałabun Figure 15. Comparison of the linear model K L = w 0 + w 1 G +w 2 B, Fig.15a, and of the nonlinear model K = f(g, B) of the multi-criterion of attractiveness of the resulting color achieved by mixing 2 component colors with different proportion-rates, Fig.15b. The nonlinear multi-criterion was identified with the method of characteristic objects. Its nonlinearity indicator equals? 8 = Conclusions Human multi-criteria representing human preferences usually are not of linear but of nonlinear character. Linearity is an idealized feature and it occurs rather seldom in the reality. The paper presented few examples of nonlinear, human multi-criteria a considerably greater number easily could be presented. Scientists, in modeling human multi-criteria should go over from linear to nonlinear models (approximations) of these criteria. The paper presented the method of characteristic objects, which enables identification of more precise, nonlinear models of human multi-criteria. Because it is difficult to visualize highdimensional multi-criteria a nonlinearity indicator was proposed. This indicator allows for error-evaluation of linear, simplified models of human multi-criteria. The method of characteristic objects and the nonlinearity indicator was conceived by Andrzej Piegat. References [1] Brans J.P., Vincke P.: A preference ranking organization method: the PROMETHEE method for MCDM. Management Science, [2] Burdzy K.: The search for certainty. World Scientific, New Jersey, London, [3] Figueira J. et al.: Multiple criteria decision analysis: state of the arts surveys. Springer Science + Business Media Inc, New York, [4] French S. at al.: Decision behavior, analysis and support. Cambridge, New York, [5] Hwang Cl., Yoon K.: Multiple attribute decision making: methods and applications. Springer-Verlag, Berlin, [6] Kahneman D., Tversky A.: Choices, values and frames. Cambridge University Press, Cambridge, New York, [7] Lu Jie at al.: Multi-objective group decision-making. Imperial College Press, London, Singapore, [8] Piegat A.: Stationary to the lecture Methods of Artificial Intelligence. Faculty of Computer Science, West Pomeranian University of Technology, Szczecin, Poland, not published. [9] Piegat A.: Fuzzy modeling and control. Springer-Verlag, Heidelberg, New York, 2001.

49 Nonlinearity of human, decisional multi-criteria 49 [10] Rao C.R.: Linear Models: Least Squares and Alternatives., Rao C.R.(eds), Springer Series in Statistics, [11] Rutkowski L.: Metody i techniki sztucznej inteligencji (Methods and techniques of artificial intelligence) [12] Saaty T.L.: How to make a decision: the analytic hierarchy process. European Journal of Operational Research, vol.48, no1, pp.9-26, [13] Saaty T.L.: Decision making with dependence and feedback: the analytic network process. RWS Publications, Pittsburg, Pennsylvania, [14] Saaty T.L., Brady C.: The encyclicon, volume 2: a dictionary of complex decisions using the analytic network process. RWS Publications, Pittsburgh, Pennsylvania, [15] Stadnicki J.: Teoria I praktyka rozwiązywania zadań optymalizacji (Theory and practice of solving optimization problems). Wydawnictwo Naukowo Techniczne, Warszawa, [16] Zarghami M., Szidarovszky F.: Multicriteria analysis. Springer, Heidelberg, New York, [17] Zeleny M.: Compromise programming. In Cochrane J.L., Zeleny M.,(eds). Multiple criteria decision-making. University of South Carolina Press, Columbia, pp , [18] Zimmermann H.J.: Fuzzy set theory and its applications. Kluwer Academic Publishers, Boston/Dordrecht/London, 1991.

50 Journal of Theoretical and Applied Computer Science Vol. 6, No. 3, 2012, pp ISSN Method of non-functional requirements balancing during service development Larisa Globa 1, Tatiana Kot 1, Andrei Reverchuk 2, Alexander Schill 3 1 National Technical University of Ukraine «Kyiv Polytechnic Institute», Ukraine 2 SITRONICS Telecom Solutions, Czech Republic a.s. 3 Technische Universitat Dresden, Fakultat Informatik, Deutschland {lgloba, tkot}@its.kpi.ua, a.v.r@list.ru, Alexander.Schill@tu-dresden.de Abstract: Today, the list of telecom services, their functionality and requirements for Service Execution Environment (SEE) are changing extremely fast. Especially when it concerns requirements for charging as they have a high influence on business. This results in the need for constant adaptation and reconfiguration of Online Charging System (OCS) used in mobile operator networks. Moreover any new functionality requested from a service can have an impact on system behavior (performance, response time, delays) which are in general nonfunctional requirements. Currently, this influence and reconfiguration strategies are poorly formalized and validated. Current state-of-the-art approaches are considered methodologies that can model non-functional or functional requirements but these approaches don t take into account interaction between functional and nonfunctional requirements and collaboration between services. All these result in time and money consuming service development and testing, and cause delays during service deployment. The balancing method proposed in this paper fills this gap. It employs a well-defined workflow with predefined stages for development and deployment process for OCS. The applicability of this novel approach is described in a separate section which contains an example of GPRS service charging. A tool, based on this method will be developed, providing automation of service functionality influence on non-functional requirements and allowing to provide a target deployment model for a particular customer. The reduction of development time and thus necessary financial input has been proved based on real-world experiments. Keywords: OCS, service deployment, non-functional requirements, requirements balancing. 1. Introduction During service design and deployment, provided by telecom operator, using OCS [1], one important aspect should be considered. It concerns NFR 1 to service provision. There is the established fact that any system and services run on the system shall be developed not only based on functional requirements, defining software functions (inputs, behavior, outputs), but non-functional ones as well. It is very important to meet non-functional requirements in the telecom industry, especially for real time systems. Generally nonfunctional parameters could be classified as follows: Performance (Response Time, Throughput, Utilization, Static Volumetric); Scalability; Capacity; Availability; Reliability; 1 Non-functional requirements

51 Method of non-functional requirements balancing during service development 51 Recoverability; Maintainability; Serviceability; Security; Regulatory; Manageability; Environmental; Data Integrity; Usability; Interoperability. Non-functional requirements specify a system s quality characteristics or quality attributes. If non-functional requirements are not considered at the designer level, then the provided service may actually be useless in practice. Currently, NFR are not considered within the perspective of the services list, provided by Telecom Operator. The main problem is that legacy methods can design service according to NFR, but cannot model an influence of concurrency services on particular NFR because of collaboration between services. This means that Operator has no tool that allows flexible balancing between services, run on OCS. Balancing can allow to model system behavior for a determined (requested) list of services to analyze how this configuration meets the NFR. This paper describes a novel NFR balancing method, focusing on collaboration between functional and non-functional requirements, allowing to automate service planning stages and to reduce the time and costs for OCS adaptation in general. The paper is structured as follows: Section 2 contains state of the art analysis of methods and approaches to considering NFR. Furthermore, NFR analysis methods are described. Section 3 introduces NFR balancing method, focusing on functional and non-functional requirements collaboration. The evaluation has been applied using a real-world scenario within a telecommunication company and it is represented in Section 4. Section 5 concludes the work with a summary and outlook on future work. 2. State of the art and non-functional testing Errors due to omission of NFR or not properly dealing with them are among the most expensive type and most difficult to correct. Recent works [2] points out that early-phase requirements engineering should address organizational and non-functional requirements, while later-phase engineering focuses on completeness, consistency and automated verification of requirements. There are reports [3, 4] showing that not properly dealing with NFR has led to considerable delays in the project and consequently to a significant increase of the final cost. There are many reasons for delays and significant increasing of costs, but one of the most important reasons relies on the fact that performance was neglected during software development, leading to several changes in both hardware and software architecture, as well as in software design and code [5, 6, 7]. There could be a situation in which the system can be deactivated just after its deployment because, among other reasons, many non-functional requirements were neglected during the system development such as: reliability (vehicles location), cost (emphasis on the best price), usability (poor control of information on the screen), and performance (the system did what it was supposed to do but performance was unacceptable). As it was mentioned above, OCS shall provide all functionality to charge telecom services (GPRS, voice, sms, mms, VAS 2 ) using Event Charging with Unit Reservation, Session Charging with Reservation Unit, Immediate Event Charging mechanisms. Each service consumes a strictly predefined volume of system resource (memory, process time, etc.) and has influence on non-functional requirements to be supported. 2 Value added services

52 52 Larisa Globa, Tatiana Kot, Andrei Reverchuk, Alexander Schill 2.1. NFR framework NFR are considered at the design level and there are several approaches that can help to model NFR within the scope of the developed service. NFR framework [7] is a methodology that guides the system to accommodate change with replaceable components. NFR framework is a goal-oriented and process-oriented quality approach guiding the NFR modeling. Non-functional requirements such as security, accuracy, performance and cost are used to drive the overall design process and choose design alternatives. It helps developers express NFR explicitly, deal with them systematically and use them to drive development process rationally [8]. In the NFR Framework, each NFR is called an NFR softgoal (depicted by a cloud), while each development technique to achieve the NFR is called an operationalizing softgoal or design softgoal (depicted by a dark cloud). Design rationale is represented by a claim softgoal (depicted by a dash cloud). The goal refinement can take place along the Type or the Topic. These three kinds of softgoals are connected by links to form the SIG 3 that records the design consideration and shows the interdependencies among softgoals KAOS Another methodology for considering NFR is KAOS [9, 10]. KAOS is a methodology for requirements engineering enabling analysts to build requirements models and to derive requirements documents from KAOS models. KAOS has been designed: to fit problem descriptions by allowing you to define and manipulate concepts relevant to problem description; to improve the problem analysis process by providing a systematic approach for discovering and structuring requirements; to clarify the responsibilities of all the project stakeholders; to let the stakeholders communicate easily and efficiently about the requirements. KAOS is independent of the development model type: waterfall, iterative, incremental, but it also doesn t take into account collaboration between FR 4 and NFR. The legacy software tools, for instance NFR-Assistant CASE [11], ARIS [12], don t provide requested functionality to model nonfunctional requirements and compare their influence on functionality Non-functional testing Testing of non-functional requirements is another issue. Non-functional testing [13] is concerned with the non-functional requirements and is designed to evaluate the readiness of a system according to several criteria not covered by functional testing. Non-functional testing covers: Load and Performance Testing; Ergonomics Testing; Stress & Volume Testing; Compatibility & Migration Testing; Data Conversion Testing; Security / Penetration Testing; Operational Readiness Testing; 3 Softgoal interdependency graph 4 Functional requirements

53 Method of non-functional requirements balancing during service development 53 Installation Testing; Security Testing (Application Security, Network Security, System Security). It enables the measurement and comparison of the testing of non-functional attributes of software systems. The cost of catching and correcting errors related to non- functional requirements is very high and could cause full redesign of developed service (system). Testing does not have to occur once the 'code' has been delivered. It can start early with analyzing the requirements and creating test criteria of 'What' it is needed to test. The process for doing this is called the V model [9] (Fig. 1.). It decomposes requirements and testing. It allows testing and coding as a parallel activity which enables the changes to occur more dynamic. NFR has a high influence on the testing process and any service that doesn t meet NFR can cause rollback of the development process to initial phases. Figure 1. V- Model 3. NFR balancing method The proposed NFR balancing method is based on creating FR and NFR collaboration model. Implementation of functional requirements is presented by listed FB 5. Each of FB is responsible for a particular logical function. The proposed method includes the following main stages: NFR Catalogue development; FR decomposition; NFR mapping; FB distribution; Balancing; Target deployment model. NFR balancing method uses NFR Catalogue, Functional Requirements to be implemented, create collaboration model between them. The main stages of the concept are represented below. 5 Functional Block