A Computation Time Comparison of Self-Organising Migrating Algorithm in Java and C#

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1 A Computation Time Comparison of Self-Organising Migrating Algorithm in Java and C# JAN KOLEK 1, PAVEL VAŘACHA 2, ROMAN JAŠEK 3 Tomas Bata University in Zlin Faculty of Applied Informatics nam. T.G..Masaryka 5555, Zlin CZECH REPUBLIC 1 kolek@fai.utb.cz, 2 varacha@fai.utb.cz, 3 jasek@fai.utb.cz Abstract: - This paper compares implementations of the Self-Organizing Migrating Algorithm (SOMA) algorithm in the C# and Java frameworks. SOMA is a highly effective tool of an evolutionary optimization aimed at the same set of problems as Genetic Algorithms. The asynchronously parallel All-to-One strategy of SOMA is used to equally distribute computation loads between several available processors/cores. This strategy is implemented in the C# and Java runtime environments to statistically evaluate the computation time efficiency of these two concurrent frameworks. The results obtained are discussed in the conclusion. Key-Words: - All-To-One, C#, asynchronous, evolutionary algorithm, Java, parallel, optimization, SOMA 1 Introduction The Self Organizing Migration Algorithm (SOMA) was created in 1999 having many successful applications on various problems of objective optimization, e.g. [1-5]. SOMA is classified as an evolutionary algorithm aiming the same set of problems as Genetic Algorithms (GA) [1]. In contrast with GA, SOMA does not create any new individuals processing the algorithm. It changes only coordinates of individuals located in an area of a possible solution. More accurately, SOMA is classified as a memetic algorithm or swarm algorithms such as Particle Swarm Optimization. The algorithm SOMA is inspired by the intelligent behaviour of groups of individuals in the nature, e. g. while searching for food or finding the shortest way towards it. As it was already mentioned, the new induviduals are not created by hybridizing but the algorithm uses cooperative search of the area of possible solutions. Such strategy is executed rather in evolution cycles than in generations as is usual for GA. Such circles are named migration loop by SOMA s inventor prof. Zelinka. Several different versions of SOMA exist, nevertheless, this article aims on the most common All-to-One version. All basic All-to-One SOMA principles important for correct understanding of executed experiment are described below. 2 SOMA All-to-One A run of the algorithm is divided into four following steps 1) Parameter definition Before starting the algorithm, SOMA s parameters: Step, PathLength, PopSize, PRT and a Cost Function needs to be defined. Table 1. indicates recommended range as well as a meaning of these parameters. Parameter Recommended range Comment PathLength [1.1 ; 5>] Control parameter Step [0.11 ; PathLength] Control parameter PRT [0 ; 1] Control parameter D dimension Dimension of the problem PopSize [10 ; define the user] Control parameter Migrations [10 ; define the user] Termination parameter MinDiv [± arbitrary ; define the user] Termination parametr Table 1.: Algorithm SOMA parameters ISBN:

The Cost Function is simply the function which returns a scalar that can directly serve as a measure of fitness. 2) Creation of the population The population of individuals is randomly generated.

2 The Cost Function is simply the function which returns a scalar that can directly serve as a measure of fitness. 2) Creation of the population The population of individuals is randomly generated. Each parameter for every individual has to be randomly chosen from a given range <Low, High>. 3) Migration loop All individuals from population (PopSize) are evaluated by the Cost Function and the Leader (individual with the highest fitness) is chosen for a current migration loop. Subsequently, remaining individuals begin to jump, (according to the Step definition) towards the Leader. Each individual is evaluated after every jump using the Cost Function. Jumping continues until a final position defined by the PathLength is reached. New position x i,j after each jump is calculated by (1). This is shown graphically in Fig. 1. Individual returns then to that position where they found the best fitness on their trajectories. To understand a process of PRTVector construction, refer an example in Table 2. j rnd j PRTVector Table 2.: An example of a PRTVector construction in four dimensional space using PRT = 0.3 4) Test for stopping condition If a maximum number of migration loops has been reached, stop and recall the best solution(s) found during the search. where t <0, by Step to, PathLegth> and ML is an actual migration loop (1) Before an individual begins its jumping towards the Leader, a random number rnd is generated (for each individual s coordinate), and then compared with PRT. If a random number generated is larger than PRT, an associated coordinate of the individual is set to 0 by the means of PRTVector. if rnd j < PRT then PRTVector j = 0 else 1 where rnd <0, 1> and j = 1, n param (2) Hence, the individual moves in the N-k dimensional subspace, which is perpendicular to the original space. This fact establishes a higher robustness of the algorithm. Earlier experiments have demonstrated that, without the use of PRT, SOMA tends to determine a local optimum rather than the global one. Fig. 1.: PRTVector and its action on individual movement [5] 3 Parallel behaviour of algorithm SOMA A scope the performed experiment is to evaluate a performance of two asynchronously parallel SOMA distributions which are realised in programming frameworks Java and.net C# The algorithm SOMA was modified to use as many threads as available processor cores. A proposal and description of such SOMA implementation was firstly published in [6]. The asynchronous algorithm SOMA (contrary to synchronous version) does not wait for all individuals to finish their paths. ISBN:

3 Every individual migrates towards the leader separately (asynchronously) and is compared with the leader immediately after it finish its path. If any individual gets better position than the current Leader, this individual becomes a new Leader instantly. Remaining individuals continue migrating towards this new Leader immediately when they asynchronously starts jumping on new path. 4 Experiment settings 1) Benchmark functions The algorithm was tested on flowing 10 test functions, proposed as a benchmark in [6]. These functions are described in the Table 3. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Table 3.: Test functions mathematical formulation ISBN:

4 2) SOMA parameter settings All tests were performed by two threads in 100 dimensional space and the process (each function has 100 coordinates inputs form x 1 to x 100 ) of optimization was repeated 100-times while arithmetic mean of founded solution was computed. In all cases, new initial population was generated as starting point of the optimization. Used parameters of SOMA were set as follows Step = 0.11, PRT = 0.1, D = 100 are shown in Table 4., (To optimize the Rosenbrock function Step = is used instead to compensate small PathLength = 0.5). Parameter which differ for individual test functions are described in Table 4. It also contains used borders and expected optimal results 3) Hardware settings The experiment was performed on the personal computer ACER equipped with two-core processor AMD Athlon 4960 (64-bit) and the operating memory 3 GB DDR2 using operating system Windows Vista (64-bit). Test function Path Length PopSize Migration loops Borders Minimum Maximum Real extreme (minimum) Ackley (1) EggHolder (2) not known Griewangk (3) Masters (4) x D Michalewicz (5) x (D 2) Rana (6) not known Rastrigin (7) (-200) x D Rosenbrock (8) 0, Schwefel (9) ( ) x D Sine Wave (10) Table 4.: Algorithm SOMA s parameters used in the experiment 5 Results Table 6. shows average solutions founded by the SOMA algorithm implemented in Java and C#. It provides a measurement of implementations effectiveness in a relation with a quality of founded solutions while wining cases are highlighted. Test function Java C# Real found minimum RMSD found minimum RMSD extreme(minimum) Ackley (1) EggHolder (2) -47 x x x x 10 3 not known Griewangk (3) Masters (4) Michalewicz (5) Rana (6) -27 x x x x 10 3 not known Rastrigin (7) x x x x x 10 2 Rosenbrock (8) Schwefel (9) -415 x x x x x 10 2 Sine Wave (10) Table 6.: Comparison the algorithm s implementations ISBN:

5 The main aim of the implementation is to compare which of two implementations (Java, C#) has better computational (time) efficiency. The results are shown in a Table 7. In a first column, there is a name of used test function. A second and third contain an average consumption of time consumed by the algorithm created in Java and C#. The table shows that the asynchronous algorithm SOMA created in C# is better in 7 cases from 10. In the Michalewicz test function, which is most computationally demanding form the set, it was more than two times faster. In comparison, the asynchronous algorithm SOMA created in Java was faster only marginally faster in 3 cases. Test function Java C# Acceleration in C# time[s] time[s] [%] Ackley (1) EggHolder (2) Griewangk (3) Masters (4) Michalewicz (5) Rana (6) Rastrigin (7) Rosenbrock (8) Schwefel (9) Sine Wave (10) Average Table 7.: Comparison of time consumption 6 Conclusion The experiment verified that both algorithm s implementations are equal considering a quality of founded solution. Table 6. shows that finding good solution depends on the random first population rather than on used implementation. The implementation in Java found better average solution in 4 and C# implementation in 6 cases. Considering statistical deviation both implementations can be considered equally effective. Regarding the main experiment s result, it can be concluded that the implementation created in C# is significantly better in time consumption. This implementation is faster in 7 from 10 cases. For the Michalewicz test function, it was even more than two times faster. In average, C# implementation, is faster for % than Java. Such results may indicate that.net Framework (C#) has a more effective library calculating complex mathematical functions as calculations of mathematical functions were the most timeconsuming operation for both as implementations Subsequently, we are going to design an experiment to prove this hypothesis and public its results in WSEAS Transaction on Computers journal. Acknowledgment This paper is supported by the Internal Grant Agency at TBU in Zlin, projects No. IGA/FAI/2012/041. References: [1] SENKERIK R., OPLATKOVA Z., ZELINKA I., DAVENDRA D. Synthesis of feedback controller for three selected chaotic systems by means of evolutionary techniques: Analytic programming, Mathematical and Computer Modelling, Available online 27 May 2011, ISSN , /j.mcm [2] CHRAMCOV B., BERAN P., DANÍČEK L., JAŠEK R.. A simulation approach to achieving more efficient production systems. International Journal of Mathematics and Computers in Simulations, 2011, year 5, issue 4, page ISSN [3] KRÁL E., VAŠEK, L., DOLINAY V., ČÁPEK P. Usage of Peak Functions in Heat Load ISBN:

6 Modeling of District Heating System. In Recent Researches in Automatic Control. Montreux : WSEAS Press, 2011, p ISBN [4] POSPÍŠILÍK M., KOUŘIL L., MOTÝL I., ADÁMEK M. Single and Double Layer Spiral Planar Inductors Optimisation with the Aid of Self-Organising Migrating Algorithm. In Proceedings of the 11th WSEAS International Conference on Signal Processing, Computational Geometry and Artificial Vision. Venice : WSEAS Press (IT), 2011, p ISBN [5] ZELINKA I., Studies in Fuzziness and Soft Computing, New York : Springer-Verlag, [6] VAŘACHA P. Innovative Strategy of SOMA Control Parameter Setting. In 12th WSEAS International Conference on Neural Networks, Fuzzy Systems, Evolutionary Computing & Automation. Timisoara : WSEAS press, 2011, p ISBN ISBN:

Innovative Strategy of SOMA Control Parameter Setting

Innovative Strategy of SOMA Control Parameter Setting PAVEL VAŘACHA Tomas Bata University in Zlin Faculty of Applied Informatics nam. T.G. Masaryka 5555, 76 1 Zlin CZECH REPUBLIC varacha@fai.utb.cz http://www.fai.utb.cz