A META-HEURISTIC APPROACH TO LOCATE OPTIMAL SWITCH LOCATIONS IN CELLULAR MOBILE NETWORKS

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1 University of East Anglia From the SelectedWorks of Amin Vafadarnikjoo Fall October 8, 2015 A META-HEURISTIC APPROACH TO LOCATE OPTIMAL SWITCH LOCATIONS IN CELLULAR MOBILE NETWORKS Amin Vafadarnikjoo Seyyed Mohammad Ali Khatami Firouzabadi Mohammadsadegh Mobin, Western New England University Afshan Roshani, Western New England University Available at:

2 Proceedings of the American Society for Engineering Management 2015 International Annual Conference S. Long, E-H. Ng, and A. Squires eds. A META-HEURISTIC APPROACH TO LOCATE OPTIMAL SWITCH LOCATIONS IN CELLULAR MOBILE NETWORKS Amin Vafadarnikjoo* Seyyed Mohammad Ali Khatami Firouzabadi Allameh Tabataba i University, Tehran, Iran Mohammadsadegh Mobin Afshan Roshani Western New England University, MA, USA *amin.vafadar.n@gmail.com Abstract With increasing usage of cellular phones, providing optimum communication service systems becomes a strategic decision to increase subscriber satisfaction. In order to respond to this growing demand it is essential to have a proper design of mobile networks by optimally locating facilities such as Base Transceiver Stations (BTS), switches, etc. In this study, a kind of honeybee-inspired algorithm called Artificial Bee Colony (ABC) algorithm is utilized to solve the problem of assigning cells to switches in the Personal Communication Services (PCS) networks. The model is mathematically developed as a binary non-linear problem with the objective of minimizing cost, which includes handoff and cabling costs. Each switch has a call handling capacity that is equal for other switches. The cells locations are known, and each cell can only be connected to one switch which makes the binary non-linear model of our problem as a single homed model. This problem is categorized as a Capacitated P-Median Problem (CPMP). It has been proven in the literature that these types of problems are Non-deterministic Polynomial-time hard (NP-hard) which need meta-heuristic algorithms to be solved. At first, various parameters of the ABC algorithm are calibrated by conducting full factorial experimental design. Numerical examples are generated in order to evaluate the performance of the ABC algorithm by comparing it with Ant Colony Optimization (ACO) in terms of objective function and CPU time. Comparison results show satisfactory performance of ABC algorithm. Keywords Artificial Bee Colony (ABC) algorithm, Cell to switch assignment problem, Mobile networks, Meta-heuristics, Capacitated P-Median Problem (CPMP). Introduction Since the last decade, there have been significant advances in the development of mobile communication systems. With increasing usage of cellular phones, existence of appropriate communications services systems is necessary to satisfy the subscribers (users). Even though significant improvement to communications infrastructure has been attained in the personal communication service industry, the issues concerning the assignment of cells to switches remain challenging and need to be resolved. Optimal design of mobile networks means locating facilities such as Base Transceiver Stations (BTS), switches in the best position. In this paper, the critical problem of how to assign cells to switches in order to minimize the cost is addressed. These problems are usually considered by the designers of such mobile communication services or the personal communication services (PCS). In mobile networks, BTSs are used for transmitting and receiving radio signals. The covered region of each BTS with hexagonal shape is called a cell. Switches manage radio signals of one or more cells, like frequency assignment or switching signals between BTSs, which is called handoff (Salcedo-Sanz et al., 2008). In the PCS networks, the signal power of one moving subscriber is controlled by the closest cells. As it is presented in Exhibit 1, if the subscriber goes from cell B to cell A, switch 1 will handoff this call. It is simple and does not need any update of the subscriber's location in the database. Now assume that the subscriber goes from cell B to cell C, in this Copyright, American Society for Engineering Management, 2015

3 case handoff between switches 1 and 2 are relatively complicated. In this case, there are two kinds of handoff; the first one includes only one switch and the second involves two switches (Merchant & Sengupta, 1995). Exhibit 1. Assignment of Cells to Switches. In order to reduce the cost of handoffs, the cells among which the handoff frequency is high should be assigned to the same switch if it is possible. However, the limited call handling capacity should be considered. The other constraint is the cabling cost that occurs when a call is connected between a call and a switch. Assigning cells to switches such that the total hybrid cost, comprising handoff cost between adjacent cells and cabling cost between cells and switches, is minimized under the constraints of the call handling capacities of switches, is called the Cell To Switch Assignment Problem (CTSAP). Merchant and Sengupta (Merchant & Sengupta, 1995) were the first people who worked on the CTSAP. Since the CTSAP is considered as an NP-hard problem, they proved that integer programming or heuristic methods are unable to determine any solution for CTSAP with more than 35 cells. Therefore, they presented a meta-heuristic algorithm for solving their integer programming problem. Different algorithms have been extensively used for solving CTSAP in the literature which some are presented in Exhibit 2: Exhibit 2. Approaches for Solving Cell to Switch Assignment Problem. Methods Authors Tabu Search (TS) (Pierre & Houéto, 2002) TS, Simulated Annealing (SA) and Parallel Genetic Algorithms (GA) with Migrations (PGAM) (Quintero & Pierre, 2003a) Standard GA (SGA), Memetic Algorithms (MA) and multi-population approach (Quintero & Pierre, 2003b) Memetic algorithms (Quintero & Pierre, 2003c) Hybridizing the local optimization k-opt technique with Ant Colony Optimization (ACO) (Fournier & Pierre, 2005) ACO (Shyu, Lin, & Hsiao, 2006) Modified Binary Particle Swarm Optimization (MBPSO) (Udgata, Anuradha, Kumar, & Udgata, 2008) Hybrid GA (Salcedo-Sanz et al., 2008) Hybrid Hopfield network Genetic Algorithm (Salcedo-Sanz & Yao, 2008) Hybridizing 2-opt and 3-opt local searches with SA (Rajalakshmi, Kumar, & Bindu, 2010) In this paper, an Artificial Bee Colony (ABC) algorithm is utilized to solve CTSAP. ABC is a honeybeeinspired algorithm which is based on honeybees foraging behavior. It has been successfully applied to cope with many classic optimization problems. It is considered as a novel meta-heuristic in comparison with other heuristics that are used for solving CTSAP. According to the best of our knowledge, this is the first time that the honeybeeinspired algorithm is applied to solve a combinatorial optimization of cell to switch assignment. Since ABC is categorized as a Swarm-based Optimization Algorithm (SOA) it can compete with other known SOA algorithms such as Ant Colony Optimization (ACO) (Shyu et al., 2006), which showed acceptable performance in solving CTSAP. Moreover, ABC has simple implementation with high performance efficiency. The rest of this paper is organized as follows. The problem formulation and mathematical model are described in the next section. Then, the ABC approach that is used to solve the proposed problem is presented. Afterwards, implementation phases of ABC algorithm, test problems characteristics and algorithm parameter calibration are presented. After that, the efficiency evaluation and computational comparisons of proposed algorithm are shown. Finally, the concluding remarks are provided. 2

4 Problem Definition In the CTSAP, there are two kinds of cost: 1- handoff costs between cells and 2- cabling cost between each cell and its associated switch. Cells locations are predetermined and the number of calls that each switch can handle is limited (first constraint). In general, cells can be single homed or dual homed, but for the sake of simplicity in this paper, cells are considered as single homed, which means each cell must connect to only one switch (second constraint). The handoff cost between two cells that are connected to one specific switch is considered zero. Details of the mathematical model are presented as follows. Mathematical Model The cell assignment mathematical model has been proposed by Merchant and Sengupta (Merchant & Sengupta, 1995). The number of cells (n), the number of switches (m), and the location of cells and switches are known. The mathematical model is binary and nonlinear. The binary decision variable is defined as Equation (1). Since each cell must be assigned to only one switch, we have a constraint defined as Equation (2). 1 cell i is assigned toswitch k xik (1) 0 otherwise m xik 1 i 1,..., n (2) k 1 The capacity constraint of each switch is shown in Equation (3). It explains that each switch can handle a specific number of calls or cells. M k is the maximum number of calls that switch k can handle per unit of time (it is equal for all switches) and λ i is the number of calls for cell i per unit of time. n i xik M k k 1,..., m (3) i 1 Equation (4) considers the handoff cost. When two different cells are connected to a specific switch, then y ij will be equal to one; otherwise it will be equal to zero. If y ij = 1, then handoff cost in the objective function (Equation 5) will be equal to zero. The h ij is the handoff cost between cell i and cell j. m y ij xik x jk i, j 1,..., n k 1 i j n n hij 1 y ij (5) i 1 j 1 The cabling cost will be calculated as shown in Equation (6). The C ik is the cabling cost between cell i and switchk per kilometer, and d ik is the distance between celliand switchkin kilometers. Finally, the objective function of CTSAP mathematical model will be minimizing Equation (7). Artificial Bee Colony (ABC) Approach n m cik dik xik i 1k 1 n m n n cik dik xik hij 1 y ij (7) i 1k 1 i 1 j 1 (4) (6) 3

5 Solutions Representation In this paper, the random key representation method for each solution is utilized. This method of representation is used for the first time in the literature of CTSAP. In this representation, solutions are shown as a (1 n) matrix (n is the number of cells) and each element of the matrix is a decimal number between 1 and m + 1 (m is the number of switches). The integer part of each number is the number of the switch that the associated cell is connected to. Among cells that have equal integer parts, the one which has a lower decimal part, is the location of the switch. For example, consider the solution below that is for a CTSAP with seven cells (n = 7) and three switches (m = 3): ( ). This solution tells us that cells 1 and 2 are assigned to switch 3, and switch 3 is located on cell 2. Cells 3 and 7 are assigned to switch 1, and switch 1 is located on cell 7. Cells 4, 5 and 6 are assigned to switch 2, and switch 2 is located on cell 4. Exhibit 3 presents how cells are assigned to switches for the aforementioned example with arbitrary coordinates. Exhibit 3. Example of the Cells to Switches Assignment. Elaboration of the Artificial Bee Colony (ABC) Algorithm The ABC algorithm is introduced by Karaboga for function optimization in Each solution (i.e. a position in the search space) represents a potential food source, and the quality of the solution is equal to the quality of that food source. Agents (artificial honeybees) search and exploit food sources in the search space (Panigrahi, Shi, & Lim, 2011). ABC utilizes three kinds of agents: Employed Bees (EB), Onlooker Bees (OB) and scouts. Employed bees are related to current solutions of the algorithm. In every step of the algorithm, an employed bee tries to improve its solution by local search and after that tries to recruit onlooker bees for its current position. Onlooker bees select among improved positions in respect to their qualities, which means better solutions attract more onlooker bees. If a recruited onlooker bee was able to find a better position, the employed bee would go to that new position; otherwise it would stay in its position. Moreover, an employed bee leaves its position; if it couldn't improve the position after a specific number of steps (this number is called the "limit"). In this case, it will become a scout and select new position in the search space randomly (Panigrahi et al., 2011). The main point that should be considered about scout bees is that they have no previous information for search (Ayanzadeh, Mousavi, & Navidi, 2011). The main steps of algorithm are as follows (Karaboga & Akay, 2009): 1. Initializing population; 2. Iterate; 3. Positioning employed bees on food sources; 4. Positioning onlooker bees on food sources with respect to their nectars; 5. Sending scouts to search space for finding new food sources; 6. Memorizing best found food sources; and 7. Until the stop criterion is met. Exhibit 4 shows how the proposed ABC algorithm works. 4

6 Exhibit 4.The Proposed ABC Algorithm. In the first step, the ABC generates the initial population (SN solutions) randomly that is equal to the number of employed bees or onlooker bees. Any solution x i (i = 1,, SN) is a D dimensional vector (D is the number of optimization parameters). After this stage, solutions will be improved by employed bees, onlooker bees and scouts during iterative cycles (c = 1,2,, MCN)(Karaboga, Akay, 2009). An artificial onlooker bee selects a food source with respect to its probability p i that is shown in Equation (8): fit p i i SN fit n n 1 (8) 5

7 where fit i is the fitness value of the solution i and is proportional to the quantity of the food source i (Karaboga & Akay, 2009). To achieve a new candidate food position from the old food position, the ABC utilizes Equation (9), V ij xij ij xij xkj (9) where k {1,2,, SN} and j {1,2,, D} are selected randomly and k j. Φ ij is a random number between [ 1,1]. If the produced value in this way exceeds its predetermined limit, it can still get an acceptable value, like the limit value (Karaboga & Akay, 2009). In the proposed algorithm, for each element of the solution vector that is lower than 1, we add it to a random number between (0,1), and then replace it. For each element of the solution vector that is equal to or greater than m + 1(m is the number of switches), we add m to a random number between (0,1) and replace it with the previous value. By knowing that x i is an abandoned food source and j {1,2,, D}, scouts will find a new food source according to Equation (10). x j i x j rand[0,1] xmax j min xmin j (10) Applying ABC Algorithm to Cell Assignment Problem In order to solve the model in the form of test problems, the values of the model parameters should be estimated. The statistical estimation method is selected according to the method provided by Pierre and Houeto (Pierre & Houéto, 2002). In Exhibit 5, these estimations are presented. Exhibit 5. Model Parameters and Corresponding Statistical Estimations. Model parameter i M k hij Statistical estimation Gamma(1,1) 1 K n 1 m i 100 i 1 i rij rij [0,1] cik 1 In estimating the M k value, K is selected between 10 and 50 uniformly to assure 10 to 50 percent excess capacity for each switch. In h ij estimation, r ij is the handoff probability (between 0 and 1). For instance, if the call from cell i can handoff to 4 other cells (i.e. handoff cost between them is not zero), 5 random numbers between [0,1] will be generated (the sum of them must be one), where j th number (j = 1,2,3,4) is the handoff probability between cell i and cell j (r ij ). Notice that the 5 th random number is the probability of the handoff not happening between cell i and cell j. The computerized programs of ABC algorithm are coded by MATLAB (R2009a) on a computer with the following specifications: MS-Windows XP Professional (SP3), Pentium(R) Dual-Core, CPU T4200@ 2.00 GHz 1.20 GHz, 2.96 GB of RAM. In order to adjust control parameters of ABC algorithm with respect to experimental considerations, the parameters including levels of Solutions (SN), Maximum Cycle Number (MCN) and Local Search (LS), are determined as shown in Exhibit 6. Exhibit 6. Levels of ABC Parameters Adjustment. Solutions (SN) Maximum Cycle Number (MCN) Local Search (LS)

8 For choosing the appropriate value for each ABC parameter, the full factorial experiment is conducted on two test problems (n = 20, m = 5 and n = 40, m = 6 on a grid ). Each problem is run in 27 scenarios (presented in Exhibit 7) for 5 times, and the final results are recorded. Exhibit Scenarios of Full Factorial Experiment. Scenario SN MCN LS Scenario SN MCN LS The average values of objective function in different scenarios are presented in Exhibit 8. According to Exhibit 8(a), the value 25 is selected for LS. In Exhibit 8(b), the calculation of average values of the objective function in the scenarios that SN is 20, 40 and 60, are shown. As can be seen in Exhibit 8(b), the third level of solutions number provides slightly better results, although it needs more computation time. Consequently, the SN value is selected as 40. Average values of objective function in the scenarios that MCN is 100, 200 and 300, are calculated and shown in Exhibit 8(c).The selected value for MCN is 200, because the third level of MCN increases computational time, and the difference of average objective function values of the second and third levels is not considerable. Exhibit 8. Average Values of Objective Function per Different Values of LS (a), SN (b) and MCN (c). (a) (b) (c) Efficiency Evaluation In order to show the efficiency of the proposed ABC algorithm, the ACO algorithm presented by Shyu, Lin and Hsiao (Shyu et al., 2006) is selected to compare with the proposed ABC algorithm. Shyu, Lin and Hsiao (Shyu et al., 2006) compared the ACO algorithm with 6 other algorithms and presented that ACO is completely efficient in terms of the objective function value and computation time. 7

9 In this paper, the comparison is conducted in terms of the objective function value and computation time (CPU time). The test problems are categorized in large, medium and small sizes of problems with three problems in each category (Exhibit 9). Exhibit 9. Designed Test Problems. size problem cells (n) switches (m) Grid small medium large * * * 200 The algorithms are run up to their stopping criterion. The stopping criterion is 200 iterations (MCN) in the proposed ABC algorithm. In the ACO the stopping criterion is100 consecutive iterations if no improvement on solutions can be attained. In addition, the algorithm will stop if the best objective function is achieved. The results of the experiments, averaged for five runs of a problem are reported in Exhibit 10. Relative Percent Deviation (RPD) value which represents ACO objective function values and computation times in comparison with ABC is calculated according to Equation (11). ACO ABC ABC 100 Exhibit 10. Comparison Results of ABC and ACO. objective function CPU time (sec.) Problem ABC ACO RPD (%) ABC ACO RPD (%) (11) With respect to the results (Exhibit 10), the ABC algorithm has better (lower) objective function values in comparison with the ACO algorithm in 8 out of 9 test problems. Only in one test problem, which is relatively small and can be solved by exact methods without help of any meta-heuristics, the ACO is slightly better than ABC in terms of objective function value. Furthermore, ACO has better performance in execution time because it starts with a relatively good solution in all problems. As an example, Exhibit 11 illustrates a medium size problem (m = 8 and n = 60). For this problem, the ABC algorithm again reaches a better solution than the ACO algorithm; however it needs more time to reach the better solution. 8

10 Exhibit 11. Convergence Diagram for m = 8 and n = 60. Conclusion The problem of cell-to-switch assignment is essential to the development of PCS or global communication services. In this paper, the Artificial Bee Colony (ABC) algorithm is proposed and utilized to solve the Cell to Switch Assignment Problem (CTSAP) which has been proven as an NP-hard problem. A single objective mathematical model with two constraints is presented for the CTSAP. Utilizing design of experiments, the parameters of the ABC algorithm are obtained. Numerical results of the experiments demonstrate the effectiveness of the ABC algorithm in coping with the cell assignment problem. For comparison purposes, several numerical examples are generated in order to compare the performance of the ABC algorithm with Ant Colony Optimization (ACO), which its efficient performance in solving CTSAP problems has been proven in the literature. The comparison is conducted in terms of the degree of optimization of the objective function and CPU time. Although ABC takes more CPU time than ACO, it could find much better approximate solutions. It is also easy to tailor ABC to resolve some extensions of the cell assignment problem with augmented virtual mobiles version yet to come. For example, the on-line version where the cells or switches would grow or shrink due to environment change or communications traffic, or the constrained version where precedence or priority relationships among cells and switches might be considered, just to name a few. References Ayanzadeh, R., Mousavi, A. S. Z., & Navidi, H. (2011). Honey bees foraging optimization for mixed nash equilibrium estimation. Trends in Applied Sciences Research, 6(12), Fournier, J. R. L., & Pierre, S. (2005). Assigning cells to switches in mobile networks using an ant colony optimization heuristic. Computer Communications, 28(1), Karaboga, D., & Akay, B. (2009). A comparative study of Artificial Bee Colony algorithm. Applied Mathematics and Computation, 214(1), Merchant, A., & Sengupta, B. (1995). Assignment of cells to switches in PCS networks. IEEE/ACM Transactions on networking, 3(5), Panigrahi, B. K., Shi, Y., & Lim, M.-H. (2011). Handbook of Swarm Intelligence: Concepts, Principles and Applications. Springer Science & Business Media. Pierre, S., & Houéto, F. (2002). A tabu search approach for assigning cells to switches in cellular mobile networks. Computer Communications, 25(5), Quintero, A., & Pierre, S. (2003a). Assigning cells to switches in cellular mobile networks: a comparative study. Computer Communications, 26(9),

11 Quintero, A., & Pierre, S. (2003b). Evolutionary approach to optimize the assignment of cells to switches in personal communication networks. Computer Communications, 26(9), Quintero, A., & Pierre, S. (2003c). Sequential and multi-population memetic algorithms for assigning cells to switches in mobile networks. Computer Networks, 43(3), Rajalakshmi, K., Kumar, P., & Bindu, H. M. (2010). Hybridizing iterative local search algorithm for assigning cells to switch in cellular mobile network. International Journal of Soft Computing, 5(1), Salcedo-Sanz, S., Portilla-Figueras, J. A., Ortiz-García, E. G., Pérez-Bellido, A. M., Thraves, C., Fernández-Anta, A., & Yao, X. (2008). Optimal switch location in mobile communication networks using hybrid genetic algorithms. Applied Soft Computing, 8(4), Salcedo-Sanz, S., & Yao, X. (2008). Assignment of cells to switches in a cellular mobile network using a hybrid Hopfield network-genetic algorithm approach. Applied Soft Computing, 8(1), Shyu, S. J., Lin, B. M. T., & Hsiao, T.-S. (2006). Ant colony optimization for the cell assignment problem in PCS networks. Computers & Operations Research, 33(6), Udgata, S. K., Anuradha, U., Kumar, G. P., & Udgata, G. K. (2008). Assignment of cells to switches in a cellular mobile environment using swarm intelligence. Proceedings of the IEEE International Conference on Information Technology (pp ). About the Authors Amin Vafadarnikjoo earned his master's degree in industrial management (operations research) in 2011 from Allameh Tabataba'i University, Iran. He also holds BSc degree in industrial engineering from Mazandaran University of Science and Technology (MUST), Iran. His current research interests are mainly in the field of business analytics utilizing a broad range of operations research methodologies such as MCDM, mathematical programming and combinatorial optimization. His articles have been published in the Expert Systems with Applications, International Journal of Operational Research, Journal of Cleaner production and Energy. S.M. Ali Khatami Firouzabadi, is an Associate Professor of industrial management at the faculty of management and accounting of Allameh Tabataba i University, Tehran, Iran. He received his PhD degree in industrial engineering from University of Leeds, UK in His main research interests are operations research, mathematical programming and decision theory. His research has been published in the Journal of Research & Health, International Journal of Management and Decision Making, Expert Systems and Computers & Industrial Engineering. Mohammadsadegh Mobin is a doctoral student in Industrial Engineering and Engineering Management at Western New England University, MA, USA. He holds a Master degree in Operations Research (OR) (2011) and a bachelor degree in Industrial Engineering (IE) (2009). He served as a quality engineer ( ) in different industries. His research interests lie in the areas of different applications of operations research tools. Afshan Roshani is a 1 st year graduate student in Industrial Engineering and Engineering Management at Western New England University. She holds an MBA (2012) and a bachelor degree in IE (2009). She works in different industries as a quality engineer ( ). Her current research activates are centered in her interest in quality engineering and supply chain. 10