# Genetic Algorithm Performance with Different Selection Methods in Solving Multi-Objective Network Design Problem

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1 etic Algorithm Performance with Different Selection Methods in Solving Multi-Objective Network Design Problem R. O. Oladele Department of Computer Science University of Ilorin P.M.B. 1515, Ilorin, NIGERIA J. S. Sadiku Department of Computer Science University of Ilorin P.M.B. 1515, Ilorin, NIGERIA ABSTRACT Selection is one of the key operations of genetic algorithm (GA). This paper presents a comparative analysis of GA performance in solving multi-objective network design problem (MONDP) using different parent selection methods. Three problem instances were tested and results show that on the average tournament selection is the most effective and most efficient for 10-node network design problem, while Ranking & Scaling is the least effective and least efficient. For 21-node and 36-node network problems, Roulette Wheel is the least effective but most efficient while Ranking & Scaling equals and outperformed tournament in effectiveness and efficiency respectively. eral Terms Evolutionary Algorithms, Combinatorial Optimization, Artificial Intelligence. Keywords etic Algorithm, Selection Methods, Network Design Problem, Performance. 1. INTRODUCTION The selection of individuals for the production of the next generation is a critical process in GA. The individuals that are chosen for reproduction and the number of children each selected individual produces are determined by the selection mechanism. The underlying principle of selection strategy is the fitter an individual is the higher is its chance of being parent. A critical parameter to be determined in GA is the selection pressure which is the process of selecting the fittest individuals for reproduction. If it is set too low, then the rate of convergence towards the optimum solution will be too slow. If the selection pressure is set too high, the algorithm is likely to be stuck in a local optimum due to the lack of diversity in the population. Therefore, the selection methods tune the selection pressure, which in turn determines the convergence rate of the algorithm. The selection mechanism should be chosen such that convergence to the global optimum solution is guaranteed. In addition the selection mechanism should encompass knowledge of the existing data. Different selection schemes will undoubtedly influence the performance of GA differently. This study aims at exploring the performance of GA when using different selection strategies particularly in solving Multi-Objective Network Design Problem (MONDP). MONDP is a typical example of NP-hard optimization problem The remainder of this paper is organized as follows: Section 2 presents a brief review of literature on selection method. Selection 3 presents a brief description of MONDP while section 4 gives an overview of the genetic algorithm for MONDP. Section 5 describes in detail the selection methods that are used in the experiments. Section 6 tests the performance of GA and discusses the experimental results. The Paper is concluded in section LITERATURE REVIEW ON SELECTION METHOD Several researchers have studied the performance of GA using differing selection schemes. However, virtually no of these researchers tested the algorithm on network design problem. The performance of GA is usually evaluated in terms of convergence rate and the number of generations to reach optimal solution [1]. Goldberg and Deb [2] were the first to study the performance of different selection schemes. They investigated the performance of proportional ranking, tournament and itor (steady state) selection schemes using solutions to differential equations as basis. Their investigation aimed at understanding the expected fitness ratio and convergence time. It was found that ranking and tournament selections outperformed proportional selection in terms of maintaining steady pressure towards convergence. They also showed that linear ranking and stochastic binary tournament selections have similar expectations, but recommended binary tournament selection due to its better time complexity. Goh et al. [3] focused on the selection process of GA and study common problems and solution methods of such selection schemes. They further proposed a new selection scheme called sexual selection and compared its performance with commonly used selection methods in solving some scheduling problems. It is claimed that the proposed scheme performed either on-par or better than roulette wheel selection on the average without the use of fitness scaling. In the more difficult test cases when no fitness scaling is used, the new scheme also performed better on the average when compared to tournament selection. Julstrom [4] studied the computing time efficiency of two types of rank-based selection probabilities namely linear ranking and exponential ranking probabilities in comparison with tournament selection. He noted that tournament selection is superior to rank-based selection because repeated tournament selection is faster than sorting the population to assign rank-based probabilities. Mashohor et al [5] analyzed the performance of PCB inspection system with the use of three GA selection methods namely tournament, deterministic and roulette wheel selections. Their findings show that deterministic method 5

3 Each link is bidirectional i.e. a path can be traversed in either direction There is no redundant link in the network 4. GENETIC ALGORITHM FOR MONDP 1 Initialization: randomly generate population of N chromosomes 2 Fitness: calculate the fitness of all chromosomes 3 Create a new population: a. Selection: select 2 chromosomes from the population b. Crossover: produce 2 offsprings from the 2 selected chromosomes c. Mutation: perform mutation on each offspring. 4 Replace: replace the current population with the new population 5 Evaluation: evaluate the objective function 6 Termination: Test if the termination condition is satisfied. If so stop. If not, go to step SELECTION METHODS FOR REPRODUCTION 5.1 Roulette Wheel selection In the Roulette wheel selection method [9], the first step is to calculate the cumulative fitness of the whole population through the sum of the fitness of all individuals. After that, the probability of selection is calculated for each individual as being pseli = fi/pfi. Then, an array is built containing cumulative probabilities of the individuals. So, n random numbers are generated in the range 0 to Pfi and for each random number an array element which can have higher value is searched for. Therefore, individuals are selected according to their probabilities of selection. 5.2 Tournament Selection Tournament selection is probably the most popular selection method in genetic algorithm due to its efficiency and simple implementation [2]. In tournament selection, n individuals are selected randomly from the larger population, and the selected individuals compete against each other. The individual with the highest fitness wins and will be included as one of the next generation population. The number of individuals competing in each tournament is referred to as tournament size, commonly set to 2 (also called binary tournament). Tournament selection also gives a chance to all individuals to be selected and thus it preserves diversity, although keeping diversity may degrade the convergence speed. The tournament selection has several advantages which include efficient time complexity, especially if implemented in parallel, low susceptibility to takeover by dominant individuals, and no requirement for fitness scaling or sorting [2, 10]. In tournament selection, larger values of tournament size lead to higher expected loss of diversity [10, 11]. The larger tournament size means that a smaller portion of the population actually contributes to genetic diversity, making the search increasingly greedy in nature. There might be two factors that lead to the loss of diversity in regular tournament selection; some individuals might not get sampled to participate in a tournament at all while other individuals might not be selected for the intermediate population because they lost a tournament 5.3 Ranking and Scaling Selection The scaling method maps raw objective function values to positive real values, and the survival probability for each chromosome is determined according to these values. Fitness scaling has a twofold intention: to maintain a reasonable differential between relative fitness ratings of chromosomes; and to prevent too-rapid takeover by some dominant chromosomes to meet the requirement to limit competition early but to stimulate it later. 6. COMPUTATIONAL EXPERIMENTS AND RESULTS Table 1:Results for 10-node network problem

4 Table 2: Results for 21-node network problem Table 3: Results for 36-node network problem CONCLUSION In this paper three types of selection strategy in the GA procedure to solve network topology design problem are described. Their relative performances in terms of solution quality and computation time are compared. From the results of experiment on three randomly generated networks. On the average, tournament selection returns the best solution both in quality and computation time while the solution returned by Ranking & Scaling is the worst both in quality and computation time for 10-node network. For 21-node and 36- node networks, Ranking & Scaling performed as well as tournament selection in solution quality but outperformed tournament in computation time. Roulette wheel has the worst solution quality but the best computation time 8. ACKNOWLEDGEMENT The authors acknowledge Hammed Sanusi who has offered programming assistance. 9. REFERENCES [1] Razali, N. M., Geraghty, J etic Algorithm Performance with Different Selection Strategies in Solving TSP. In Proceedings of the World Congress on Engineering, vol. II, London, UK. [2] Goldberg, D. E. and Deb Kalyanmoy A Comparative Analysis of Selection Schemes Used in etic Algorithms. In: G.J.E. Rawlins (Ed), Foundations of etic Algorithms, Morgan Kaufmann, Los Altos, [3] Goh, K. S., Lim, A., Rodrigues, B Sexual Selection for etic Algorithms. Artificial Intelligence Review 19: , Kluwer Academic Publishers. [4] Julstrom, B. A It s All the Same to Me: Revisiting Rank-Based Probabilities and Tournaments, Department of Computer Science, St. Cloud State University. [5] Mashohor, S.Evans, J. R., Arslan, T Elitist Selection Schemes for etic Algorithm based Printed Circuit Board Inspection System, Department of Electronics and Electrical Engineering, University of Edinburgh, [6] Zhong, J., Hu, X., Gu, M., Zhang, J Comparison of Performance between Different Selection Strategies on Simple etic Algorithms. In Proceeding of the International Conference on Computational Intelligence for Modelling, Control and automation, and International Conference of Intelligent Agents, Web Technologies and Internet Commerce. [7] Jadaan, O.A., Rajamani, L., Rao, C. R Improved Selection Operator for GA. Journal of Theoretical and Applied Information Technology. 8

5 [8] Banerjee, N., Kumar, R Multiobjective Network Design for Realistic Traffic Models. In Proc. etic and Evolutionary Computations Conference (GECCO- 07), [9] Holland, J. H Adaptation in Natural and Artificial Systems, 2nd Ed, MIT Press. [10] Blickle, T, Thiele, L. A Comparison of Selection Schemes used in etic Algorithms. TIK-Report, Zurich.. [11] Whitley, D The genitor algorithm and selection pressure: Why rank-based allocation of reproductive trials is the best. In Proceeding of the 3rd International Conference on etic Algorithms. [12] Sivaraj, R.,Ravichandran, T A Review of Selection Methods in etic Algorithm. International Journal of Engineering Science and Technology (IJEST). Vol.3, no. 5,

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