AN EVALUATION OF A CONSTRAINED MULTI-OBJECTIVE GENETIC ALGORITHM

Abstract

Real world optimization problems involve multiple conflicting objectives (such as minimizing cost while maximizing the quality of a product) and are subject to constraints (such as physical feasibility or budget limitations) which makes them interesting to solve. Over the last decades, evolutionary algorithms have been largely used in solving optimization problems in various fields of science. The aim of this study is to evaluate the performance of a constrained version of the Non-dominated Sorting Genetic Algorithm 2 (NSGA 2), a multi-objective evolutionary optimization algorithm, written in MATLAB. The developed NSGA 2 is compared, in terms of convergence and diversity of the obtained solutions, to a number of popular constrained multi-objective evolutionary algorithms from the literature. Widely used four benchmark problems (including CONSTR, OSY, SRN, and TNK problems) with varying difficulty and type of constraints are reviewed and used. The NSGA 2 obtained the lowest values of inverse generational distance (IGD) values for almost all the problems. These results show that the developed constrained NSGA 2 is an effective technique and is competitive to the other optimization methods in the literature.

Keywords

• Genetic algorithms,Evolutionary algorithms,Non-dominated Sorting Genetic Algorithm 2,Multi-objective optimization,constrained multi-objective optimization.

Kaynakça

1. COELLO, C. A. C., LAMONT, G. B., & VAN VELDHUIZEN, D. A. (2007). Evolutionary algorithms for solving multi-objective problems (Vol. 5): Springer.
2. DEB, K., PRATAP, A., AGARWAL, S., & MEYARIVAN, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. doi:Pii S 1089-778x(02)04101-2 Doi 10.1109/4235.996017
3. FAN, Z., LI, H., CAIMIN, W., LI, W., HAN, H., CAI, X., & CAI, Z. (2016, 6-9 Dec. 2016). An improved epsilon constraint handling method embedded in MOEA/D for constrained multi-objective optimization problems. Paper presented at the 2016 IEEE Symposium Series on Computational Intelligence (SSCI).
4. FAN, Z., YI, F., LI, W., JIEWEI, L., CAI, X., & CAIMIN, W. (2017, 5-8 June 2017). A comparative study of constrained multi-objective evolutionary algorithms on constrained multi-objective optimization problems. Paper presented at the 2017 IEEE Congress on Evolutionary Computation (CEC).
5. GOLDBERG, D. E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning: Addison-Wesley Longman Publishing Co., Inc.
6. KALYANMOY, D. (2001). Multi-Objective Optimization Using Evolutionary Algorithms: John Wiley \& Sons, Inc.
7. OSYCZKA, A., & KUNDU, S. (1995). A New Method to Solve Generalized Multicriteria Optimization Problems Using the Simple Genetic Algorithm. Structural Optimization, 10(2), 94-99. doi:Doi 10.1007/Bf01743536
8. RAY, T., SINGH, H. K., ISAACS, A., & SMITH, W. (2009). Infeasibility Driven Evolutionary Algorithm for Constrained Optimization. In E. Mezura-Montes (Ed.), Constraint-Handling in Evolutionary Optimization (pp. 145-165). Berlin, Heidelberg: Springer Berlin Heidelberg.

9. RAY, T., TAI, K., & SEOW, K. C. (2001). MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM. Engineering Optimization, 33(4), 399-424. doi:10.1080/03052150108940926
10. SRINIVAS, N., & DEB, K. (1994). Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation, 2(3), 221-248. doi:10.1162/evco.1994.2.3.221
11. TANAKA, M., WATANABE, H., FURUKAWA, Y., & TANINO, T. (1995). GA-based decision support system for multicriteria optimization. 1995 Ieee International Conference on Systems, Man and Cybernetics, Vols 1-5, 1556-1561.
12. WANG, Y., CAI, Z., ZHOU, Y., & ZENG, W. (2008). An Adaptive Tradeoff Model for Constrained Evolutionary Optimization. IEEE Transactions on Evolutionary Computation, 12(1), 80-92. doi:10.1109/TEVC.2007.902851
13. WOLDESENBET, Y. G., YEN, G. G., & TESSEMA, B. G. (2009). Constraint Handling in Multiobjective Evolutionary Optimization. IEEE Transactions on Evolutionary Computation, 13(3), 514-525. doi:10.1109/TEVC.2008.2009032