Performance Analysis of Current Multi-Objective Metaheuristic Optimization Algorithms for Unconstrained Problems

Multi-objective optimization is a method used to produce suitable solutions for problems with more than one Objective. Various multi-objective optimization algorithms have been developed to apply this method to problems. In multi-objective optimization algorithms, the pareto optimal method is used to find the appropriate solution set over the problems. In the Pareto optimal method, the Pareto optimal set, which consists of the solutions reached by the multi-objective optimization, includes all the best solutions of the problems in certain intervals. For this reason, the Pareto optimal method is a very effective method to find the closest value to the optimum. In this study, the Multi-Objective Golden Sine Algorithm we developed (MOGoldSA), the recently published Multi-Objective Artificial Hummingbird Algorithm (MOAHA), and the Non-Dominant Sequencing Genetic Algorithm II (NSGA-II), which has an important place among the multi-objective optimization algorithms in the literature, are discussed. In order to see the performance of the algorithms on unconstrained comparison functions and engineering problems, performance comparisons were made on performance metrics

Keywords:

Multi-objective optimization, Pareto Optimal unconstrained benchmark functions, performance metrics,

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[1] K. Murty, “Optimization Models For Decision Making”,http://wwwpersonal.umich.edu/~murty/books/opti_model/junior-0.pdf),, 2003.
[2] E. Eröz and E. Tanyildizi, "Çok Amaçlı Metasezgisel Optimizasyon Algoritmalarının Performans Karşılaştırması," 2019 International Artificial Intelligence and Data Processing Symposium (IDAP), 2019, pp. 1-11, doi: 10.1109/IDAP.2019.8875955.
[3] E. Talbi, “Metaheuristic: Design to Implementation, 2nd Edition”, New Jersey: Wiley, 2009.
[4] Alataş. B., “Kaotik Haritalı Parçacık Sürü Optimizasyonu Algoritmaları Geliştirme” 2007.
[5] S. Mirjalili,”Dragonfly Algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems” Neural Comput & Applic 27, pp. 1053-1073, 2016.
[6] S. Mirjalili,”Dragonfly Algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems” Neural Comput & Applic 27, pp. 1053-1073, 2016.
[7] S. M. P. J. S. S., “Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems,” Appl Intell, DOI 10.1007/s10489-016-0825-8, 2016.
[8] K. P. Rainer S., “Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces,” Journal of Global Optimization 11, pp. 341-359, 1997.
[9] S. S. S. M. M. L. S. C. Seyedali M., “Multi-objective grey Wolf optimizer:A novel Algorithm for multi-criterion Optimization,” Expert SystemsWithApplications47, pp. 106-119, 2016.
[10] G. P. M. L. C.A.C. Coello,” Handling multiple objectives with particle swarm Optimization,” IEEE Transactions on Evolutionary Computation Volume: 8, Issue: 3 , 2004.
[11] K. D. N. Sirinivas, “Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms,” Journal of Evolutionary Computation, Vol. 2, No. 3, pp. 221-248, 1994.
[12] Zhao W, Zhang Z, Mirjalili S, Wang L, Khodadadi N, Mirjalili SM, “An effective multi-objective artificial hummingbird algorithm with dynamic elimination-based crowding distance for solving engineering design problems”, Computer Methods in Applied Mechanics and Engineering, 2022; 398, https://doi.org/10.1016/j.cma.2022.115223
[13] A. B., “Kaotik Haritalı Parçacık Sürü Optimizasyonu Algoritmaları Geliştirme, Doktora
[14] Tanyıldızı E, Demir G. Golden Sine Algorithm: A Novel Math-Inspired Algorithm. Adv Electr Comput En, 2017; 17(2):71-78.
[15] W. Zhao, L. Wang, S. Mirjalili, Artifical hummingbird algorithm: A new bia-inspired optimizer with its engineering applications, Comput. Methods Appl. Mech. Engrg. 388 (2022) 318
[16] .K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," in IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, pp. 182-197, April 2002, doi: 10.1109/4235.996017.
[17] M.B. Patil, Using external archive for improved performance in multi-objective optimization, 2018, arXiv preprint arXiv:1811.09196.
[18] Patil, M.B. (2018). Using External Archive for Improved Performance in Multi-Objective Optimization. ArXiv, abs/1811.09196.
[19] Deb K. Multi-objective optimization using evolutionary algorithms. New York: John Wiley&Sons, 2001.
[20] Van Veldhuizen, DA and Lamont GB. Multiobjective evolutionary algorithm research: A history and analysis. Technical Report TR-98-03, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, WrightPatterson AFB, Ohio, 1998
[21] Zitzler E. Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications, Ph.D Thesis, Swiss Federal Institute of Technology, Switzerland. 1999.
[22] Miettinen K. Nonlinear multiobjective optimization, Kluwer Academic Publishers, Boston: SpringerScience& Bus Media. 1999.
[23] Schott JR. Fault Tolerant Design Using Single and Multi-Criteria Genetic Algorithms. Master of Science Thesis, Massachusetts Institute of Technology, Cambridge, 1995.