Document Type : Original/Review Paper


1 Department of Electrical and Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Computer Engineering, South Tehran Branch, Islamic Azad University Tehran, Iran.


Many of the real-world issues have multiple conflicting objectives that the optimization between contradictory objectives is very difficult. In recent years, the Multi-objective Evolutionary Algorithms (MOEAs) have shown great performance to optimize such problems. So, the development of MOEAs will always lead to the advancement of science. The Non-dominated Sorting Genetic Algorithm II (NSGAII) is considered as one of the most used evolutionary algorithms, and many MOEAs have emerged to resolve NSGAII problems, such as the Sequential Multi-Objective Algorithm (SEQ-MOGA). SEQ-MOGA presents a new survival selection that arranges individuals systematically, and the chromosomes can cover the entire Pareto Front region. In this study, the Archive Sequential Multi-Objective Algorithm (ASMOGA) is proposed to develop and improve SEQ-MOGA. ASMOGA uses the archive technique to save the history of the search procedure, so that the maintenance of the diversity in the decision space is satisfied adequately. To demonstrate the performance of ASMOGA, it is used and compared with several state-of-the-art MOEAs for optimizing benchmark functions and designing the I-Beam problem. The optimization results are evaluated by Performance Metrics such as hypervolume, Generational Distance, Spacing, and the t-test (a statistical test); based on the results, the superiority of the proposed algorithm is identified clearly.


[1] B. Huang, B. Buckley, and T.-M. Kechadi, "Multi-objective feature selection by using NSGA-II for customer churn prediction in telecommunications," Expert Systems with Applications, vol. 37, no. 5, pp. 3638-3646, 2010.
[2] M. R. Nikoo, I. Varjavand, R. Kerachian, M. D. Pirooz, and A. Karimi, "Multi-objective optimumA design of double-layer perforated-wall breakwaters: Application of NSGA-II and bargaining models," Applied Ocean Research, vol. 47, pp. 47-52, 2014.
[3] A. Nourbakhsh, H. Safikhani, and S. Derakhshan, "The comparison of multi-objective particle swarm optimization and NSGA II algorithm: applications in centrifugal pumps," Engineering Optimization, vol. 43, no. 10, pp. 1095-1113, 2011.
[4] G. Sun, G. Li, Z. Gong, G. He, and Q. Li, "Radial basis functional model for multi-objective sheet metal forming optimization," Engineering Optimization, vol. 43, no. 12, pp. 1351-1366, 2011.
[5] J. Zeng, X. Zhang, and X. Guan, "Path Planning for General Aircrafts Under Complex Scenarios Using an Improved NSGA-II Algorithm⋆," Journal of Computational Information Systems, vol. 9, no. 16, pp. 6545-6553, 2013.
[6] C. A. C. Coello, G. B. Lamont, and D. A. Van Veldhuizen, Evolutionary algorithms for solving multi-objective problems. Springer, 2007.
[7] F. Sabahi, "Fuzzy Adaptive Granulation Multi-Objective Multi-microgrid Energy Management," Journal of AI and Data Mining, vol. 8, no. 4, pp. 481-489, 2020.
[8] K. Deb, Multi-objective optimization using evolutionary algorithms. John Wiley & Sons, 2001.
[9] E. Zitzler and L. Thiele, "Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach," IEEE transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257-271, 1999.
[10] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," Evolutionary Computation, IEEE Transactions on, vol. 6, no. 2, pp. 182-197, 2002.
[11] K. K. Annamdas and S. S. Rao, "Multi-objective optimization of engineering systems using game theory and particle swarm optimization," Engineering optimization, vol. 41, no. 8, pp. 737-752, 2009.
[12] N. Srinivas and K. Deb, "Muiltiobjective optimization using nondominated sorting in genetic algorithms," Evolutionary computation, vol. 2, no. 3, pp. 221-248, 1994.
[13] E. Zitzler and L. Thiele, "Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach," evolutionary computation, IEEE transactions on, vol. 3, no. 4, pp. 257-271, 1999.
[14] R. B. Agrawal, K. Deb, and R. Agrawal, "Simulated binary crossover for continuous search space," Complex systems, vol. 9, no. 2, pp. 115-148, 1995.
[15] X. Li, "A non-dominated sorting particle swarm optimizer for multiobjective optimization," in Genetic and Evolutionary Computation—GECCO 2003, 2003: Springer, pp. 37-48.
[16] M. Mahfouf, M. Chen, and D. A. Linkens, "Adaptive weighted particle swarm optimisation for multi-objective optimal design of alloy steels," in Parallel problem solving from nature-ppsn viii, 2004: Springer, pp. 762-771.
[17] J. A. Rangel-González et al., "Fuzzy Multi-objective Particle Swarm Optimization Solving the Three-Objective Portfolio Optimization Problem," International Journal of Fuzzy Systems, pp. 1-9, 2020.
[18] L. Falahiazar and H. Shah-Hosseini, "The Sequential Multi-Objective Genetic Algorithm: A novel multi-objective genetic algorithm  " presented at the International Conference on New Research Achievements in Electrical and Computer Engineering, International Federation of Inventors Association in Iran, 2016.
[19] J. D. Knowles and D. W. Corne, "Approximating the nondominated front using the Pareto archived evolution strategy," Evolutionary computation, vol. 8, no. 2, pp. 149-172, 2000.
[20] S.-K. S. Fan, J.-M. Chang, and Y.-C. Chuang, "A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies," Engineering Optimization, vol. 47, no. 6, pp. 750-770, 2015.
[21] S.-T. Hsieh, S.-Y. Chiu, and S.-J. Yen, "An improved multi-objective genetic algorithm for solving multi-objective problems," Applied Mathematics & Information Sciences, vol. 7, no. 5, p. 1933, 2013.
[22] M. Kim, T. Hiroyasu, M. Miki, and S. Watanabe, "SPEA2+: Improving the performance of the strength Pareto evolutionary algorithm 2," in International Conference on Parallel Problem Solving from Nature, 2004: Springer, pp. 742-751.
[23] Y. Xiang, Y. Zhou, and H. Liu, "An elitism based multi-objective artificial bee colony algorithm," European Journal of Operational Research, vol. 245, no. 1, pp. 168-193, 2015.
[24] Z. Xu, "A Novel Hybrid Algorithm for Constrained Multi-objective Optimization," International Journal of Hybrid Information Technology, vol. 7, no. 3, pp. 265-274, 2014.
[25] E. Zitzler, M. Laumanns, and L. Thiele, "SPEA2: Improving the strength Pareto evolutionary algorithm," TIK-report, vol. 103, 2001.
[26] P. Hajela and C.-J. Shih, "Multiobjective optimum design in mixed integer and discrete design variable problems," AIAA journal, vol. 28, no. 4, pp. 670-675, 1990.
[27] R. Eberhart and J. Kennedy, "Particle swarm optimization, proceeding of IEEE International Conference on Neural Network," Perth, Australia, pp. 1942-1948, 1995.
[28] X. Li, "A non-dominated sorting particle swarm optimizer for multiobjective optimization," in Genetic and Evolutionary Computation Conference, 2003: Springer, pp. 37-48.
[29] D. E. Goldberg and J. Richardson, "Genetic algorithms with sharing for multimodal function optimization," in Genetic algorithms and their applications: Proceedings of the Second International Conference on Genetic Algorithms, 1987: Hillsdale, NJ: Lawrence Erlbaum, pp. 41-49.
[30] V. S. Ghomsheh, M. A. Khanehsar, and M. Teshnehlab, "Improving the non-dominate sorting genetic algorithm for multi-objective optimization," in Computational Intelligence and Security Workshops, 2007. CISW 2007. International Conference on, 2007: IEEE, pp. 89-92.
[31] R. Cheng and M. Gen, "Genetic algorithms for multi-row machine layout problem," Engineering Design and Automation, pp. 876-881, 1996.
[32] Z. Michalewicz, C. Z. Janikow, and J. B. Krawczyk, "A modified genetic algorithm for optimal control problems," Computers & Mathematics with Applications, vol. 23, no. 12, pp. 83-94, 1992.
[33] D. A. Van Veldhuizen, "Multiobjective evolutionary algorithms: classifications, analyses, and new innovations," AIR FORCE INST OF TECH WRIGHT-PATTERSONAFB OH SCHOOL OF ENGINEERING, 1999.
[34] Y. Chen, X. Chen, and C. Wang, "Experimental and finite element analysis research on I-beam under web crippling," Materials and Structures, vol. 49, no. 1-2, pp. 421-437, 2016.
[35] N. D. Hai, H. Mutsuyoshi, S. Asamoto, and T. Matsui, "Structural behavior of hybrid FRP composite I-beam," Construction and Building Materials, vol. 24, no. 6, pp. 956-969, 2010.
[36] Q.-Y. Song, A. Heidarpour, X.-L. Zhao, and L.-H. Han, "Performance of double-angle bolted steel I-beam to hollow square column connections under static and cyclic loadings," International Journal of Structural Stability and Dynamics, p. 1450098, 2014.
[37] Q.-Y. Song, A. Heidarpour, X.-L. Zhao, and L.-H. Han, "Post-earthquake fire behavior of welded steel I-beam to hollow column connections: An experimental investigation," Thin-Walled Structures, vol. 98, pp. 143-153, 2016.
[38] W. Wang, T.-M. Chan, and H. Shao, "Numerical investigation on I-beam to CHS column connections equipped with NiTi shape memory alloy and steel tendons under cyclic loads," in Structures, 2015, vol. 4: Elsevier, pp. 114-124.
[39] Hong-Zhong Huanga and X. D. Ying-Kui Gu, "An interactive fuzzy multi-objective optimization method for engineering design," Engineering Applications of Artificial Intelligence,Elsevier, 2006.
[40] D. Veldhuizen, "Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. 1999," School of Engineering of the Air Force Institute of Technology, Dayton, Ohio, 1999.
[41] K. Bösecke, "Value creation in mergers and acquisitions–theoretical paradigms and past research," in Value Creation in Mergers, Acquisitions, and Alliances. Dissertation Jacobs University Bremen, 2009: Springer, 2009, p. 92.
[42] T. Lumley, P. Diehr, S. Emerson, and L. Chen, "The importance of the normality assumption in large public health data sets," Annual review of public health, vol. 23, no. 1, pp. 151-169, 2002.
[43] E. Zitzler and L. Thiele, "Multiobjective optimization using evolutionary algorithms—a comparative case study," in International conference on parallel problem solving from nature, 1998: Springer, pp. 292-301.
[44] J. R. Schott, "Fault tolerant design using single and multicriteria genetic algorithm optimization," Air Force Inst of Tech Wright-Patterson AFB OH, 1995.
[45] S. García, D. Molina, M. Lozano, and F. Herrera, "A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization," Journal of Heuristics, vol. 15, no. 6, p. 617, 2009.