Solving Multi-objective Optimization Problems Using the Society Deciling Process Algorithm

Document Type : Original Article

Authors

1 Faculty of Information Technology and Computer Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran, Email: aylar.p.2000@gmail.com

2 Corresponding author, Faculty of Information Technology and Computer Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran, Email: pira@azaruniv.ac.ir

3 Faculty of Information Technology and Computer Engineering, Azarbaijan Shahid Madani University, Tabriz, Iran, Email: m.khodizadeh@azaruniv.ac.ir

4 Department of Computer Engineering, Malayer University, Malayer, Iran. Email: sajad.a1367@gmail.com

10.22091/jemsc.2026.13697.1297

Abstract

Advancements in technology and the emergence of multi-objective optimization problems across various scientific domains have spurred research and development of novel metaheuristic algorithms to address these challenges. Although these methods have largely succeeded in approaching the Pareto-optimal front, the optimization process has not been fully realized. This paper introduces a multi-objective version of the Social Division Process (SDP) algorithm, termed MOSDP, aimed at improving the quality of Pareto front solutions. The MOSDP algorithm employs a memory structure as an archive to store non-dominated solutions. Additionally, it utilizes a non-dominated sorting mechanism based on crowding distance to establish a hierarchical social division structure and guide the evolutionary process in the multi-objective problem space. The performance of MOSDP is evaluated using 18 well-known multi-objective test functions, UF, and IMOP, and compared with the Multi-Objective City Councils Evolution (MOCCE), Multi-Objective Ant Lion Optimization (MOALO), Multi-Objective Slime Mould Algorithm (MOSMA), and Multi-Objective Artificial Hummingbird Algorithm (MOAHA). The results of the Friedman average rank test demonstrate the superiority of MOSDP over the aforementioned algorithms in terms of Inverted Generational Distance (IGD), Generational Distance (GD), and Maximum Spread (MS) metrics.

Keywords

Main Subjects


Abbass, H. A., Sarker, R., & Newton, C. (2001). PDE: A Pareto-frontier differential evolution approach for multi-objective optimization problems. In Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546).
Akbari, R., Hedayatzadeh, R., Ziarati, K., & Hassanizadeh, B. (2012). A multi-objective artificial bee colony algorithm. Swarm and Evolutionary Computation, 2, 39-52.
Alaya, I., Solnon, C., & Ghedira, K. (2007). Ant colony optimization for multi-objective optimization problems. In 19th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2007).
Cao, J., Zhang, J., Zhao, F., & Chen, Z. (2021). A two-stage evolutionary strategy based MOEA/D to multi-objective problems. Expert Systems with Applications, 185, 115654.
Coello, C. C., & Lechuga, M. S. (2002). MOPSO: A proposal for multiple objective particle swarm optimization. In Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No. 02TH8600).
Deb, K., Agrawal, S., Pratap, A., & Meyarivan, T. (2000a). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In International Conference on Parallel Problem Solving from Nature.
Deb, K., Agrawal, S., Pratap, A., & Meyarivan, T. (2000b, September 18–20). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. Parallel Problem Solving from Nature PPSN VI. In 6th International Conference. Paris, France.
Dorigo, M., Birattari, M., & Stutzle, T. (2006). Ant colony optimization. IEEE Computational Intelligence Magazine, 1(4), 28-39.
Faramarzi, A., Heidarinejad, M., Stephens, B., & Mirjalili, S. (2020). Equilibrium optimizer: A novel optimization algorithm. Knowledge-Based Systems, 191, 105190.
Friedman, M. (1940). A comparison of alternative tests of significance for the problem of m rankings. The Annals of Mathematical Statistics, 11(1), 86-92.
Ghaffar Alishahi, M., Pira, E., & Rouhi, A. (2023). Development of city councils evolution algorithm for multi-objective optimization problems. Soft Computing Journal.
Gómez, R. H., & Coello, C. A. C. (2013). MOMBI: A new metaheuristic for many-objective optimization based on the R2 indicator. 2013 IEEE Congress on Evolutionary Computation.
Holland, J. H. (1992). Genetic algorithms. Scientific American, 267(1), 66-73.
Horn, J., Nafpliotis, N., & Goldberg, D. E. (1994). A niched Pareto genetic algorithm for multiobjective optimization. In Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress On Computational Intelligence.
Kaur, H., Rai, A., Bhatia, S. S., & Dhiman, G. (2020). MOEPO: A novel multi-objective emperor penguin optimizer for global optimization: Special application in ranking of cloud service providers. Engineering Applications of Artificial Intelligence, 96, 104008.
Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of ICNN'95-International Conference on Neural Networks.
Khishe, M., Orouji, N., & Mosavi, M. R. (2023). Multi-objective chimp optimizer: an innovative algorithm for multi-objective problems. Expert Systems with Applications, 211, 118734.
Khodadadi, N., Mirjalili, S. M., Zhao, W., Zhang, Z., Wang, L., & Mirjalili, S. (2022). Multi-objective artificial hummingbird algorithm. In Advances in Swarm Intelligence: Variations and Adaptations for Optimization Problems (pp. 407-419). Springer.
Mirjalili, S., Jangir, P., & Saremi, S. (2017). Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems. Applied Intelligence, 46(1), 79-95.
Mirjalili, S., Mirjalili, S. M., & Hatamlou, A. (2016). Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Computing and Applications, 27(2), 495-513.
Mirjalili, S., Saremi, S., Mirjalili, S. M., & Coelho, L. d. S. (2016). Multi-objective grey wolf optimizer: A novel algorithm for multi-criterion optimization. Expert Systems with Applications, 47, 106-119.
Murata, T., & Ishibuchi, H. (1995). MOGA: multi-objective genetic algorithms. In IEEE International Conference on Evolutionary Computation.
Naruei, I., & Keynia, F. (2021). Wild horse optimizer: A new meta-heuristic algorithm for solving engineering optimization problems. Engineering with Computers, 1-32.
Pira, E. (2022). City councils evolution: A socio-inspired metaheuristic optimization algorithm. Journal of Ambient Intelligence and Humanized Computing, 1-50.
Pira, E., & Rouhi, A. (2024). Society deciling process: A socio-inspired meta-heuristic algorithm. Journal of Electrical and Computer Engineering Innovations (JECEI), 12(2), 535-556.
Połap, D., & Woźniak, M. (2021). Red fox optimization algorithm. Expert Systems with Applications, 166, 114107.
Premkumar, M., Jangir, P., & Sowmya, R. (2021). MOGBO: A new multiobjective gradient-based optimizer for real-world structural optimization problems. Knowledge-Based Systems, 218, 106856.
Premkumar, M., Jangir, P., Sowmya, R., Alhelou, H. H., Heidari, A. A., & Chen, H. (2020). MOSMA: Multi-objective slime mould algorithm based on elitist non-dominated sorting. IEEE Access, 9, 3229-3248.
Premkumar, M., Jangir, P., Sowmya, R., Alhelou, H. H., Mirjalili, S., & Kumar, B. S. (2022). Multi-objective equilibrium optimizer: Framework and development for solving multi-objective optimization problems. Journal of Computational Design and Engineering, 9(1), 24-50.
Sadollah, A., Eskandar, H., & Kim, J. H. (2015). Water cycle algorithm for solving constrained multi-objective optimization problems. Applied Soft Computing, 27, 279-298.
Xue, L., Zeng, P., & Yu, H. (2020). SETNDS: A SET-based non-dominated sorting algorithm for multi-objective optimization problems. Applied Sciences, 10(19), 6858.
Zeng, S.-Y., Chen, G., Zheng, L., Shi, H., de Garis, H., Ding, L., & Kang, L. (2006). A dynamic multi-objective evolutionary algorithm based on an orthogonal design. In 2006 IEEE International Conference on Evolutionary Computation.
Zhang, Q., & Li, H. (2007). MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation, 11(6), 712-731.
Zitzler, E., & Künzli, S. (2004). Indicator-based selection in multiobjective search. In International Conference on Parallel Problem Solving from Nature.
Zitzler, E., Laumanns, M., & Thiele, L. (2001). SPEA2: Improving the strength Pareto evolutionary algorithm. TIK-Report, 103.
CAPTCHA Image