Document Type : Original/Review Paper
Authors
1 Department of Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 Intelligent Systems Laboratory, Faculty of Electrical and Computer Engineering, K. N. Toosi University of Technology, Tehran, Iran.
3 Faculty of Engineering, University of Nottingham, Nottingham, UK.
Abstract
A new multi-objective evolutionary optimization algorithm is presented based on the competitive optimization algorithm (COOA) to solve multi-objective optimization problems (MOPs). Based on nature-inspired competition, the competitive optimization algorithm acts between animals such as birds, cats, bees, ants, etc. The present study entails main contributions as follows: First, a novel method is presented to prune the external archive and at the same time keep the diversity of the Pareto front (PF). Second, a hybrid approach of powerful mechanisms such as opposition-based learning and chaotic maps is used to maintain the diversity in the search space of the initial population. Third, a novel method is provided to transform a multi-objective optimization problem into a single-objective optimization problem. A comparison of the result of the simulation for the proposed algorithm was made with some well-known optimization algorithms. The comparisons show that the proposed approach can be a better candidate to solve MOPs.
Keywords
[1] G. Zhang, H. Wang, W. Zhao, Z. Guan, and P. Li, “Application of Improved Multi-objective Ant Colony Optimization Algorithm in Ship Weather Routing,” Journal of Ocean University of China, 20(1), pp.45-55, 2021.
[2] A. Kaveh, P. Rahmani, and A.D. Eslamlou, “An efficient hybrid approach based on Harris Hawks optimization and imperialist competitive algorithm for structural optimization,” Engineering with Computers, pp.1-29, 2021.
[3] Y. Sun, G. G. Yen, and Z. Yi, “IGD indicator-based evolutionary algorithm for many-objective optimization problems,” IEEE Transactions on Evolutionary Computation, Vol. 23 (2), pp. 173-87, 2018.
[4] N. Yerpula, “Cat Swarm Optimization Algorithm for Antenna Array Synthesis,” Turkish Journal of Computer and Mathematics Education (TURCOMAT), 12(2), pp.1466-1474, 2021.
[5] F. Han, W.T. Chen, Q.H. Ling, and H. Han, “Multi-objective particle swarm optimization with adaptive strategies for feature selection,” Swarm and Evolutionary Computation, 62, p.100847, 2021.
[6] K. Deb, A. Pratap, S. Agarwal, and T. A. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE transactions on evolutionary computation, Vol. 6 (2), pp. 182-97, 2002.
[7] M. Khanali, A. Akram, J. Behzadi, F. Mostashari-Rad, Z., Saber, K.W. Chau, and A. Nabavi-Pelesaraei, “Multi-objective optimization of energy use and environmental emissions for walnut production using imperialist competitive algorithm,” Applied Energy, 284, p.116342, 2021.
[8] F. A. Fortin and M. Parizeau, “Revisiting the NSGA-II crowding-distance computation,” InProceedings of the 15th annual conference on Genetic and evolutionary computation; pp. 623-630, 2013.
[9] X. Zhou, J. Lu, J. Huang, M. Zhong, and M. Wang, “Enhancing artificial bee colony algorithm with multi-elite guidance,” Information Sciences, 543, pp.242-258, 2021.
[10] K. Shang, H. Ishibuchi, L. He, and L.M. Pang, “A survey on the hypervolume indicator in evolutionary multi-objective optimization,” IEEE Transactions on Evolutionary Computation, 25(1), pp.1-20, 2020.
[11] X. Ma, F. Liu, Y. Qi, M. Gong, M. Yin, L. Li, L. Jiao, and J. Wu, “MOEA/D with opposition-based learning for multi-objective optimization problem,” Neurocomputing, Vol. 146, pp. 48-64, 2014.
[12] Y. Gao, L. Peng, F. Li, M. Liu, and W. Li, “Multi-objective opposition-based learning fully informed particle swarm optimizer with favour ranking,” In2013 IEEE International Conference on Granular Computing (GrC), pp. 114-119, 2013.
[13] Y. Yang, B. Yang, S. Wang, T. Jin, S. Li, “An enhanced multi-objective grey wolf optimizer for service composition in cloud manufacturing,” Applied Soft Computing, 87, p.106003, 2020.
[14] D. Yan, H. Cao, Y. Yu, Y. Wang, and X. Yu, “Single-objective/multi-objective cat swarm optimization clustering analysis for data partition,” IEEE Transactions on Automation Science and Engineering, 17(3), pp.1633-1646, 2020.
[15] L. M. Antonio and C. A. Coello, “Coevolutionary multi-objective evolutionary algorithms: Survey of the state-of-the-art,” IEEE Transactions on Evolutionary Computation, Vol. 22 (6), pp. 851-65, 2017.
[16] Y. Sharafi, M. A. Khanesar, and M. Teshnehlab, “COOA: Competitive optimization algorithm,” Swarm and Evolutionary Computation, Vol. 30, pp. 39-63, 2016.
[17] B. Guan, Y. Zhao, and Y. Li, “An improved ant colony optimization with an automatic updating mechanism for constraint satisfaction problems,” Expert Systems with Applications, 164, p.114021, 2021.
[18] F. Wang, H. Zhang, and A. Zhou, “a particle swarm optimization algorithm for mixed-variable optimization problems,” Swarm and Evolutionary Computation, 60, p.100808, 2021.
[19] S. Talatahari and M. Aziz, “Chaos Game Optimization: a novel metaheuristic algorithm,” Artificial Intelligence Review, 54(2), pp.917-1004, 2021.
[20] T. Joyce and J. M. Herrmann, “A review of no free lunch theorems, and their implications for metaheuristic optimization,” InNature-inspired algorithms and applied optimization;Springer, Cham, pp. 27-51, 2018.
[21] X. Yu, W. Xu, and C. Li, “Opposition-based learning grey wolf optimizer for global optimization,” Knowledge-Based Systems, 226, p.107139, 2021.
[22] G. Dhiman and M. Garg, MoSSE: “a novel hybrid multi-objective meta-heuristic algorithm for engineering design problems,” Soft Computing, 24(24), pp.18379-18398, 2020.
[23] S. Kukkonen and K. Deb, “A fast and effective method for pruning of non-dominated solutions in many-objective problems,” InParallel Problem Solving from Nature-PPSN IX;Berlin, Heidelberg, pp. 553-562, 2006.
[24] L. T. Bui and T. T. Nguyen, “A competitive co-evolutionary approach for the multi-objective evolutionary algorithms,” IEEE Access, 8, pp.56927-56947, 2020.
[25] Y. Tian, X. Zhang, R. Cheng, and Y. Jin, “A multi-objective evolutionary algorithm based on an enhanced inverted generational distance metric,” In2016 IEEE congress on evolutionary computation (CEC), pp. 5222-5229, 2016.
[26] S. Zapotecas-Martíne, A. López-Jaimes, and A. García-Nájera, “Libea: A lebesgue indicator-based evolutionary algorithm for multi-objective optimization,” Swarm and evolutionary computation, Vol. 44, pp. 404-19, 2019.
[27] N.T. Tam, T.H. Hung, and H.T.T. Binh, “a decomposition-based multi-objective optimization approach for balancing the energy consumption of wireless sensor networks,” Applied Soft Computing, 107, p.107365, 2021.
[28] W. Peng and Q. Zhang, “A decomposition-based multi-objective particle swarm optimization algorithm for continuous optimization problems,” In2008 IEEE international conference on granular computing, pp. 534-537, 2008.
[29] S.A.N. Alexandropoulos, C.K. Aridas, S.B. Kotsiantis, and M.N. Vrahatis, “Multi-objective evolutionary optimization algorithms for machine learning: A recent survey,” In Approximation and optimization (pp. 35-55). Springer, Cham, 2019.
[30] M. Li, S. Yang, and X. Liu, “Pareto or non-Pareto: Bi-criterion evolution in multiobjective optimization,” IEEE Transactions on Evolutionary Computation, Vol. 20(5), pp. 645-665, 2015.
[31] H. Kaur, A. Rai, S.S. Bhatia, and G. Dhiman, “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, p.104008, 2020.
[32] R. A. El Sehiemy, F. Selim, B. Bentouati, and M.A. Abido, “A novel multi-objective hybrid particle swarm and salp optimization algorithm for technical-economical-environmental operation in power systems,” Energy, 193, p.116817, 2020.
[33] K. Shang, H. Ishibuchi, L. He, and L.M. Pang, “A survey on the hypervolume indicator in evolutionary multiobjective optimization,” IEEE Transactions on Evolutionary Computation, 25(1), pp.1-20, 2020.
[34] J.G. Falcón-Cardona and C.A.C. Coello, “Indicator-based multi-objective evolutionary algorithms: A comprehensive survey,” ACM Computing Surveys (CSUR), 53(2), pp.1-35, 2020.
[35] X. Zhang, H. Liu, and L. Tu, “A modified particle swarm optimization for multimodal multi-objective optimization,” Engineering Applications of Artificial Intelligence, 95, p.103905, 2020.
[36] W. A. N. G. Na, S. U. Yuchao, C.H.E.N. Xiaohong, L.I. Xia, and L.I.U. Dui, “a∊-indicator-based shuffled frog leaping algorithm for many-objective optimization problems,” Journal of Systems Engineering and Electronics, 31(1), pp.142-155, 2020.
[37] C. Audet, J. Bigeon, D. Cartier, S. Le Digabel, and L. Salomon, “Performance indicators in multiobjective optimization,” European journal of operational research, 2020.
[38] G. Dhiman, K. K. Singh, M. Soni, A. Nagar, M. Dehghani, A. Slowik, A. Kaur, A. Sharma, E.H. Houssein, and K. Cengiz, “MOSOA: a new multi-objective seagull optimization algorithm,” Expert Systems with Applications, 167, p.114150, 2021.
[39] Q. Xu, Z. Xu, and T. Ma, “a survey of multiobjective evolutionary algorithms based on decomposition: Variants, challenges and future directions,” IEEE Access, 8, pp.41588-41614, 2020.
[40] X. Ma, Y. Yu, X. Li, Y. Qi, and Z. Zhu, “A survey of weight vector adjustment methods for decomposition-based multiobjective evolutionary algorithms,” IEEE Transactions on Evolutionary Computation, 24(4), pp.634-649, 2020.
[41] Y. Xie, J. Qiao, D. Wang, and B. Yin, “a novel decomposition-based multiobjective evolutionary algorithm using improved multiple adaptive dynamic selection strategies,” Information Sciences, 556, pp.472-494, 2021.
[42] Z. Liao, W. Gong, L. Wang, X. Yan, and C. Hu, “a decomposition-based differential evolution with reinitialization for nonlinear equations systems,” Knowledge-Based Systems, 191, p.105312, 2020.
[43] M. S. Nasrabadi, Y. Sharafi, and M. Tayari, “A parallel grey wolf optimizer combined with opposition-based learning,” In 2016 1st Conference on Swarm Intelligence and Evolutionary Computation (CSIEC) (pp. 18-23). IEEE, 2016.
[44] J. Shi, M. Gong, W. Ma, and L. Jiao, “A multi-population coevolutionary strategy for multi-objective immune algorithm,” The Scientific World Journal, 2014.
[45] V. Kumar and D. Kumar, “A systematic review on firefly algorithm: past, present, and future,” Archives of Computational Methods in Engineering, 28(4), pp.3269-3291, 2021.
[46] S. Mahdavi, S. Rahnamayan, and K. Deb, “Opposition based learning: A literature review,” Swarm and evolutionary computation, 39, pp.1-23, 2018.
[47] S. Lotfi, and F. Karimi, “A Hybrid MOEA/D-TS for solving multi-objective problems,” Journal of AI and Data Mining, 5(2), pp.183-195, 2017.
[48] H. Motameni, “PSO for multi-objective problems: Criteria for leader selection and uniformity distribution,” Journal of AI and Data Mining, 4(1), pp.67-76, 2016.
[49] N. Nekooghadirli, R. Tavakkoli-Moghaddam, and V.R. Ghezavati, “Efficiency of a multi-objective imperialist competitive algorithm: A bi-objective location-routing-inventory problem with probabilistic routes,” Journal of AI and Data Mining, 2(2), pp.105-112, 2014.
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