Abstract
The present paper proposes a new algorithm designed for solving optimization problems. This algorithm is a hybrid of Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms. The proposed algorithm uses a coalition or cooperation model in the game theory to combine the DE and PSO algorithms. This is done in an attempt to keep a balance between the exploration and exploitation capabilities by preventing population stagnation and avoiding the local optimum. The DE and PSO algorithms are two players in the state space, which play cooperative games together using the Nash bargaining theory to find the best solution. To evaluate the performance of the proposed algorithm, 25 benchmark functions are used in terms of the CEC2005 structure. The proposed algorithm is then compared with the classical DE and PSO algorithms and the hybrid algorithms recently proposed. The results indicated that the proposed hybrid algorithm outperformed the classical algorithms and other hybrid models.
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Pham Q-V, Mirjalili S, Kumar N, Alazab M, Hwang W-J (2020) Whale optimization algorithm with applications to resource allocation in wireless networks. IEEE Trans Veh Technol 69(4):4285–4297
Mapetu JPB, Chen Z, Kong L (2019) Low-time complexity and low-cost binary particle swarm optimization algorithm for task scheduling and load balancing in cloud computing. Appl Intell 49(9):3308–3330
Song C, Xu Z, Zhang Y, Wang X (2020) Dynamic hesitant fuzzy Bayesian network and its application in the optimal investment port decision making problem of “twenty-first century maritime silk road”. Applied Intelligence:1–13
Meng X, Liu Y, Gao X, Zhang H A new bio-inspired algorithm: chicken swarm optimization. In: International conference in swarm intelligence, 2014. Springer, pp 86–94
Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Pan W-T (2012) A new fruit fly optimization algorithm: taking the financial distress model as an example. Knowl-Based Syst 26:69–74
Chu S-C, Tsai P-W, Pan J-S (2006) Cat swarm optimization. Pacific rim international conference on artificial intelligence springer pp 854-858
Meng X-B, Gao XZ, Lu L, Liu Y, Zhang H (2016) A new bio-inspired optimisation algorithm: bird swarm algorithm. Journal of Experimental & Theoretical Artificial Intelligence 28(4):673–687
Yang X-S (2010) A new metaheuristic bat-inspired algorithm. Nature inspired cooperative strategies for optimization (NICSO 2010) springer pp 65-74
Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Askarzadeh A (2016) A novel metaheuristic method for solving constrained engineering optimization problems: crow search algorithm. Comput Struct 169:1–12
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. MHS ' 95. Proceedings of the sixth international symposium on micro machine and human science IEEE: 39-43
Yu X, Cao J, Shan H, Zhu L, Guo J (2014) An adaptive hybrid algorithm based on particle swarm optimization and differential evolution for global optimization The Scientific World Journal 2014
Mao B, Xie Z, Wang Y, Handroos H, Wu H (2018) A hybrid strategy of differential evolution and modified particle swarm optimization for numerical solution of a parallel manipulator Mathematical Problems in Engineering 2018
Abbas Q, Ahmad J, Jabeen H (2017) OPSODE: opposition based particle swarm optimization instilled with differential evolution. International journal of advanced and applied sciences 4(7):50–58
Price K, Storn RM, Lampinen JA (2006) Differential evolution: a practical approach to global optimization. Springer Science & Business Media
Thangaraj R, Pant M, Abraham A, Bouvry P (2011) Particle swarm optimization: hybridization perspectives and experimental illustrations. Appl Math Comput 217(12):5208–5226
Lin G-H, Zhang J, Liu Z-H (2018) Hybrid particle swarm optimization with differential evolution for numerical and engineering optimization. Int J Autom Comput 15(1):103–114
Myerson RB (2013) Game theory. Harvard university press
Lin M, Wang Z, Wang F (2019) Hybrid Differential Evolution and Particle Swarm Optimization Algorithm Based on Random Inertia Weight. 2019 34rd Youth Academic Annual Conference of Chinese Association of Automation (YAC) IEEE:411–414
Wang H, Zuo L, Yang X (2019) A novel PSOEDE algorithm for vehicle scheduling problem in public transportation. International conference on swarm intelligence springer: 148-155
Wang S, Li Y, Yang H (2019) Self-adaptive mutation differential evolution algorithm based on particle swarm optimization. Appl Soft Comput 81:105496
Fan D, Lee J (2019) A hybrid mechanism of particle swarm optimization and differential evolution algorithms based on spark
Liu H, Zhang X, Tu L (2020) A modified particle swarm optimization using adaptive strategy. Expert systems with applications:113353
Wang H, Zuo L, Liu J, Yi W, Niu B (2018) Ensemble particle swarm optimization and differential evolution with alternative mutation method. Nat Comput:1–14
Tang B, Xiang K, Pang M (2018) An integrated particle swarm optimization approach hybridizing a new self-adaptive particle swarm optimization with a modified differential evolution. Neural Computing and Applications:1–35
Chen Y, Li L, Peng H, Xiao J, Yang Y, Shi Y (2017) Particle swarm optimizer with two differential mutation. Appl Soft Comput 61:314–330
Du S-Y, Liu Z-G (2020) Hybridizing particle swarm optimization with JADE for continuous optimization. Multimedia Tools and Application 79(7):4619–4636
Shi Y, Eberhart RC (1999) Empirical study of particle swarm optimization. Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406) IEEE:1945–1950
Zhan Z-H, Zhang J, Li Y, Chung HS-H (2009) Adaptive particle swarm optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 39(6):1362–1381
Abdoli GH (2007) Game theory and its applications (incomplete information, evolutionary and cooperative games). The organization for researching and composing university textbooks in the humanities
Suganthan PN, Hansen N, Liang JJ, Deb K, Chen Y-P, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. KanGAL report 2005005:2005
Clerc M, Kennedy J (2002) The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans Evol Comput 6(1):58–73
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Dadvar, M., Navidi, H., Javadi, H.H.S. et al. A cooperative approach for combining particle swarm optimization and differential evolution algorithms to solve single-objective optimization problems. Appl Intell 52, 4089–4108 (2022). https://doi.org/10.1007/s10489-021-02605-x
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DOI: https://doi.org/10.1007/s10489-021-02605-x