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PC-SSRD: a paradigm crossover-based differential evolution algorithm with search space reduction. (English) Zbl 07897609

Summary: The optimization of complex problems has always been a difficult task in the realm of evolutionary computation, as complex problems often have a large search space. Adding more dimensions to the decision variables also makes the search space more complicated, which slows down the algorithm. However, as the number of locally optimal solutions to the complex problem grows exponentially, it becomes easy for the algorithm to land in a local optimal region. In light of this background, this paper proposes a paradigm-crossover-based differential evolution algorithm with search space reduction and diversity exploration. During the evolution process, the proposed algorithm obtains the correlation coefficient for each dimension of the problem. Based on this correlation, it generates a paradigm that participates in crossover, accelerating the population’s movement towards promising regions. When the algorithm faces premature convergence and stagnation, it executes search space reduction and diversity exploration at the dimensional level to discard the unpromising search space and enhance the population diversity in the promising search space. We compared our proposed algorithm with eight state-of-the-art evolutionary algorithms in the CEC2017-BC test set to confirm its effectiveness, and the experimental results demonstrated its notable advantages for solution accuracy and convergence speed on high-dimensional complex problems.

MSC:

90Cxx Mathematical programming
Full Text: DOI

References:

[1] Gong, Y.-J., Distributed evolutionary algorithms and their models: A survey of the state-of-the-art, Appl. Soft Comput., 34, 286-300, 2015
[2] Katoch, S.; Chauhan, S. S.; Kumar, V., A review on genetic algorithm: past, present, and future, Multimed. Tools Appl., 80, 8091-8126, 2021
[3] Fogel, D. B., An introduction to simulated evolutionary optimization, IEEE Trans. Neural Netw., 5, 1, 3-14, 1994
[4] Storn, R.; Price, K., Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces, J. Glob. Optim., 11, 4, 341-359, 1997 · Zbl 0888.90135
[5] Pant, M., Differential Evolution: A review of more than two decades of research, Eng. Appl. Artif. Intellig., 90, Article 103479 pp., 2020
[6] Ahmad, M. F.; Isa, N. A.M.; Lim, W. H., Differential evolution: A recent review based on state-of-the-art works, Alex. Eng. J., 61, 5, 3831-3872, 2022
[7] Mohamed, A. W.; Mohamed, A. K., Adaptive guided differential evolution algorithm with novel mutation for numerical optimization, Int. J. Mach. Learn. Cybern., 10, 253-277, 2019
[8] Huang, Y. L.; Li, W., A differential evolution algorithm with ternary search tree for solving the three-dimensional packing problem, Inf. Sci., 606, 440-452, 2022
[9] Jebaraj, L., Application of differential evolution algorithm in static and dynamic economic or emission dispatch problem: A review, Renew. Sustain. Energy Rev., 77, 1206-1220, 2017
[10] Su, J.; Wang, H., An improved adaptive differential evolution algorithm for single unmanned aerial vehicle multitasking, Defence Technology, 17, 6, 1967-1975, 2021
[11] Nguyen, T. T.; Vu Quynh, N.; Duong, M. Q., Modified differential evolution algorithm: A novel approach to optimize the operation of hydrothermal power systems while considering the different constraints and valve point loading effect, Energies, 11, 3, 540, 2018
[12] Rajesh, C.; Kumar, S., An evolutionary block based network for medical image denoising using Differential Evolution, Appl. Soft Comput., 121, Article 108776 pp., 2022
[13] Li, H.; Wang, X.; Peng, J., A hybrid differential evolution algorithm for flexible job shop scheduling with outsourcing operations and job priority constraints, Expert Syst. Appl., 201, Article 117182 pp., 2022
[14] Gao, Z.; Zhang, M.; Zhang, L., Ship-unloading scheduling optimization with differential evolution, Inf. Sci., 591, 88-102, 2022
[15] Sallam, K. M.; Chakrabortty, R. K.; Ryan, M. J., A two-stage multi-operator differential evolution algorithm for solving resource constrained project scheduling problems, Futur. Gener. Comput. Syst., 108, 432-444, 2020
[16] Lobato, F. S.; Machado, V. S.; Steffen, V., Determination of an optimal control strategy for drug administration in tumor treatment using multi-objective optimization differential evolution, Comput. Methods Programs Biomed., 131, 51-61, 2016
[17] Dumka, A. V.D.; Loganathan, J., Data dissemination for green-VANETs communication: an opportunistic optimization approach, International Journal of Pervasive Computing and Communications, 17, 1, 89-108, 2021
[18] Ali, I. M.; Essam, D.; Kasmarik, K., A novel design of differential evolution for solving discrete traveling salesman problems, Swarm Evol. Comput., 52, Article 100607 pp., 2020
[19] Zeng, Z.; Zhang, M.; Chen, T., A new selection operator for differential evolution algorithm, Knowl.-Based Syst., 226, Article 107150 pp., 2021
[20] Li, A. D.; Xue, B.; Zhang, M., Improved binary particle swarm optimization for feature selection with new initialization and search space reduction strategies, Appl. Soft Comput., 106, Article 107302 pp., 2021
[21] da Silva E F, Rahmani M, Rider M J, A Search Space Reduction Strategy and a Mathematical Model for Multistage Transmission Expansion Planning with N-1 Security Constrains, Journal of Control, Automation and Electrical Systems, 26(1)(2015)57-67.
[22] Bidgoli, A. A.; Rahnamayan, S., A collective intelligence strategy for enhancing population-based optimization algorithms, (2020 IEEE Congress on Evolutionary Computation (CEC), 2020), 1-9
[23] Li Ming Zheng, Sheng Xin Zhang, Differential evolution powered by collective information, Information Sciences 399 (2017) 13-29.
[24] Yang, Q.; Yan, J. Q.; Gao, X. D., Random neighbor elite guided differential evolution for global numerical optimization, Inf. Sci., 607, 1408-1438, 2022
[25] Gupta, S.; Su, R., An efficient differential evolution with fitness-based dynamic mutation strategy and control parameters, Knowl.-Based Syst., 251, Article 109280 pp., 2022
[26] Zou, L.; Pan, Z.; Gao, Z., Improving the search accuracy of differential evolution by using the number of consecutive unsuccessful updates, Knowl.-Based Syst., 250, Article 109005 pp., 2022
[27] Lampinen, J.; Zelinka, I., On stagnation of the differential evolution algorithm, Proceedings of MENDEL, 76-83, 2000
[28] Yang, Q.; Yuan, S.; Gao, H., Differential evolution with migration mechanism and information reutilization for global optimization, Expert Syst. Appl., 238, Article 122076 pp., 2024
[29] Tian, M.; Gao, X., Differential evolution with neighborhood-based adaptive evolution mechanism for numerical optimization, Inf. Sci., 478, 422-448, 2019
[30] Prabha, S.; Yadav, R., Differential evolution with biological-based mutation operator, Eng. Sci. Technol. Int. J., 23, 2, 253-263, 2020
[31] Li, C., A population state evaluation-based improvement framework for differential evolution, Inf. Sci., 629, 15-38, 2023
[32] Deng, L.-B.; Li, C.-L., An adaptive dimension level adjustment framework for differential evolution, Knowl.-Based Syst., 206, Article 106388 pp., 2020
[33] Sun, G.; Li, C.; Deng, L., An adaptive regeneration framework based on search space adjustment for differential evolution, Neural Comput. Appl., 33, 9503-9519, 2021
[34] Opara, K. R.; Arabas, J., Differential Evolution, A survey of theoretical analyses, Swarm, Evol. Comput., 44, 546-558, 2019
[35] Yang, M.; Li, C.; Cai, Z.; Guan, J., Differential evolution with auto-enhanced population diversity, IEEE Trans. Cybern., 45, 2, 302-315, 2015
[36] J. Guan, Differential evolution with a dimensional mutation strategy for global optimization, in: 2016 IEEE Congress on Evolutionary Computation (CEC)(2016)2799-2804.
[37] Qiao, K.; Liang, J.; Qu, B., Differential evolution with level-based learning mechanism, Complex System Modeling and Simulation, 2, 1, 35-58, 2022
[38] Yi, W.; Chen, Y.; Pei, Z., Adaptive differential evolution with ensembling operators for continuous optimization problems, Swarm Evol. Comput., 69, Article 100994 pp., 2022
[39] Cheng, J.; Pan, Z., Differential evolution algorithm with fitness and diversity ranking-based mutation operator, Swarm Evol. Comput., 61, Article 100816 pp., 2021
[40] Tang, L.; Dong, Y.; Liu, J., Differential evolution with an individual-dependent mechanism, IEEE Trans. Evol. Comput., 19, 560-574, 2014
[41] Meng, Z.; Yang, C., Two-stage differential evolution with novel parameter control, Inf. Sci., 596, 321-342, 2022 · Zbl 1533.92150
[42] Tanabe R, Fukunaga A S. Improving the search performance of SHADE using linear population size reduction[C]//2014 IEEE congress on evolutionary computation (CEC). IEEE, 2014: 1658-1665.
[43] Zhang, J.; Sanderson, A. C., JADE: adaptive differential evolution with optional external archive, IEEE Trans. Evol. Comput., 13, 5, 945-958, 2009
[44] Tanabe R, Fukunaga A. Success-history based parameter adaptation for differential evolution[C]//2013 IEEE congress on evolutionary computation. IEEE, 2013: 71-78.
[45] Maharana D, Kommadath R, Kotecha P. Dynamic Yin-Yang Pair Optimization and its performance on single objective real parameter problems of CEC 2017[C]//2017 IEEE Congress on Evolutionary Computation (CEC). IEEE, 2017: 2390-2396.
[46] Awad N H, Ali M Z, Suganthan P N. Ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood for solving CEC2017 benchmark problems[C]//2017 IEEE congress on evolutionary computation (CEC). IEEE, 2017: 372-379.
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