Differential Evolution Algorithm Based on Coupling and Coordinating Population State Assessment
FENG Quanxi1,2, JIN Peiyuan1, CEN Jianmin1, AI Wu1,2, LIN Bin1,2
1. College of Science, Guilin University of Technology, Guilin 541004; 2. Guangxi Colleges and Universities Key Laboratory of Applied Statistics, Guilin University of Technology, Guilin 541004
Abstract：Differential evolution is a global stochastic search algorithm based on the differences between individuals within a population. The mutation operator is an important component of the differential evolution algorithm, and different mutation operators are suitable for different population distributions. To effectively identify the evolutionary state of the population, a differential evolution algorithm based on coupling and coordinating population state assessment(CCPDE) is proposed. The evolutionary state of the population in the iteration process is evaluated by calculating the coupling coordination degree between four different levels of fitness values and individual distances. The population is classified based on the evaluation results into three evolutionary states: search, balance and convergence, and corresponding mutation operator pools are constructed for different evolutionary states. In addition, the convergence speed of CCPDE is accelerated by adaptive adjustment of the Powell method. Numerical experiments on CEC2017 test functions show the effectiveness of CCPDE.
封全喜, 金培源, 岑健铭, 艾武, 林彬. 基于耦合协调种群状态评估的差分进化算法[J]. 模式识别与人工智能, 2023, 36(8): 733-748.
FENG Quanxi, JIN Peiyuan, CEN Jianmin, AI Wu, LIN Bin. Differential Evolution Algorithm Based on Coupling and Coordinating Population State Assessment. Pattern Recognition and Artificial Intelligence, 2023, 36(8): 733-748.
[1] STORN R, PRICE K. Differential Evolution-A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization, 1997, 11(4): 341-359. [2] YU X B, JIANG N J, WANG X M, et al. A Hybrid Algorithm Based on Grey Wolf Optimizer and Differential Evolution for UAV Path Planning. Expert Systems with Applications, 2023, 215. DOI: 10.1016/j.eswa.2022.119327. [3] GUO J J, GUAN Z G. Optimization of the Cable Forces of Completed Cable-Stayed Bridges with Differential Evolution Method. Structures, 2023, 47: 1416-1427. [4] GUO X F, YANG Q, ZHENG H R, et al. Optimization of Power Distribution for Electrothermal Anti-Icing Systems by Differential Evolution Algorithm. Applied Thermal Engineering, 2023, 221. DOI: 10.1016/j.applthermaleng.2022.119875. [5] 李爱军,王景,李佳,等.基于差分进化算法的飞行控制律评估.模式识别与人工智能, 2014, 27(3): 256-262. (LI A J, WANG J, LI J, et al. Clearance of Flight Control Law Based on Cultural Differential Evolution Algorithm. Pattern Recognition and Artificial Intelligence, 2014, 27(3): 256-262.) [6] 杜彦斌,周志杰,许磊,等.基于灰色关联分析与自适应混沌差分进化算法的激光熔覆工艺参数优化方法.计算机集成制造系统, 2022, 28(1): 149-160. (DU Y B, ZHOU Z J, XU L, et al. Laser Cladding Process Para-meter Optimization Method Based on Grey Relational Analysis and ACDE Algorithm. Computer Integrated Manufacturing Systems, 2022, 28(1): 149-160.) [7] QIN A K, HUANG V L, SUGANTHAN P N. Differential Evolution Algorithm with Strategy Adaptation for Global Numerical Optimization. IEEE Transactions on Evolutionary Computation, 2009, 13(2): 398-417. [8] LIU X F, ZHAN Z H, LIN Y, et al. Historical and Heuristic-Based Adaptive Differential Evolution. IEEE Transactions on Systems, Man, and Cybernetics(Systems), 2019, 49(12): 2623-2635. [9] PAN Q K, SUGANTHAN P N, WANG L, et al. A Differential Evolution Algorithm with Self-Adapting Strategy and Control Parameters. Computers and Operations Research, 2011, 38(1): 394-408. [10] WANG Y, CAI Z X, ZHANG Q F. Differential Evolution with Composite Trial Vector Generation Strategies and Control Parameters. IEEE Transactions on Evolutionary Computation, 2011, 15(1): 55-66. [11] WANG B C, LI H X, LI J P, et al. Composite Differential Evolution for Constrained Evolutionary Optimization. IEEE Transactions on Systems, Man, and Cybernetics(Systems), 2019, 49(7): 1482-1495. [12] WU G H, MALLIPEDDI R, SUGANTHAN P N, et al. Differential Evolution with Multi-population Based Ensemble of Mutation Stra-tegies. Information Sciences, 2016, 329: 329-345. [13] LIU Z Z, WANG Y, YANG S X, et al. Differential Evolution with a Two-Stage Optimization Mechanism for Numerical Optimization// Proc of the IEEE Congress on Evolutionary Computation. Wa-shington, USA: IEEE, 2016: 3170-3177. [14] ZHOU X G, ZHANG G J, HAO X H, et al. Differential Evolution with Multi-stage Strategies for Global Optimization// Proc of the IEEE Congress on Evolutionary Computation. Washington, USA: IEEE, 2016: 2550-2557. [15] ZHAN Z H, ZHANG J, LI Y, et al. Adaptive Particle Swarm Optimization. IEEE Transactions on Systems, Man, and Cybernetics (Cybernetics), 2009, 39(6): 1362-1381. [16] YU W J, SHEN M, CHEN W N, et al. Differential Evolution with Two-Level Parameter Adaptation. IEEE Transactions on Cyberne-tics, 2014, 44(7): 1080-1099. [17] ZHAN Z H, WANG Z J, JIN H, et al. Adaptive Distributed Differential Evolution. IEEE Transactions on Cybernetics, 2020, 50(11): 4633-4647. [18] LI Y, LI G H. Differential Evolutionary Algorithm with an Evolutionary State Estimation Method and a Two-Level Selection Mechanism. Soft Computing, 2020, 24(15): 11561-11581. [19] FENG Q X, LIU S Y, ZHANG J K, et al. Improved Biogeography-Based Optimization with Random Ring Topology and Powell's Method. Applied Mathematical Modelling, 2017, 41: 630-649. [20] ZHANG J Q, SANDERSON A C. JADE: Adaptive Differential Evolution with Optional External Archive. IEEE Transactions on Evolutionary Computation, 2009, 13(5): 945-958. [21] ZHENG L M, ZHANG S X, TANG K S, et al. Differential Evolution Powered by Collective Information. Information Sciences, 2017, 399: 13-29. [22] MORITA M, OCHIAI H, TAMURA K, et al. Multi-point Search Combinatorial Optimization Method Based on Neighborhood Search Using Evaluation of Big Valley Structure// Proc of the IEEE International Conference on Systems, Man, and Cybernetics. Washington, USA: IEEE, 2015: 2835-2840. [23] WOLPERT D H, MACREADY W G. No Free Lunch Theorems for Optimization. IEEE Transactions on Evolutionary Computation, 1997, 1(1): 67-82. [24] KEDEM O, CAPLAN S R. Degree of Coupling and Its Relation to Efficiency of Energy Conversion. Transactions of the Faraday Society, 1965, 61: 1897-1911. [25] CHENG M L, LI Q, WEN Z G. Coupling Coordination Degree Analysis and Driving Factors of Innovation Network and ECO-Efficiency in China. Environmental Impact Assessment Review, 2023, 99. DOI: 10.1016/j.eiar.2022.107008. [26] SONG M J, ZHAO Y, LIANG J, et al. Spatial-Temporal Variability of Carbon Emission and Sequestration and Coupling Coordination Degree in Beijing District Territory. Cleaner Environmental Systems, 2023, 8. DOI: 10.1016/j.cesys.2022.100102. [27] POWELL M J D. Restart Procedures for the Conjugate Gradient Method. Mathematical Programming, 1977, 12(1): 241-254. [28] AWAD N H, ALI M Z, SUGANTHAN P N, et al. Problem Definitions and Evaluation Criteria for the CEC 2017 Special Session and Competition on Single Objective Bound Constrained Real-Parameter Numerical Optimization. Technical Report. Singapore, Singapore: Nanyang Technological University, 2016. [29] MALLIPEDDI R, SUGANTHAN P N. Differential Evolution Algorithm with Ensemble of Parameters and Mutation and Crossover Strategies// Proc of the International Conference on Swarm, Evolutionary, and Memetic Computing. Berlin, Germany: Springer, 2010: 71-78. [30] XIA X W, GUI L, ZHANG Y L, et al. A Fitness-Based Adaptive Differential Evolution Algorithm. Information Sciences, 2021, 549: 116-141. [31] GAO S C, YU Y, WANG Y R, et al. Chaotic Local Search-Based Differential Evolution Algorithms for Optimization. IEEE Transactions on Systems, Man, and Cybernetics(Systems), 2021, 51(6): 3954-3967. [32] SALLAM K M, ELSAYED S M, CHAKRABORTTY R K, et al. Improved Multi-operator Differential Evolution Algorithm for Solving Unconstrained Problems// Proc of the IEEE Congress on Evolutionary Computation. Washington, USA: IEEE, 2020. DOI: 10.1109/CEC48606.2020.9185577. [33] SALGOTRA R, SINGH U, SAHA S, et al. Improving Cuckoo Search: Incorporating Changes for CEC 2017 and CEC 2020 Benchmark Problems// Proc of the IEEE Congress on Evolutionary Computation. Washington, USA: IEEE, 2020. DOI: 10.1109/CEC48606.2020.9185684. [34] TANGHERLONI A, RUNDO L, NOBILE M S. Proactive Particles in Swarm Optimization: A Settings-Free Algorithm for Real-Para-meter Single Objective Optimization Problems// Proc of the IEEE Congress on Evolutionary Computation. Washington, USA: IEEE, 2017. DOI: 10.1109/CEC.2017.7969538. [35] TALATAHARI S, AZIZI M. Chaos Game Optimization: A Novel Metaheuristic Algorithm. Artificial Intelligence Review, 2021, 54(2): 917-1004. [36] CAI Z H, GAO S C, YANG X, et al. Alternate Search Pattern-Based Brain Storm Optimization. Knowledge-Based Systems, 2022, 238. DOI: 10.1016/j.knosys.2021.107896. [37] HANSEN N, MÜLLER S D, KOUMOUTSAKOS P. Reducing the Time Complexity of the Derandomized Evolution Strategy with Covariance Matrix Adaptation(CMA-ES). Evolutionary Computation, 2003, 11(1): 1-18.
2023, Vol. 36 
