|
|
|
| Constrained Differential Evolution Algorithm with Dynamic Elite Learning |
| ZHOU Xinyu1,2, JIANG Jinfeng1, GAO Weifeng3, WANG Hui4, PENG Hu5 |
1. School of Artificial Intelligence, Jiangxi Normal University, Nanchang 330022;
2. Key Laboratory of Intelligent Information Processing and Emotional Computing in Jiangxi Province, Jiangxi Normal University, Nanchang 330022;
3. School of Mathematics and Statistics, Xidian University, Xi'an 710071;
4. School of Information Engineering, Jiangxi University of Water Resources and Electric Power, Nanchang 330099;
5. School of Computer and Big Data Science, Jiujiang University, Jiujiang 332005 |
|
|
|
|
Abstract Constrained differential evolution(CDE) algorithm is an effective way to solve constrained optimization problems. However, the existing research mainly focuses on constraint handling techniques, while the differential evolution algorithm itself is neglected, resulting in some problems, including unbalanced exploration and exploitation capabilities, and a low survival rate of offspring individuals of feasible solutions. To address these issues, a dynamic elite learning strategy is designed to improve the performance of the CDE algorithm. In this strategy, the individuals in the population are divided into ordinary feasible solutions, elite feasible solutions and infeasible solutions, and individualized mutation operators are adopted for each of these three types of individuals to balance the exploration and exploitation capabilities. Meanwhile, the elite feasible solutions are introduced to improve the classical mutation operators, thereby increasing the survival rate of offspring of feasible solutions. According to the characteristics of infeasible solutions, a fine-tuned feasibility rule is also designed as a constraint handling technique to better guide the population into the feasible region. Experiments on CEC2006, CEC2010 and CEC2017 test sets as well as three real-world engineering optimization problems demonstrate that the proposed algorithm achieves superior performance compared with six state-of-art constrained optimization evolutionary algorithms.
|
|
Received: 20 August 2025
|
|
|
| Fund:National Natural Science Foundation of China(No.62366022,62276202,62166027,62266024), Natural Science Foundation of Jiangxi Province(No.20232BAB202048), Outstan- ding Youth Foundation of Natural Science Foundation of Jiangxi Province(No.20212ACB212004) |
|
Corresponding Authors:
PENG Hu, Ph.D., professor. His research interests include evolutionary computation and its applications.
|
About author:: ZHOU Xinyu, Ph.D., associate profe-ssor. His research interests include intelligent computation.
JIANG Jinfeng, Master. His research interests include constrained evolutionary optimization.
GAO Weifeng, Ph.D., professor. His research interests include intelligent computation and deep learning.
WANG Hui, Ph.D., professor. His research interests include intelligent computation. |
|
|
|
[1] MA Y H, SHEN B, PAN A Q.Constrained Evolutionary Optimization Based on Dynamic Knowledge Transfer. Expert Systems with Applications, 2024, 240. DOI: 10.1016/j.eswa.2023.122450.
[2] LIU H, CAI Z X, WANG Y.Hybridizing Particle Swarm Optimization with Differential Evolution for Constrained Numerical and Engi-neering Optimization. Applied Soft Computing, 2010, 10(2): 629-640.
[3] QIAO K J, LIANG J, YU K J, et al. Self-Adaptive Resources Allocation-Based Differential Evolution for Constrained Evolutionary Optimization. Knowledge-Based Systems, 2022, 235. DOI: 10.1016/j.knosys.2021.107653.
[4] CUI C G, YANG X F, GAO T Y.A Self-Adaptive Interior Penalty Based Differential Evolution Algorithm for Constrained Optimization// Proc of the 5th International Conference on Advances in Swarm Intelligence. Berlin, Germany: Springer, 2014: 309-318.
[5] GAO W F, YEN G G, LIU S Y.A Dual-Population Differential Evolution with Coevolution for Constrained Optimization. IEEE Transactions on Cybernetics, 2015, 45(5): 1108-1121.
[6] LI K S, ZUO L, LI W, et al. A Novel Differential Evolution Algorithm Based on JADE for Constrained Optimization// Proc of the 7th International Symposium on Computational Intelligence and Intelligent Systems. Berlin, Germany: Springer, 2016: 84-94.
[7] ZHANG J Q, SANDERSON A C.JADE: Adaptive Differential Evolution with Optional External Archive. IEEE Transactions on Evolutionary Computation, 2009, 13(5): 945-958.
[8] GONG W Y, CAI Z H, LIANG D W.Adaptive Ranking Mutation Operator Based Differential Evolution for Constrained Optimization. IEEE Transactions on Cybernetics, 2015, 45(4): 716-727.
[9] HAMZA N M, ESSAM D L, SARKER R A.Constraint Consensus Mutation-Based Differential Evolution for Constrained Optimization. IEEE Transactions on Evolutionary Computation, 2016, 20(3): 447-459.
[10] YU X B, LI C L, ZHOU J F.A Constrained Differential Evolution Algorithm to Solve UAV Path Planning in Disaster Scenarios. Knowledge-Based Systems, 2020, 204. DOI: 10.1016/j.knosys.2020.106209.
[11] WANG Y, WANG B C, LI H X, et al. Incorporating Objective Function Information into the Feasibility Rule for Constrained Evolutionary Optimization. IEEE Transactions on Cybernetics, 2016, 46(12): 2938-2952.
[12] WANG B C, LI H X, ZHANG Q F, et al. Decomposition-Based Multiobjective Optimization for Constrained Evolutionary Optimization. IEEE Transactions on Systems, Man, and Cybernetics(Systems), 2021, 51(1): 574-587.
[13] LI Y C, GONG W Y, HU Z Z, et al. A Competitive and Cooperative Evolutionary Framework for Ensemble of Constraint Handling Techniques. IEEE Transactions on Systems, Man, and Cybernetics(Systems), 2024, 54(4): 2440-2451.
[14] 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.
[15] WANG Y, CAI Z X, ZHANG Q F.Differential Evolution with Composite Trial Vector Generation Strategies and Control Parame-ters. IEEE Transactions on Evolutionary Computation, 2011, 15(1): 55-66.
[16] DANG Q L.Multiple Dynamic Penalties Based on Decomposition for Constrained Optimization. Expert Systems with Applications, 2022, 206. DOI: 10.1016/j.eswa.2022.117820.
[17] YUAN Y F, GAO W F, HUANG L L, et al. A Two-Phase Constraint-Handling Technique for Constrained Optimization. IEEE Transactions on Systems, Man, and Cybernetics(Systems), 2023, 53(10): 6194-6203.
[18] HUANG H, XU Y T, XIANG Y, et al. Correlation-Based Dyna-mic Allocation Scheme of Fitness Evaluations for Constrained Evolutionary Optimization. IEEE Transactions on Evolutionary Computation, 2024, 28(5): 1250-1264.
[19] LI J Q, LI G H, WANG Z K, et al. Differential Evolution with an Adaptive Penalty Coefficient Mechanism and a Search History Exploitation Mechanism. Expert Systems with Applications, 2023, 230. DOI: 10.1016/j.eswa.2023.120530.
[20] HU Z Z, GONG W Y, PEDRYCZ W, et al. Deep Reinforcement Learning Assisted Co-evolutionary Differential Evolution for Con-strained Optimization. Swarm and Evolutionary Computation, 2023, 83. DOI: 10.1016/j.swevo.2023.101387.
[21] WANG B C, FENG Y, LI H X.Individual-Dependent Feasibility Rule for Constrained Differential Evolution. Information Sciences, 2020, 506: 174-195
[22] LIANG J, RUNARSSON T P, MEZURA-MONTES E, et al. Pro-blem Definitions and Evaluation Criteria for the CEC 2006 Special Session on Constrained Real-Parameter Optimization. Technical Report. Singapore, Singapore: Nanyang Technological University, 2006.
[23] MALLIPEDDI R, SUGANTHAN P N. Problem Definitions and Eva-luation Criteria for the CEC 2010 Competition on Constrained Real-Parameter Optimization. Technical Report. Singapore, CEC 2010 Competition on Constrained Real-Parameter Optimization. Technical Report. Singapore, Singapore: Nanyang Technological University, 2010.
[24] WU G H, MALLIPEDDI R, SUGANTHAN P N.Problem Definitions and Evaluation Criteria for the CEC 2017 Competition on Constrained Real-Parameter Optimization. Technical Report. Changsha, China: National University of Defense Technology, 2017.
[25] POLAKOVA R.L-SHADE with Competing Strategies Applied to Con-strained Optimization// Proc of the IEEE Congress on Evolutionary Computation. Washington, USA: IEEE, 2017: 1683-1689
[26] HUANG F Z, WANG L, HE Q.An Effective Co-evolutionary Di-fferential Evolution for Constrained Optimization. Applied Mathematics and Computation, 2007, 186(1): 340-356 |
|
|
|
2025, Vol. 38 
