Proceedings of the
The Nineteenth International Conference on Computational Intelligence and Security (CIS 2023)
December 1 – 4, 2023, Haikou, China
Multi-Stage Co-Evolutionary Differential Evolution for Solving Constrained Optimization Problems
School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai, China.
ABSTRACT
Solving constrained optimization problems (COPs) is very difficult. Because the objective functions and constraints need to be simultaneously considered, especially when the extremely complex constraints are involved. Combining evolutionary algorithm with multi-stage evolutionary strategy is an effective way to solve COPs. In view of this consideration, we propose a multi-stage co-evolutionary differential evolution (MSCODE) to efficiently solve the COPs. In our method, constraints are considered separately and only one constraint is optimized in each stage. All of first, constraints are dealt with one by one in multiple stages, but solved as a whole at the later stages. This not only reduces the computational complexity but also makes populations easily converge to potential feasible region. In addition, the population is divided into two sub-populations. Based on the co-evolutionary framework, the interaction information between the sub-populations is utilized to help the population through infeasible region. Finally, MSCODE is tested on 18 benchmark problems in the CEC2010 test suite. The experimental results show that MSCODE performs better in dealing with complex COPs. The results of Friedman's test and Wilcoxons test also verify the effectiveness of the algorithm.
Keywords: Constrained optimization problem, Multi-stage, Co-evolutionary method, Differential evolution.
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School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai, China.
ABSTRACT
Solving constrained optimization problems (COPs) is very difficult. Because the objective functions and constraints need to be simultaneously considered, especially when the extremely complex constraints are involved. Combining evolutionary algorithm with multi-stage evolutionary strategy is an effective way to solve COPs. In view of this consideration, we propose a multi-stage co-evolutionary differential evolution (MSCODE) to efficiently solve the COPs. In our method, constraints are considered separately and only one constraint is optimized in each stage. All of first, constraints are dealt with one by one in multiple stages, but solved as a whole at the later stages. This not only reduces the computational complexity but also makes populations easily converge to potential feasible region. In addition, the population is divided into two sub-populations. Based on the co-evolutionary framework, the interaction information between the sub-populations is utilized to help the population through infeasible region. Finally, MSCODE is tested on 18 benchmark problems in the CEC2010 test suite. The experimental results show that MSCODE performs better in dealing with complex COPs. The results of Friedman's test and Wilcoxons test also verify the effectiveness of the algorithm.
Keywords: Constrained optimization problem, Multi-stage, Co-evolutionary method, Differential evolution.
Download PDF