求解约束优化问题的引导多目标差分进化算法

Guiding multi-objective differential evolution algorithm for constrained optimization

将约束优化问题转化为带偏好的双目标优化问题,用差分进化算法求解转化问题。为了克服基于Pareto支配关系的多目标算法求解转化问题时没有考虑问题偏好、收敛慢等缺点,借助多目标α-支配关系的特点,提出了基于动态α-支配的新适应度函数。新适应度函数根据种群中可行解的比例动态平衡进化过程中对两个目标的偏好,引导算法不断向问题的偏好区域靠近,从而快速收敛到约束优化问题的最优解。对6个标准测试函数的数值实验结果表明:基于α-支配的动态引导多目标差分进化算法能快速收敛到问题的最优解。与3种经典高效算法的比较说明,所提出算法的鲁棒性强且效率高。

In this paper,the Constrained Optimization Problem（COP）is converted into a bi-objective optimization problem with preference.Then the problem is solved with a Guiding Multi-objective Differential Evolution（GMODE）algorithm.The other methods based on Pareto dominance treat both objectives as equal importance without bias to either objective.In contrast,the proposed GMODE algorithm is guided byα-domination to search with dynamic bias to different objectives,which overcomes the drawback of the methods based on Pareto dominance and improves the convergence speed of the algorithm.Numerical experiments on several well-known benchmark functions and comparison with the other three state-of-the-art methods demonstrate that the GMODE algorithm is competitive with,in some cases superior to the other methods in terms of the quality,efficiency and robustness.