基于新型双目标模型的约束优化进化算法

利用双目标模型求解约束优化问题时,由于它们的最优解集并不相等,因此需要增加特殊机制确保求解双目标问题的算法收敛到原问题的最优解.为克服这一缺点,本文首先将约束优化问题转化为新的双目标优化模型,并证明了新模型的最优解集与原问题的最优解集相等.其次,以简单的差分进化为搜索算法,基于多目标Pareto支配关系的非支配排序为选择准则,提出了求解新模型的差分进化算法.最后,用10个标准测试函数的数值试验说明了新模型及求解算法的有效性.

Novel bi-objective model-based evolutionary algorithm for constrained optimization problems

When applied to a constrained optimization problem (COP), the optimal solution set of the formulated bi- objective model is not the same as that of COP. Thus, extra mechanisms should be designed to ensure that the algorithms for bi-objective model converge to the optimal solution of COP. To overcome the drawback, a novel bi-objective model is proposed, and the optimal solution set of the novel model is shown to be the same as that of COP. Then, a simple differential evolution (DE) algorithm is presented for solving the novel bi-objective model, in which DE/rand/1/bin is employed as the search engine and Pareto dominance-based non-dominated sorting is used as the selection criterion. Numerical experiments for 10 standard test functions with different characteristics have been carried out, and the results show the effectiveness of the novel model and the proposed algorithm.