Abstract: Dynamic multi-objective constrained optimization problem is a kind of NP-hard problem. The rank and the scalar constraint violation of the individual for evolution population under the dynamic environments are defined. Based on the two definitions, a new selection operator is presented. Based on an environment changing operator, a new dynamic constrained multi-objective optimization evolutionary algorithm, which is used to solve a class of constrained dynamic multi-objective optimization problems in which the environment variable is defined on the positive integer set, is given. The proposed algorithm has been tested on two constrained dynamic multi-objective optimization benchmark problems. The results obtained have been compared with the other algorithm. Simulations demonstrate the new algorithm can obtain good quality and uniformed distribution solution set in different environments for constrained dynamic multi-objective optimization problems.

Key words: constrained dynamic multi-objective optimization, evolutionary algorithm, environment changing, Pareto convergence

摘要： 动态多目标约束优化问题是一类NP-Hard问题，定义了动态环境下进化种群中个体的序值和个体的约束度，结合这两个定义给出了一种选择算子。在一种环境变化判断算子下给出了求解环境变量取值于正整数集[?+]的一类带约束动态多目标优化问题的进化算法。通过几个典型的Benchmark函数对算法的性能进行了测试，其结果表明新算法能够较好地求出带约束动态多目标优化问题在不同环境下质量较好、分布较均匀的Pareto最优解集。

关键词: 约束动态多目标优化, 进化算法, 环境变化, Pareto最优解