Abstract: In dealing with constrained many-objective optimization problems, a key issue of evolutionary algorithms is constraint handling and the tradeoffs between convergence anddiversity. However, the constraints in the search space hinder the population from finding the Pareto front, which tends to make the population fall into a local optimum, while the discrete feasible areas make the population less diverse. Therefore, a two-stage search strategywith the combined operator （TSCO） is proposed. TSCO deals with the constraints in two stages. Firstly, the algorithm only optimizes the objective function and the population is not constrained to approach the Pareto front direction rapidly. Secondly, the constraint violation degree is treated as a new objective function to solve the original constraint problem by objective transformation. A combined operator consisting of the simulated binary crossover operator and the DE/current-to-pbest/1 operator is used in the search process to generate individuals with excellent convergence and diversity. To verify the strategy effectiveness, AGE-MOEA combined with TSCO（TSCOEA） is compared with four state-of-the-art constrained many-objective evolutionary algorithms on the C_DTLZ, DC_DTLZ, and MW test suites. Experiments show that TSCOEA obtains better population convergence and diversity on most problems.

Key words: constrained many-objective optimization, evolutionary algorithm, two-stage search, combined operator, Minkowski distance

摘要： 解决约束超多目标优化问题的关键在于约束处理和均衡收敛性与多样性，搜索空间中的约束阻碍种群寻找Pareto前沿面，容易使种群陷入局部最优，而离散的可行域则使种群的多样性较差。提出组合算子型双阶段搜索策略（two-stagesearch strategy with combined operator，TSCO）。TSCO分两阶段处理约束：一阶段算法仅优化目标函数，种群不受约束制约快速向Pareto前沿面方向接近；二阶段通过目标转换将约束违反度视作一个新目标函数以解决原始约束问题。在搜索过程中使用模拟二进制交叉算子和DE/current-to-pbest/1算子构成的组合算子生成收敛性和多样性优秀的个体。为验证策略有效性，结合TSCO策略的AGE-MOEA（TSCOEA）在C_DTLZ、DC_DTLZ和MW测试集上同4种性能优异的约束超多目标进化算法进行对比。实验表明，在大多数问题上，TSCOEA获得的种群收敛性和多样性更好。

关键词: 约束超多目标优化, 进化算法, 双阶段搜索, 组合算子, Minkowski距离