Abstract: In order to improve the convergence and diversity of many-objective evolutionary algorithms, a many-objective differential evolution algorithm using a relaxed dominance relation is proposed. In the proposed algorithm, a relaxed domination relation is designed and incorporated to increase the selection pressure of individuals. Population is coevolved with an external archive, and the child population is generated by the mixed differential mutation operators. The fitness of each individual is evaluated based on an indicator method, and the population is updated. The archive is updated according to the Lp norm （0<p<1） distance based diversity maintenance strategy. In order to validate the effectiveness of the proposed algorithm in many-objective optimization, experiments in a set of state-of-the-art benchmarks are carried out. Compared with two other classical algorithms, the proposed algorithm can generate a set of non-dominated solutions with better convergence and distribution in many-objective optimization problems.

Key words: many-objective optimization, differential evolution algorithm, relaxed dominance, co-evolutionary, mutation

摘要： 为了提高进化算法在求解高维多目标优化问题时的收敛性和多样性，提出了采用放松支配关系的高维多目标微分进化算法。该算法采用放松的Pareto支配关系，以增加个体的选择压力；采用群体和外部存储器协同进化的方案，并通过混合微分变异算子，生成子代群体；采用基于指标的方法计算个体的适应度并对群体进行更新；采用基于Lp范数（0<p<1）距离的多样性维护策略更新外部存储器。为了评估所提算法在高维多目标优化中的求解性能，将它在一组标准测试函数中进行了仿真实验。与其他两种经典算法的比较结果表明，所提算法能够在高维多目标优化问题中产生一组收敛性能和分布性能均较优的非支配解。

关键词: 高维多目标优化, 微分进化算法, 放松支配, 协同进化, 变异