摘要： 约束多目标优化(CMOP)问题的求解旨在将有限的搜索资源合理地配置到约束条件的满足与目标函数的优化2个方面,但问题约束的日趋复杂给求解算法带来了巨大挑战。提出一种基于协同演化的自适应约束多目标进化算法,该算法同时进化2个功能互补的种群(主种群和存档种群),使算法在求解复杂约束问题时能够实现约束处理与目标优化之间的良好平衡。首先,主种群进行双重繁殖,首次繁殖过程通过动态适应度分配函数自适应地利用不可行解所携带的有价值信息,使种群在进化前期强调对目标函数的优化,后期强调可行性,二次繁殖则与存档种群进行合作,以提高种群收敛性并维护多样性。然后,提出一种基于角度的选择方案更新存档种群,在保证种群良好多样性的同时保持种群向Pareto前沿的搜索压力。最后,与5种先进的约束多目标进化算法在33个基准问题上进行对比实验,结果表明,所提出的算法在解决各类CMOP问题时与对比算法相比更具优势,其效率平均提高了约67%。

关键词: 协同演化算法, 约束多目标优化, 双重繁殖, 动态适应度分配函数, 不可行解

Abstract: The solution of Constrained Multi-Objective Optimization(CMOP) problems aims to reasonably allocate limited search resources to satisfy constraints and optimize the objective functions. However, the increasing complexity of the problem constraints has led to significant challenges to the solution algorithm. To address this challenge, this study proposes an adaptive constrained multi-objective evolutionary algorithm based on co-evolutionary, named ACMCA. The algorithm simultaneously evolves two populations(the main population and the archive population) with complementary functions to achieve a good balance between constraint processing and objective optimization when addressing complex constraint problems. First, the main population performs a dual reproduction. In the first reproduction process, the valuable information carried by the infeasible solution is adaptively used through the dynamic fitness distribution function such that the population emphasizes the optimization of the objective function in the early stage of evolution and feasibility in the later stage. The second reproduction cooperates with the archived population to improve the convergence and maintain diversity. Subsequently, an angle-based selection scheme is proposed to update the archived population, which ensures satisfactory population diversity while maintaining the search pressure on the Pareto Front(PF). Finally, the algorithm conducts comparison experiments with five advanced Constrained Multi-Objective Evolutionary Algorithms(CMOEAs) on 33 benchmark problems. The test results demonstrate that the proposed algorithm is more advantageous than the comparison algorithms in handling various types of CMOP problems, and its efficiency is improved by an average of about 67%.

Key words: co-evolutionary algorithm, Constrained Multi-Objective Optimization(CMOP), dual reproduction, dynamic fitness distribution function, infeasible solutions

中图分类号: 

• TP301.6