Abstract:

For Multi-objective Optimization Problem （MOP）， the goal is to obtain a well-distributed set of Pareto optimal solutions. When the variables are constrained， the Pareto solutions are typically located in different feasible regions. For large-scale and tightly constrained optimization problems， the existing evolutionary algorithms have difficulty in balancing diversity and convergence of individuals， resulting in the search population may not being able to cross multiple infeasible regions and then converging prematurely. To address this issue， an effective Information-guided Adaptive Constrained Multi-objective Evolutionary Algorithm （IACMEA） was proposed. First， a co-evolutionary mode of main and auxiliary populations was adopted： the main population mainly searched within the feasible regions and converged to the Pareto fronts， and the auxiliary population retained infeasible solutions with small objective function values through environmental selection based on the constraint threshold， thereby maintaining population diversity. Second， to improve the quality of individuals in the populations， a mating pool selection strategy was designed on the basis of the feasible solution ratio. Experimental results on the CF， LIRCMOP， and DASCMOP benchmark test sets show that， comparing IACMEA with six similar algorithms including CCMO （Coevolutionary Constrained Multi-objective Optimization framework）， IACMEA achieves 23 best Inverted Generational Distance （IGD） values and 22 best HyperVolume （HV） values out of 33 problems. It can be observed that IACMEA demonstrates certain advantages in handling nonlinear Constrained Multi-objective Optimization Problems （CMOPs）.

Key words: Multi-objective Optimization Problem (MOP), evolutionary algorithm, constraint, selection strategy, optimal solution

摘要：

多目标优化问题（MOP）旨在找到一组均匀分布的Pareto最优解。当问题存在约束限制时，Pareto最优解集往往分散在不同的可行区域。对于大规模紧约束优化问题，现有进化算法很难兼顾个体的多样性和收敛性，导致搜索种群可能无法跨越多个不可行区域而早熟收敛。针对该问题，提出一种有效信息引导的自适应约束多目标进化算法（IACMEA）。首先，采取主种群和辅助种群协同进化模式，主种群主要在可行区域进行搜索并且收敛到Pareto前沿，而辅助种群通过基于约束阈值的环境选择，保留目标函数值小的不可行解，以维持种群多样性；其次，为了改进种群个体质量，基于可行解比率设计交配池选择策略。将IACMEA与CCMO（Coevolutionary Constrained Multi-objective Optimization framework）等6种同类算法在CF、LIRCMOP和DASCMOP 3个基准测试集上进行的实验结果表明，IACMEA在33个问题中获得了23个最好的反向世代距离（IGD）值和22个最好的超体积（HV）值。可见，IACMEA在处理非线性约束多目标优化问题（CMOP）时具有一定的优势。

关键词: 多目标优化问题, 进化算法, 约束, 选择策略, 最优解