The paper presents a new balanced selection operator applied to the proposed Balanced Non-dominated Tournament Genetic Algorithm (B-NTGA) that actively uses archive to solve multi- and many-objective NP-hard combinatorial optimization problems with constraints. The primary motivation is to make B-NTGA more efficient in exploring Pareto Front Approximation (PFa), focusing on 'gaps' and reducing some PFa regions' sampling too frequently. Such a balancing mechanism allows B-NTGA to be more adaptive and focus on less explored PFa regions. The proposed B-NTGA is investigated on two benchmark multi- and many-objective optimization real-world problems, like Thief Traveling Problem and Multi-Skill Resource-Constrained Project Scheduling Problem. The results of experiments show that B-NTGA has a higher efficiency and better performance than state-of-the-art methods.

翻译：本文提出了一种新的平衡选择算子，应用于所提出的平衡非支配锦标赛遗传算法（B-NTGA）。该算法主动利用存档来解决带约束的多目标与超多目标NP难组合优化问题。其主要动机是使B-NTGA在探索帕累托前沿近似（PFa）时更加高效，重点关注PFa中的“间隙”区域，并减少对某些PFa区域的过度频繁采样。这种平衡机制使B-NTGA更具自适应性，并能聚焦于探索较少的PFa区域。所提出的B-NTGA在两个基准多目标与超多目标优化实际问题上进行了验证，例如窃贼旅行问题和多技能资源受限项目调度问题。实验结果表明，B-NTGA相比现有先进方法具有更高的效率和更优的性能。