通过平衡解的分散与集中，提升多目标优化解的质量。
Maximum Dispersion, Maximum Concentration: Enhancing the Quality of MOP Solutions
- 在决策空间保持解的均匀分布，同时聚焦目标空间特定区域。
- 实验表明该方法有效平衡了多样性与收敛性，减少解聚集偏差。
- 适合需要高质量、均衡解集的多目标优化场景。
多目标优化问题（MOPs）常需在目标空间中的多样性与收敛性之间权衡。本文提出一种改进MOP解质量的方法：在决策空间优化解的分散性，在目标空间特定区域增强解的聚集性。方法基于锥形区域定义决策者偏好的目标空间兴趣区（ROI），并利用均匀性度量提升决策空间的解分散性。结合目标空间的解集中与决策空间的解分散，强化对帕累托最优解的搜索，同时提升解的多样性。该设计可避免解在决策空间特定区域过度聚集导致的偏差。初步实验表明，该方法能生成有效平衡分散与集中特性的解，从而改善多目标优化性能。
原文摘要 · Abstract (English)
Multi-objective optimization problems (MOPs) often require a trade-off between conflicting objectives, maximizing diversity and convergence in the objective space. This study presents an approach to improve the quality of MOP solutions by optimizing the dispersion in the decision space and the convergence in a specific region of the objective space. Our approach defines a Region of Interest (ROI) based on a cone representing the decision maker's preferences in the objective space, while enhancing the dispersion of solutions in the decision space using a uniformity measure. Combining solution concentration in the objective space with dispersion in the decision space intensifies the search for Pareto-optimal solutions while increasing solution diversity. When combined, these characteristics improve the quality of solutions and avoid the bias caused by clustering solutions in a specific region of the decision space. Preliminary experiments suggest that this method enhances multi-objective optimization by generating solutions that effectively balance dispersion and concentration, thereby mitigating bias in the decision space.
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