The quality of solution sets generated by decomposition-based evolutionary multi-objective optimisation (EMO) algorithms depends heavily on the consistency between a given problem's Pareto front shape and the specified weights' distribution. A set of weights distributed uniformly in a simplex often leads to a set of well-distributed solutions on a Pareto front with a simplex-like shape, but may fail on other Pareto front shapes. It is an open problem on how to specify a set of appropriate weights without the information of the problem's Pareto front beforehand. In this article, we propose an approach to adapt weights during the evolutionary process (called AdaW). AdaW progressively seeks a suitable distribution of weights for the given problem by elaborating several key parts in weight adaptation—weight generation, weight addition, weight deletion, and weight update frequency. Experimental results have shown the effectiveness of the proposed approach. AdaW works well for Pareto fronts with very different shapes: 1) the simplex-like, 2) the inverted simplex-like, 3) the highly nonlinear, 4) the disconnect, 5) the degenerate, 6) the scaled, and 7) the high-dimensional.

中文翻译：

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什么重量适合你？在基于分解的进化多目标优化中为任何帕累托前沿形状调整权重

由基于分解的进化多目标优化 (EMO) 算法生成的解决方案集的质量在很大程度上取决于给定问题的帕累托前沿形状与指定权重分布之间的一致性。在单纯形中均匀分布的一组权重通常会在具有类似单纯形的形状的 Pareto 前沿上产生一组分布良好的解，但在其他 Pareto 前沿形状上可能会失败。在没有问题的帕累托前沿信息的情况下，如何指定一组合适的权重是一个悬而未决的问题。在本文中，我们提出了一种在进化过程中调整权重的方法（称为 AdaW）。AdaW 通过阐述权重适应中的几个关键部分——权重生成、权重添加、权重删除，权重更新频率。实验结果表明了所提出方法的有效性。AdaW 适用于具有非常不同形状的 Pareto 前沿：1) 类单纯形，2) 倒类单纯形，3) 高度非线性，4) 断开，5) 退化，6) 缩放，以及 7)高维。