Multiobjective evolutionary algorithms based on decomposition (MOEA/D) have attracted tremendous attention and achieved great success in the fields of optimization and decision-making. MOEA/Ds work by decomposing the target multiobjective optimization problem (MOP) into multiple single-objective subproblems based on a set of weight vectors. The subproblems are solved cooperatively in an evolutionary algorithm framework. Since weight vectors define the search directions and, to a certain extent, the distribution of the final solution set, the configuration of weight vectors is pivotal to the success of MOEA/Ds. The most straightforward method is to use predefined and uniformly distributed weight vectors. However, it usually leads to the deteriorated performance of MOEA/Ds on solving MOPs with irregular Pareto fronts. To deal with this issue, many weight vector adjustment methods have been proposed by periodically adjusting the weight vectors in a random, predefined, or adaptive way. This article focuses on weight vector adjustment on a simplex and presents a comprehensive survey of these weight vector adjustment methods covering the weight vector adaptation strategies, theoretical analyses, benchmark test problems, and applications. The current limitations, new challenges, and future directions of weight vector adjustment are also discussed.

中文翻译：

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基于分解的多目标进化算法权向量调整方法综述

基于分解的多目标进化算法（MOEA/D）引起了极大的关注，并在优化和决策领域取得了巨大成功。MOEA/D 的工作原理是将目标多目标优化问题 (MOP) 分解为基于一组权重向量的多个单目标子问题。子问题在进化算法框架中协同解决。由于权重向量定义了搜索方向，并在一定程度上定义了最终解集的分布，权重向量的配置对于 MOEA/Ds 的成功至关重要。最直接的方法是使用预定义且均匀分布的权重向量。然而，这通常会导致 MOEA/Ds 在解决具有不规则 Pareto 前沿的 MOP 时的性能下降。为了处理这个问题，通过以随机的、预定义的或自适应的方式周期性地调整权向量，已经提出了许多权向量调整方法。本文重点介绍单纯形上的权向量调整，并全面介绍了这些权向量调整方法，包括权向量适应策略、理论分析、基准测试问题和应用。还讨论了权重向量调整的当前限制、新挑战和未来方向。基准测试问题和应用。还讨论了权重向量调整的当前限制、新挑战和未来方向。基准测试问题和应用。还讨论了权重向量调整的当前限制、新挑战和未来方向。