UMOEA/D：一种基于分解的均匀 Pareto 目标多目标进化算法
UMOEA/D: A Multiobjective Evolutionary Algorithm for Uniform Pareto Objectives based on Decomposition
AI总结：
本文提出UMOEA/D算法，通过神经网络优化Pareto前沿上的最大最小距离，首次定义并实现MOO问题的均匀性，生成多样且具代表性的均匀Pareto目标，性能超越现有方法。
摘要：
多目标优化（MOO）在众多应用中普遍存在，其中构建 Pareto 前沿（PF）以展示各种偏好下的最优解。先前的方法通常利用 Pareto 目标集（PF 上的粒子）来表示整个 PF。然而，PF 上 Pareto 目标的经验分布很少被研究，这隐含地阻碍了先前方法生成多样且具代表性的 Pareto 目标。为弥补这一差距，本文建议在 PF 上构建均匀分布的 Pareto 目标，以缓解先前 MOO 方法中多样性有限的问题。我们首次正式定义了 MOO 问题的“均匀性”概念。我们使用神经网络优化 Pareto 前沿上的最大最小距离，从而产生渐近和非渐近均匀的 Pareto 目标。所提方法通过在现实世界和合成问题上的实验得到验证，证明了其在生成高质量均匀 Pareto 目标方面的有效性，以及超越现有最先进方法的令人鼓舞的性能。详细的模型实现和代码计划在发表后开源。
英文摘要：
Multiobjective optimization (MOO) is prevalent in numerous applications, in which a Pareto front (PF) is constructed to display optima under various preferences. Previous methods commonly utilize the set of Pareto objectives (particles on the PF) to represent the entire PF. However, the empirical distribution of the Pareto objectives on the PF is rarely studied, which implicitly impedes the generation of diverse and representative Pareto objectives in previous methods. To bridge the gap, we suggest in this paper constructing \emph{uniformly distributed} Pareto objectives on the PF, so as to alleviate the limited diversity found in previous MOO approaches. We are the first to formally define the concept of ``uniformity" for an MOO problem. We optimize the maximal minimal distances on the Pareto front using a neural network, resulting in both asymptotically and non-asymptotically uniform Pareto objectives. Our proposed method is validated through experiments on real-world and synthetic problems, which demonstrates the efficacy in generating high-quality uniform Pareto objectives and the encouraging performance exceeding existing state-of-the-art methods. The detailed model implementation and the code are scheduled to be open-sourced upon publication.
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