Over the past two decades, research in evolutionary multi-objective optimization has predominantly focused on continuous domains, with comparatively limited attention given to multi-objective combinatorial optimization problems (MOCOPs). Combinatorial problems differ significantly from continuous ones in terms of problem structure and landscape. Recent studies have shown that on MOCOPs multi-objective evolutionary algorithms (MOEAs) can even be outperformed by simple randomised local search. Starting with a randomly sampled solution in search space, randomised local search iteratively draws a random solution (from an archive) to perform local variation within its neighbourhood. However, in most existing methods, the local variation relies on a fixed neighbourhood, which limits exploration and makes the search easy to get trapped in local optima. In this paper, we present a simple yet effective local search method, called variable stepsize randomized local search (VS-RLS), which adjusts the stepsize during the search. VS-RLS transitions gradually from a broad, exploratory search in the early phases to a more focused, fine-grained search as the search progresses. We demonstrate the effectiveness and generalizability of VS-RLS through extensive evaluations against local search and MOEAs methods on diverse MOCOPs.

翻译：过去二十年间，进化多目标优化领域的研究主要集中于连续域问题，对多目标组合优化问题的关注相对有限。组合问题在问题结构与解空间形态上与连续问题存在显著差异。近期研究表明，在多目标组合优化问题上，简单的随机局部搜索方法甚至能超越多目标进化算法。随机局部搜索从搜索空间中随机采样初始解开始，迭代地从存档中抽取随机解在其邻域内进行局部变异。然而，现有方法大多依赖固定邻域进行局部变异，这限制了搜索的探索能力，并使搜索容易陷入局部最优。本文提出一种简单而有效的局部搜索方法——变步长随机局部搜索，该方法在搜索过程中动态调整步长。VS-RLS 在搜索早期采用宽泛的探索性搜索，随着搜索进程逐步过渡到更聚焦的精细搜索。通过对多种多目标组合优化问题进行局部搜索与多目标进化算法的广泛对比评估，我们验证了 VS-RLS 的有效性与泛化能力。