This paper presents a highly effective reinforcement learning enhancement of multi-neighborhood tabu search for the max-mean dispersion problem. The reinforcement learning component uses the Q-learning mechanism that incorporates the accumulated feedback information collected from the actions performed during the search to guide the generation of diversified solutions. The tabu search component employs 1-flip and reduced 2-flip neighborhoods to collaboratively perform the neighborhood exploration for attaining high-quality local optima. A learning automata method is integrated in tabu search to adaptively determine the probability of selecting each neighborhood. Computational experiments on 80 challenging benchmark instances demonstrate that the proposed algorithm is favorably competitive with the state-of-the-art algorithms in the literature, by finding new lower bounds for 3 instances and matching the best known results for the other instances. Key elements and properties are also analyzed to disclose the source of the benefits of our integration of learning mechanisms and tabu search.

本文提出了一种最大邻域禁忌搜索的最大均值离散问题的高效强化学习增强方法。强化学习组件使用Q学习机制，该机制结合了从搜索过程中执行的操作收集的累积反馈信息，以指导生成多种解决方案。禁忌搜索组件采用1翻转和简化2翻转的邻域来协作执行邻域探索，以获得高质量的局部最优。在禁忌搜索中集成了学习自动机方法，以自适应地确定选择每个邻域的概率。在80个具有挑战性的基准实例上进行的计算实验表明，该算法与文献中的最新算法具有良好的竞争性，通过为3个实例找到新的下限，并为其他实例匹配最知名的结果。还分析了关键元素和属性，以揭示我们整合学习机制和禁忌搜索的好处的来源。