Reinforcement learning enhanced multi-neighborhood tabu search for the max-mean dispersion problem

Abstract 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.