Reinforcement learning-enhanced variable neighborhood search strategies for the k-clustering minimum biclique completion problem

Abstract

In scenarios where different groups of users need to receive the same broadcast or in social media platforms where user interactions form distinct clusters, addressing the problems of minimizing communication channels or understanding user communities can be critical. These problems are modeled as the $k$-clustering minimum biclique completion problem, which is recognized as an NP-hard combinatorial optimization problem. This paper presents a novel approach to solving such a problem through reinforcement learning-enhanced variable neighborhood search. The proposed method features an innovative strategy based on probability learning. It integrates a range of neighborhood techniques with a tabu strategy to enable an exploration of the search space. A key aspect of the method is its implementation of a perturbation procedure through probability learning, which significantly enhances the iterative process by guiding the search towards previously unexplored and promising regions. Experimental evaluations on benchmark instances from existing literature highlight the method’s robustness and high competitiveness. The results reveal its superior performance compared to leading solvers such as Cplex and other recently published methods. Additionally, statistical analyses, including the sign test and the Wilcoxon signed-rank test, are conducted to determine the most effective approach among those tested. These analyses confirm that the method not only achieves new performance bounds but also shows its ability to deliver promising solutions.