A biased random-key genetic algorithm for the minimum quasi-clique partitioning problem

Let G=(V, E) be a graph with vertex set V and edge set E , and consider γ∈ [0,1) to be a real constant. A γ -clique (or quasi-clique) is a subset V'⊆ V inducing a subgraph of G with edge density at least γ . In this paper, we tackle the minimum quasi-clique partitioning problem (MQCPP), which consists of obtaining a minimum-cardinality partition of V into quasi-cliques. We propose a biased random-key genetic algorithm (BRKGA) relying on an efficient partitioning decoder that allows merge operations to combine smaller quasi-cliques into larger ones. Furthermore, we show that MQCPP and the problem of covering the graph with a minimum number of quasi-cliques are not equivalent. Computational experiments indicate that the proposed BRKGA is very effective in obtaining high-quality solutions for MQCPP in low computational times. More specifically, it can at least match all the best solutions available in the literature, strictly improving over them for 20.3