An Elite-guided Weighted Simulated Annealing Algorithm for the Clique Partitioning Problem

Abstract The clique partitioning problem (CPP) aims to find a partition of vertices of a complete graph in order to maximize the sum of edge weights within each partition (clique), which has been proven to be NP-hard and has wide real-world applications. In this paper, we propose an elite-guided weighted simulated annealing algorithm called EWSA to solve the CPP. First, EWSA employs two specific configurations and alternates between them via an oscillation strategy, which balances the exploitation and exploration of the search. Second, a weighting strategy is introduced to improve the scoring function in traditional simulated annealing, which is able to guide the search to explore diverse solutions. Finally, a partition restriction strategy is adopted to reduce search space and increase the search efficiency. Experiments on 255 instances demonstrate the competitiveness of EWSA. For 130 open instances, EWSA discovers new upper bounds in 32 cases and matches the best known results for the others. For the remaining 125 closed instances, EWSA achieves the best known objective values within a short computational time.