A Hybrid Evolutionary Algorithm for the Clique Partitioning Problem

Improving Simulated Annealing for Clique Partitioning Problems

“…Heuristics, especially local search methods that move from solution to solution in the space of candidate solutions by applying local changes, play an important role in solving NP-hard problems. For the last decades, various heuristic algorithms have been proposed to find high-quality solutions for large-scale instances in an acceptable time and computer memory (Wang et al, 2017;Lu et al, 2020;Zhang et al, 2021;Lu et al, 2021;Bilandi et al, 2021). Among heuristic algorithms, tabu search (Glover, 1989(Glover, , 1990 and simulated annealing (Skiscim & Golden, 1983;Kirkpatrick et al, 1983), which solved many graph problems successfully (Palubeckis et al, 2014;Bilandi et al, 2021;Lu et al, 2019), showed their efficiency in solving many benchmark instances of the CPP.…”

“…They also showed that their algorithm has a comparable performance with CPP-P 3 and outperforms other existing algorithms on benchmark instances with 2000 vertices at most. Very recently, Lu et al (2021) have proposed an evolutionary algorithm, denoted by MDMCP, combining a crossover operator to improve individuals by preserving good properties of parents and incorporating an effective simulated annealing algorithm to enhance local search. They tested a wide range of benchmarks, including most instances used in previous experiments as well as some new large-scale instances whose vertex number is up to 7000, and carefully analyzed experimental results, showing that MDMCP dominates existing algorithms, such as ITS, SGVNS, CPP-P 3 .…”

“…The framework of simulated annealing used in our algorithm is derived from the version in (Lu et al, 2021). Algorithm 1 depicts the detailed procedure of the proposed simulated annealing.…”

“…The temperature is cooled down after each iteration. We use the same termination condition as used in (Lu et al, 2021), and parameters for controlling the simulated annealing algorithm are set to the same values as MDMCP, since the parameters were well-tuned and MDMCP was proved to work well for the CPP.…”

Subnetwork Constraints for Tighter Upper Bounds and Exact Solution of the Clique Partitioning Problem

“…Among such approaches were simulated annealing and tabu search [18], ejection chain and Kernighan-Lin heuristic [19], noising method [20], neighborhood search [21,22], iterative tabu search [23], and their combinations [24]. Usually, graphs considered in operational research are not too big, comprising hundreds to a few thousands of nodes, and the quality of approximate solutions is high [25,26]. At the same time, in network science, graphs could be extremely large, spanning over millions of nodes.…”