Solving Graph Partitioning Problems with Parallel Metaheuristics Zbigniew Kokosi ´ nski and Marcin Bala Abstract In this article we describe computer experiments while testing a family of parallel and hybrid metaheuristics against a small set of graph partitioning problems like clustering, partitioning into cliques and coloring. In all cases the search space is composed of vertex partitions satisfying specific problem requirements. The solver application contains two sequential and nine parallel/hybrid algorithms developed on the basis of SA and TS metaheuristics. A number of tests are reported and conclusions concerning metaheuristics’ performance that result from the conducted experiments are derived. The article provides a case study in which partitioning numbers ψ k (G), k ≥ 2, of DIMACS graph coloring instances are evaluated experimentally by means of H-SP metaheuristic which is found to be the most efficient in terms of solution quality. Keywords Simulated annealing · Tabu search · Parallel metaheuristic · Hybrid metaheuristic · Graph partitioning problem · Graph partitioning number 1 Introduction Computational optimization attracts researchers and practitioners interested in solv- ing combinatorial problems by means of various computational methods and tools. In particular, many NPO problems require new versatile tools in order to find approxi- mate solutions [1, 10]. Parallel and hybrid metaheuristics are among the most promis- ing methods to be developed in the nearest time [2, 20]. Many new algorithms have been already designed and compared with existing methodologies [7, 15], but there is still a room for significant progress in this area. Z. Kokosi´ nski (B ) Faculty of Electrical and Computer Engineering, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland e-mail: zk@pk.edu.pl M. Bala Salumanus Sp. z o.o., ul. Walerego Slawka 8a, 30-633 Kraków, Poland e-mail: bala.marcin@gmail.com © Springer International Publishing AG 2018 S. Fidanova (ed.), Recent Advances in Computational Optimization, Studies in Computational Intelligence 717, DOI 10.1007/978-3-319-59861-1_6 89