The Use of an Exact Algorithm within a Tabu Search Maximum Clique Algorithm

Algorithms

Roberto Montemanni¹  DerekH. Smith²  Stephanie Perkins² 

[1] Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Via Amendola 2 (Pad. Morselli), 42122 Modena MO, Italy;School of Computing and Mathematics, University of South Wales, Pontypridd, CF37 1DL Cardiff, UK;

关键词: combinatorial optimization;    maximum clique;    hybrid algorithm;    tabu search;    benchmarks;   

DOI  :  10.3390/a13100253

来源: DOAJ

【 摘 要 】

Let $G=(V,E)$ be an undirected graph with vertex set V and edge set E. A clique C of G is a subset of the vertices of V with every pair of vertices of C adjacent. A maximum clique is a clique with the maximum number of vertices. A tabu search algorithm for the maximum clique problem that uses an exact algorithm on subproblems is presented. The exact algorithm uses a graph coloring upper bound for pruning, and the best such algorithm to use in this context is considered. The final tabu search algorithm successfully finds the optimal or best known solution for all standard benchmarks considered. It is compared with a state-of-the-art algorithm that does not use exact search. It is slower to find the known optimal solution for most instances but is faster for five instances and finds a larger clique for two instances.

【 授权许可】

Unknown