Solving maximum clique problem using chemical reaction optimization

The maximum clique problem (MCP) deals with a given arbitrary graph that finds the maximum clique in the graph. The target is to maximize the size of the clique which means maximizing the size of a complete subgraph. The MCP finds the largest complete subgraph or clique of a given graph. Several metaheuristic approaches were proposed to solve the problem as it is an NP-hard problem. To solve the maximum clique problem we propose a metaheuristic algorithm named chemical reaction optimization (CRO). It is an algorithm that is usually used to solve optimization problems. Solving optimization problems the algorithm gives better results than any other related metaheuristics. It can search the solution space locally as well as globally over a large population with the help of its four reaction operators. We are proposing a method to solve MCP by tuning all the initial parameters and redesigning four reaction operators of CRO. An additional repair operator is also designed to find optimal solutions in less computational time. Three benchmark datasets are used to observe the efficiency of the proposed algorithm. We obtained better results with less average errors in comparison to the state of art methods for the three datasets. For most of the graphs, the algorithm gives the best-known results mentioned in the datasets. The results are shown with the repair operator for all the datasets to understand the improvement in results clearly.