Solving Maximum Clique Problem using a novel Quantum-inspired Evolutionary Algorithm

Maximum Clique Problem (MCP) is one of the most important NP-hard problems in the area of soft computing and it has many real world applications in numerous fields ranging from coding theory to the determination of the structure of a protein molecule. Different heuristic, Meta heuristic and hybrid solution approaches have been applied to obtain the solution. In this paper, we demonstrate a Quantum-inspired Evolutionary Algorithm (QEA) to solve MCP. We have used one dimensional arrays of Q-bits called Q-bit individuals to produce binary individuals. After production of binary individuals, we have repaired and improved them. Here, Q-gate is the main variation operator applied on Q-bit individuals. Our algorithm was tested on DIMACS benchmark graphs and 40 of them were tested. The results obtained here are extremely encouraging. For almost all of the datasets, we get the optimal results reported on DIMACS benchmark and also compared our results with other related works. For some cases we get better results than other works.