Generalized vertex cover using chemical reaction optimization

Abstract

The generalized vertex cover problem (GVC) is a new variant of classic vertex cover problem which considers both vertex and weight of the edge into the objective function. The GVC is a renowned NP-hard optimization problem that finds the vertex subset where the sum of vertices and edge weight are minimized. In the mathematical field of electrical, networking and telecommunication GVC is used to solve the vertex cover problem. Finding the minimum vertex cover using GVC has a great impact on graph theory. Some exact algorithms were proposed to solve this problem, but they failed to solve it for real-world instances. Some approximation and metaheuristic algorithms also were proposed to solve this problem. Chemical Reaction Optimization (CRO) is an established population-based metaheuristic for optimization and comparing with other existing optimization algorithms it gives better results in most of the cases. The CRO algorithm helps to explore the search space locally and globally over the large population area. In this paper, we are proposing an algorithm by redesigning the basic four operators of CRO to solve GVC problem and an additional operator named repair function is used to generate optimal or near-optimal solutions. We named the proposed algorithm as GVC_CRO. Our proposed GVC_CRO algorithm is compared with the hybrid metaheuristic algorithm (MAGVCP), the local search with tabu strategy and perturbation mechanism (LSTP) and Genetic Algorithm (GA), which are state of the arts. The experimental results show that our proposed method gives better results than other existing algorithms to solve the GVC problem with less execution time in maximum cases. Statistical test has been performed to demonstrate the superiority of the proposed algorithm over the compared algorithm.