A Hybrid Immunological Search for the Weighted Feedback Vertex Set Problem

In this paper we present a hybrid immunological inspired algorithm (Hybrid-IA) for solving the Minimum Weighted Feedback Vertex Set (M W F V S) problem. MWFV S is one of the most interesting and challenging combinatorial optimization problem, which finds application in many fields and in many real life tasks. The proposed algorithm is inspired by the clonal selection principle, and therefore it takes advantage of the main strength characteristics of the operators of (i) cloning; (ii) hypermutation; and (iii) aging. Along with these operators, the algorithm uses a local search procedure, based on a deterministic approach, whose purpose is to refine the solutions found so far. In order to evaluate the efficiency and robustness of Hybrid-IA several experiments were performed on different instances, and for each instance it was compared to three different algorithms: (1) a memetic algorithm based on a genetic algorithm (MA); (2) a tabu search metaheuristic (XTS); and (3) an iterative tabu search (ITS). The obtained results prove the efficiency and reliability of hybrid-IA on all instances in term of the best solutions found and also similar performances with all compared algorithms, which represent nowadays the state-of-the-art on for MWFV S problem.