A master-apprentice evolutionary algorithm for maximum weighted set K-covering problem

The maximum weighted set k-covering problem (MWKCP) is a fundamental optimization problem, which depicts the application scenario of resource-constrained environment and user preference selection. In this paper, the mathematical formulation of MWKCP is given for the first time. Then, a novel master-apprentice evolutionary algorithm (MAE) is proposed for solving this NP-hard optimization problem. In order to make MAE applicable to MWKCP, a path re-linking operator is designed as the mutual learning process of two individuals, and a bare bones fireworks algorithm with explosion amplitude adaptation is adopted as the self-learning stage. Experimental results on 150 classical instances show that the proposed algorithm performs best among all competitors including an exact solver and three heuristic algorithms.