Combining max–min ant system with effective local search for solving the maximum set k-covering problem

Abstract

The maximum set k-covering problem (MKCP) is a well-known combinatorial NP-hard problem with rich application scenarios, with the objective of covering as many elements as possible with a limited number of candidate sets. In this paper, an effective ant colony optimization (ACO) algorithm, namely MMAS-ML, is proposed to solve this important problem. Specifically, the double-layer selection heuristic is presented to obtain a high-quality solution, which is used in the initialization process to accelerate the convergence of the algorithm. Moreover, a customized local search is carefully designed, empowering ants with exploitation capacity around the food sources. For such local search procedures, some useful techniques, that is, the scoring function, delayed configuration checking, oblivious row weighting, and best from multiple selections, have been developed to enhance the performance. In addition, the max–min ant system with memory ants is further designed to confine the upper and lower bounds of the pheromone to avoid ACO stagnation. A detailed experimental evaluation of various instances reveals that the newly proposed algorithm outperforms other state-of-the-art heuristics for the MKCP, and the developed components contribute to the entire framework.