A multi-neighborhood tabu search for solving multi-budget maximum coverage problem

Abstract

Many practical decision-making problems involve selecting k distinct subsets of objects from a set of candidate objects such that the chosen objects optimize a given goal while satisfying some constraints. The multi-budget maximum coverage problem (MMCP) is a general model that facilitates formulating such decision-making problems. Given a budget of k, a set of elements with profits, and a set of items with costs where each item is composed of a subset of the elements, the MMCP aims to select k disjoint subsets of items that maximize the total profits of the elements covered by these subsets, while their costs do not exceed their respective budgets. In this work, we present a multi-neighborhood tabu search (MTS) for this NP-hard problem. MTS comprises three essential components that employ four efficient neighborhoods to collaboratively perform the neighborhood exploration to obtain high-quality local optima, select neighborhood solutions with added perturbations, and generate offspring solutions based on population information exchange. To evaluate the effectiveness of MTS, we performed computations on 30 benchmark instances of the extended BMCP. We compared the results with the approximation algorithm, genetic algorithm, particle swarm optimization algorithm, and CPLEX solver. We also provide experiments to highlight the beneficial effect of the essential components in the MTS algorithm. The experimental results demonstrate that MTS not only performs efficiently but also yields solutions of superior quality.