Solution-based tabu search for the capacitated dispersion problem

Given a weighted graph with a capacity associated to each node (element), the capacitated dispersion problem (CDP) consists in selecting a subset of elements satisfying a capacity constraint, in such a way that the minimum distance among them is maximized. The purpose of this work is to tackle this NP-hard problem, by developing an effective and parameter-free heuristic algorithm based on the solution-based tabu search. Specifically, we propose a fast greedy construction heuristic to obtain high-quality initial solutions. To ensure a high search efficiency, our algorithm exploits the combination of three neighborhoods, including a new neighborhood based on the constrained swap strategy, and uses hash functions to identify eligible candidate solutions. Extensive computational experiments on benchmark instances in the literature are performed to demonstrate the high performance of our algorithm and get insights into the influences of the algorithmic components. The application of our algorithm to a realistic location problem further shows the usefulness of our approach for practical problems.