A Multi-population Integrated Approach for Capacitated Location Routing

The capacitated location-routing problem involves determining the depots from a set of candidate capacitated depot locations and finding the required routes from the selected depots to serve a set of customers whereas minimizing a cost function that includes the cost of opening the chosen depots, the fixed utilization cost per vehicle used, and the total cost (distance) of the routes. This paper presents a multi-population integrated framework in which a multi-depot edge assembly crossover generates promising offspring solutions from the perspective of both depot location and route edge assembly. The method includes an effective neighborhood-based local search, a feasibility-restoring procedure and a diversification-oriented mutation. Of particular interest is the multi-population scheme which organizes the population into multiple subpopulations based on depot configurations. Extensive experiments on 281 benchmark instances from the literature show that the algorithm performs remarkably well, by improving 101 best-known results (new upper bounds) and matching 84 best-known results. Additional experiments are presented to gain insight into the role of the key elements of the algorithm.