A simulated annealing based heuristic for a location-routing problem with two-dimensional loading constraints

A hybrid heuristic is proposed to solve a location-routing problem with two-dimensional loading constraints. This problem appears in military situations and natural disasters in such a way that decisions are taken in a short time horizon. The proposed heuristic combines the simulated annealing method and the artificial algae algorithm. Simulated annealing is used to handle the location-routing problem, while the artificial algae algorithm is used to determine the sequence in which the items will be packed. Therefore, we apply the Skyline technique to find a feasible packing of such items onto the vehicle’s rectangular surface. As there is no other work in the literature handling the location-routing problem with two-dimensional loading constraints that we can compare the results, we evaluate the heuristic performance on its subproblems: the location-routing problem and the vehicle routing problem with two-dimensional loading constraints. Although the heuristic is not designed for these subproblems, it still obtains competitive results, with an average relative difference of 1.26% and equal or better solutions for more than 90 instances. Regarding the problem under study, the heuristic obtains solutions close to an estimated lower bound for instances having more items per customer. [Display omitted] •The location-routing problem with loading constraints is handled.•A hybrid heuristic is proposed that solves problem variants too.•The heuristic combines the Simulated Annealing and Artificial Algae Algorithm.•Diversification and perturbation procedures are proposed to escape from local optima.•The heuristic solutions are competitive with state-of-the-art methods.