Fixed Set Search Applied to the Territory Design Problem

In this paper, we apply the novel fixed set search (FSS) metaheuristic in combination with mixed-integer programming to solve the Territory Design Problem (TDP). In this matheuristic approach, we select the territory centers with an extended greedy randomised adaptive search procedure (GRASP) while optimising the subproblem of the territory-center allocation with a standard mixed-integer programming solver. The FSS adds a learning procedure to GRASP and helps us to narrow down the most common territory centers in the solution population in order to fix them. This improves the speed of the optimisation and helps to find high-quality solutions on all instances of our computational study at least once within a small number of runs.