A hybrid heuristic for districting problems with routing criteria

In this paper we consider districting problems with routing criteria. Such problems arise when clients in a commercial district need to be attended daily and the time to visit them is limited, for example by working hours of retail businesses. Routing costs are modeled by traveling salesman tours starting from predetermined depot locations. Besides having low routing costs, districts must also satisfy balancing (e.g. of total demand or workload) and contiguity constraints, and may also be required to be geographically compact. We propose a general heuristic for solving such problems. It iteratively builds new solutions by a greedy constructive heuristic, and then improves them by a hybrid alternating tabu search strategy. We further propose an efficient scheme for maintaining high-quality routes under small modifications to districts, for example incurred by neighborhood search operators. In extensive computational experiments we study the different components of our method, and show that it is effective in treating a number of problem variants with different constraints.