A generic approach to districting with diameter or center-based objectives

ABSTRACTDistricting is the problem of grouping basic geographic units into clusters called districts. Districts are typically required to be geometrically compact, contiguous, and evenly balanced with respect to attributes of the basic units. Though most applications share these core criteria, domain-specific constraints and objective functions are common. This leads to a fragmented literature with different approaches for similar domains and hinders comparisons between these approaches. In this paper we study a unified heuristic approach that can handle three of the most common objective functions concerning compactness: diameter, p-center and p-median, as well as a variable number of balancing attributes. We propose a multistart method which iteratively constructs greedy randomized solutions followed by an improvement phase which alternates between optimizing compactness and satisfying balancing constraints through a series of tabu searches. Experiments show that the proposed method is competitive when compared to approaches in the literature which are specific to each objective, improving known upper bounds in some cases.