A multistart and recombination algorithm for finding many unique solutions to spatial aggregation problems

Abstract

AbstractSpatial aggregation is essential for applications where data at low level spatial units such as census blocks are grouped into larger regions. This type of problem can be formulated as spatial optimization problems where the goal is to minimize the difference between the grouped regions. These problems are difficult to solve because of their computational intensity. In addition, these problems often have multiple, instead of singular, optimal solutions that have the same or similar objective function values but exhibit different spatial configurations. Existing solution methods often aim to find single solutions to these problems. In this paper, we discuss a new heuristic method that can be used to find a set of unique optimal or near-optimal solutions to spatial aggregation problems. The algorithm consists of two phases. A multistart phase first generates a pool of random solutions to a problem. The size of the pool is specified by the user and contains the number of solutions desired to be found. Each random solution is then improved using an efficient algorithm called give-and-take. The second phase uses a recombination algorithm to create new solutions based on solutions randomly selected from the pool. The worst solution in the pool will be replaced by the new solution if the latter is better and does not exist in the pool. We test this multistart and recombination algorithm (MSRA) using a variety of problems with different sizes and the results suggest the effectiveness of the algorithm in finding multiple unique optimal or near-optimal solutions.