Genetic algorithm for regionalization problem with adaptive equity constraint

The regionalization problem involves aggregating several spatially contiguous basic geographical units into regions while optimizing a defined objective. Equity is one of its most important constraints with the aim to ensure the value of one or several interesting spatial attributes at a certain level and to provide solutions to specific requirements in applications. This paper tackles a new regionalization scenario in which the threshold used in equity constraint is a regional mean measurement and depends on an unknown amount of regions. A novel nonlinear mixed integer programming model is developed. For the solution of the model a parallel genetic algorithm capable of solving large-scale, real-world instances, is designed. Our efforts in designing a genetic algorithm that integrates an upper bound heuristic are reported. A group of 30 synthetic lattice data is generated according to the spatial auto regressive function to evaluate the proposed genetic algorithm. Equity attributes with both Uniform distribution and Poisson distribution are considered to make a comparison. This work makes an original contribution in the solution of the regionalization problem with adaptive equity constraint.