An Efficient Solving Approach for the p-Dispersion Problem Based on the Distance-Based Spatially Informed Property

Abstract

The p-dispersion problem is a spatial optimization problem that aims to maximize the minimum separation distance among all assigned nodes. This problem is characterized by an innate spatial structure based on distance attributes. This research proposes a novel approach, named the distance-based spatially informed property (D-SIP) method to reduce the problem size of the p-dispersion instances, facilitating a more efficient solution while maintaining optimality in nearly all cases. The D-SIP is derived from investigating the underlying spatial characteristics from the behaviors of the p-dispersion problem in determining the optimal location of nodes. To define the D-SIP, this research applies Ripley's K-function to the different types of point patterns, given that the optimal solutions of the p-dispersion problem are strongly associated with the spatial proximity among points discovered by Ripley's K-function. The results demonstrate that the D-SIP identifies collective dominances of optimal solutions, leading to building the spatially informed p-dispersion model. The simulation-based experiments show that the proposed method significantly diminishes the size of problems, improves computational performance, and secures optimal solutions for 99.9% of instances (999 out of 1,000 instances) under diverse conditions.