Multi-objective, multi-type, continuous space maximal covering problem: an application to points- and areas-of interest

Purpose The purpose of this work is to identify optimal air-defense locations in a multi-objective (MO) setting considering multiple and sometimes competing objectives within a large search space at the national scale. Design/methodology/approach First, a mathematical MO maximal covering location problem is formulated. This formulation includes the following three objectives: (1) providing coverage to densely populated areas, (2) providing coverage to areas having high residential and commercial property value and (3) providing coverage to infrastructure of national or regional significance. Three algorithms are applied to solve the problem, and their performance compared (1) Non-dominated Sorting Genetic Algorithm II (NSGA-II), (2) an augmented NSGA-II-A and (3) Strength Pareto Evolutationary Algorithm II (SPEA-II). Findings Within the context of our computing environment, specific parameter settings, implementations and case instances, our results indicate that the NSGA-II-A algorithm outperforms both the NSGA-II and SPEA-II algorithms in that the NSGA-II-A algorithm concentrates solutions toward the estimated Pareto front within reasonable computational effort. Originality/value The originality of this study lies in its integrated approach to defense location planning, combining multiple defense-resource types, point- and area-based coverage priorities and an application-specific non-overlap requirement within a single decision-support model. The model is demonstrated using real-world geospatial data at resolutions as fine as a 5-km grid.