The Minimization of Public Facilities with Enhanced Genetic Algorithms Using War Elimination

Abstract

In this paper, we focus on the problem of minimizing a network of state facilities that provide essential public services (schools, offices, and hospitals). The goal is to reduce the size of the network in order to minimize the costs associated with it. However, it is essential that every customer should be able to access an appropriate service center within a reachable distance. This problem can arise in various scenarios, such as a government cutting back on public service spending in remote areas or as a reaction to changing demographics (population increase/decrease). In general, this task is NP-hard which makes the problem particularly hard to scale. Therefore, for larger problems, heuristic methods must be employed to find an approximation of the optimum. To solve this problem with satisfactory results, we have presented an enhanced version of the genetic algorithm based on war elimination and migration operations. This modification overcomes the well-known shortcoming of GAs when the population becomes gradually more and more similar, these results in a diversity decrease which in turn leads to a sub-optimal local minimum. We test the performance of the novel algorithm against the standard heuristic benchmarks on the widely accepted Beasley OR-library dataset for optimization problems. Finally, we provide a case study based on real data, where a municipality tries to minimize the number of schools in a region while satisfying accessibility and other region-specific constraints.