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. INDEX TERMS Genetic algorithms, minimisation, public facilities, set covering problem, war elimination.

On Mathematical Modelling of Automated Coverage Optimization in Wireless 5G and beyond Deployments

“…According to our previous work [65], the network infrastructure can be defined as the following graph. Assume that the network infrastructure contains m vertices (service centres), and n vertices (customer locations), and for each pair of vertices i (considered as service centres) and j (customer locations) their signal strength p ij is given using a suitable propagation model (see more detailed discussion on the Equation 42).…”

“…If we need to consider the existing services from models described in Section 2.3, we can do this in the same way as we did in [65] for the necessary services. This refers to adding dummy columns or directly setting x i to 1.…”

“…In that case, we know from previous sections that this problem has at least the complexity of O(2 n ). For that reason, for more than 60 rows (X > 60) we can expect that the duration of computation with exact methods, on a typical desktop computer with 3 GHz processor, will be in the range of years [65]. The common exact methods used for calculations with X < 60 are: (i) branch-and-bound [78][79][80][81]; and (ii) removal algorithm [82].…”

“…Similarly for decision variables x i , x i = 1 means that the service centre i is selected, while x i = 0 means that it is not selected. Then, the set covering problem can be described by the following mathematical model [38,[65][66][67][68][69][70].…”

“…To solve the above-described model, we have utilized an enhanced genetic algorithm as one of the possible solutions [65]. This was used for minimizing the number of schools in the selected area in Central Europe, but the theoretical concept was the same.…”