Two Objective Public Service System Design Problem

Jaroslav Janáček,René Fabricius,Michal Koháni,Dobroslav Grygar

doi:10.26552/com.c.2021.4.e68-e75

Abstract

The public service system serves population spread over a geographical area from a given number of service centers. One of the possible approaches to the problem with two or more simultaneously applied contradicting objectives is determination of the so-called Pareto front, i.e. set of all the feasible non-dominated solutions. The Pareto front determination represents a crucial computational deal, when a large public service system is designed using an exact method. This process complexity evoked an idea to use an evolutionary metaheuristic, which can build up a set of non-dominated solution continuously in the form of an elite set. Nevertheless, the latter approach does not assure that the resulting set of solutions represents the true Pareto front of the multi-objective problem solutions. Within this paper, authors deal with both approaches to evaluate the difference between the exact and heuristic approaches.

Highlights

The public service system design problem is usually formulated as a task of selection of p-center locations from a finite set of possible center location so that a given objective, based on user’s distances to the nearest service center, is minimal
This research was devoted to inspection of the genetic algorithm ability in obtaining an approximation of the Pareto front of the p-location problem solutions
To be able to perform proper analysis of the approximate results, the exact Pareto front were determined for each benchmark, by an exact optimization method and comparing it to the Pareto front approximation, authors came to the following findings

Summary

Introduction

The public service system design problem is usually formulated as a task of selection of p-center locations from a finite set of possible center location so that a given objective, based on user’s distances to the nearest service center, is minimal. The most usual one is the way that prefers the solution with minimal average user’s distances to the service center This objective is called the min-sum or system objective and it has been used by many authors in emergency system designing. The most known one is the min-max objective, where the maximal distance from a user to the nearest service center should be minimal This formulation of the public service design is called the p - center problem. It is necessary to consider that each run of the sequence represents solving of a hard and large combinatorial problem, which solution is obtained by time demanding inspection of a vast searching tree To avoid this computational burden, professionals prefer a heuristic approach based on imitating the biological processes [18,19].

Radial formulation of the min-sum problem with the limited distance

The Pareto front determination using the exact approach

The genetic algorithm for the set of nondominated solutions

Computational study

Conclusions