Evolutionary Metaheuristics to Solve Multiobjective Assignment Problem in Telecommunication Network: Multiobjective Assignment Problem

Evolutionary Metaheuristics to Solve Multiobjective Assignment Problem in Telecommunication Network: Multiobjective Assignment Problem

Benkanoun Yazid (DGRSDT, USTHB, AMCD-RO Laboratory, BP32 El-Alia, Bab Ezzouar, Algiers, Algeria), Bouroubi Sadek (DGRSDT, USTHB, L'IFORCE Laboratory, BP32 El-Alia, Bab Ezzouar, Algiers, Algeria) and Chaabane Djamal (DGRSDT, USTHB, AMCD-RO Laboratory, BP32 El-Alia, Bab Ezzouar, Algiers, Algeria)
Copyright: © 2020 |Pages: 21
DOI: 10.4018/IJAMC.2020040103

Abstract

The authors propose a computing approach for solving a multiobjective problem in the telecommunication network field, suggested by an Algerian industrial company. The principal goal is in developing a palliative solution to overcome some generated problems existing in the current management system. A mathematical operational model has been established. The exact algorithms that solve multiobjective optimization problems are not appropriate for large scale problems. However, the application of metaheuristics approach leads perfectly to approximate the Pareto optimal set. In this paper, the authors apply a well-known multiobjective evolutionary algorithm, the Non-dominated Sorting Genetic Algorithm (NSGA-II), compare the obtained results with those generated by the Strength Pareto Evolutionary Algorithm-II (SPEA2) and propose a way to help the decision maker, who is often confronted with the choice of a final solution, to make his preferences afterward using a utility function based on a Choquet integral measure. Finally, numerical experiments are presented to validate the approach.
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1. Introduction

With the aim of increasing its profitability and ensuring its perenniality, in a modern evolutionary and competing world, a serious economic company must offer its customers a harmonious and effective service. To full fill its obligations, the company must install a system of telecommunication including technical transmission supports between its different centers (nodes). This system is confronted with the tough need for a compromise between cost and quality. In actual decision-making situations, a major concern is that most decision problems involve multiple objectives.

Within this framework, we were proposed to deliver a mathematical model and develop a data-processing solution respecting the problem constraints. For this purpose, our problem is divided into two parts. First of all, one must determine an optimal topology of the tele-exploitation network. The Mathematical model suggested for this part is based on graphs. Indeed, during the design phase of tele-exploitation system, one needs to inter-connect N centers (nodes) between them, using an arrangement of IJAMC.2020040103.m01 transmission supports, each one connects two nodes. Among all possible arrangements, the one using a minimum length of transmission supports is often the most desirable. One can model this problem using a non-directed graphIJAMC.2020040103.m02, where IJAMC.2020040103.m03 represents the set of nodes, and IJAMC.2020040103.m04 represents the set of possible inter-connections between each pair of nodes. Each edge IJAMC.2020040103.m05 is provided with a weight IJAMC.2020040103.m06 which represents the length of transmission support connecting IJAMC.2020040103.m07 to IJAMC.2020040103.m08. The goal is then to find a “Minimum-Weight Spanning Tree (MWST)” of IJAMC.2020040103.m09 for which the total weight is minimum. This is easily obtained by a polynomial algorithm such as the Kruskal algorithm (Lust et al., 2013).

The main problem lies in the second part, for which we were asked to determine an optimal assignment of transmission supports to connect nodes between them in order to optimize the current operating telecommunication system.

To guarantee its optimal safety, the company for which this work was dedicated accepted to set up a system of tele-exploitation which is a set of transmission supports for information and order, as did many industrial companies. The installation of this system will make it possible to quickly reach essential information needed for the correct economic operation. To collect and exchange all this information, electronics components must be installed at each node, allowing transferring the information to the other nodes, via transmission supports such as, telephone lines, optical fiber, GSM, etc. Let notice, that the search space has IJAMC.2020040103.m10 feasible solutions, where IJAMC.2020040103.m11 designs the number of supports and IJAMC.2020040103.m12 the number of edges in the network. Figure1 represents an example of an assignment of five different supports on a very small input network instance, where the supports are represented by different colors. The number of solutions is IJAMC.2020040103.m13.

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