A separation based optimization approach to Dynamic Maximal Covering Location Problems with switched structure

Vadim Azhmyakov; Juan P. Fernández-Gutiérrez; Erik I. Verriest; Stefan W. Pickl

doi:10.3934/jimo.2019128

Article Contents

2021, Volume 17, Issue 2: 669-686. Doi: 10.3934/jimo.2019128

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A separation based optimization approach to Dynamic Maximal Covering Location Problems with switched structure

1.
Department of Mathematical Sciences, Universidad EAFIT, Medellín, Colombia
2.
Department of Basic Science, Universidad de Medellín, Medellín, Colombia
3.
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, USA
4.
Department of Computer Science, Universität der Bundeswehr München, München, Germany

^* Corresponding author: V. Azhmyakov
^* Corresponding author: V. Azhmyakov

Received: December 2018

Revised: May 2019

Early access: October 2019

Published: March 2021

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Abstract

This paper extends a newly developed computational optimization approach to a specific class of Maximal Covering Location Problems (MCLPs) with a switched dynamic structure. Most of the results obtained for the conventional MCLP address the "static" case where an optimal decision is determined on a fixed time-period. In our contribution we consider a dynamic MCLP based optimal decision making and propose an effective computational method for the numerical treatment of the switched-type Dynamic Maximal Covering Location Problem (DMCLP). A generic geometrical structure of the constraints under consideration makes it possible to separate the originally given dynamic optimization problem and reduce it to a specific family of relative simple auxiliary problems. The generalized Separation Method (SM) for the DMCLP with a switched structure finally leads to a computational solution scheme. The resulting numerical algorithm also includes the classic Lagrange relaxation. We present a rigorous formal analysis of the DMCLP optimization methodology and also discuss computational aspects. The proposed SM based algorithm is finally applied to a practically oriented example, namely, to an optimal design of a (dynamic) mobile network configuration.

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Mathematics Subject Classification: Primary: 90C10, 49M30; Secondary: 90C30.

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Figure 1. Optimal dynamics of the switched decision variables $ y^{opt}(t) $

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