# American Institute of Mathematical Sciences

March  2021, 17(2): 669-686. doi: 10.3934/jimo.2019128

## 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

Received  December 2018 Revised  May 2019 Published  October 2019

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.

Citation: Vadim Azhmyakov, Juan P. Fernández-Gutiérrez, Erik I. Verriest, Stefan W. Pickl. A separation based optimization approach to Dynamic Maximal Covering Location Problems with switched structure. Journal of Industrial & Management Optimization, 2021, 17 (2) : 669-686. doi: 10.3934/jimo.2019128
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Optimal dynamics of the switched decision variables $y^{opt}(t)$