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Robust covering problems : formulations, algorithms and an application

Abstract : Two robust optimization NP-Hard problems are studied in this thesis: the min-max regret Weighted Set Covering Problem (min-max regret WSCP) and the min-max regret Maximal Coverage Location Problem (min-max regret MCLP). The min-max regret WSCP and min-max regret MCLP are, respectively, the robust optimization counterparts of the Set Covering Problem and of the Maximal Coverage Location Problem. The uncertain data in these problems is modeled by intervals and only the minimum and maximum values for each interval are known. However, while the min-max regret WSCP is mainly studied theoretically, the min-max regret MCLP has an application in disaster logistics which is also investigated in this thesis. Two other robust optimization criteria were derived for the MCLP: the max-max MCLP and the min-max MCLP. In terms of methods, mathematical formulations, exact algorithms and heuristics were developed and applied to both problems. Computational experiments showed that the exact algorithms efficiently solved 14 out of 75 instances generated to the min-max regret WSCP and all realistic instances created to the min-max regret MCLP. For the simulated instances that was not solved to optimally in both problems, the heuristics developed in this thesis found solutions, as good as, or better than the exact algorithms in almost all instances. Concerning the application in disaster logistics, the robust models found similar solutions for realistic scenarios of the earthquakes that hit Kathmandu, Nepal in 2015. This indicates that we have got a robust solution, according to all optimization models
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Submitted on : Friday, December 20, 2019 - 3:13:07 PM
Last modification on : Saturday, December 21, 2019 - 1:41:14 AM
Long-term archiving on: : Saturday, March 21, 2020 - 5:10:54 PM


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  • HAL Id : tel-02421538, version 1




Amadeu Almeida Coco. Robust covering problems : formulations, algorithms and an application. Business administration. Université de Technologie de Troyes; Universidade federal de Minas Gerais, 2017. English. ⟨NNT : 2017TROY0026⟩. ⟨tel-02421538⟩



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