A study of problems with multiple interdependent components - Part I

by   Mohamed El Yafrani, et al.

Recognising that real-world optimisation problems have multiple interdependent components can be quite easy. However, providing a generic and formal model for dependencies between components can be a tricky task. In fact, a PMIC can be considered simply as a single optimisation problem and the dependencies between components could be investigated by studying the decomposability of the problem and the correlations between the sub-problems. In this work, we attempt to define PMICs by reasoning from a reverse perspective. Instead of considering a decomposable problem, we model multiple problems (the components) and define how these components could be connected. In this document, we introduce notions related to problems with mutliple interndependent components. We start by introducing realistic examples from logistics and supply chain management to illustrate the composite nature and dependencies in these problems. Afterwards, we provide our attempt to formalise and classify dependency in multi-component problems.



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This document contains the first part of my Ph.D. dissertation. This work have been prepared within the laboratory of research in computer science and telecommunications (LRIT) at Mohammed V University under the supervision of Pr. Belaïd Ahiod. This thesis was defended on 14 September 2018, before the following board members:

  • Abdelhakim Ameur El Imrani, Jury president, Professor, Mohammed V University in Rabat

  • Salma Mouline, Reporter, Professor, Mohammed V University in Rabat

  • Mohamed Ouzineb, Examiner, Habilitated professor, INSEA

  • Markus Wagner, Reporter, Senior Lecturer, The University of Adelaide

  • Myriam Delgado, Examiner, Professor, Federal University of Technology of Paraná

  • Belaïd Ahiod, Advisor, Habilitated professor, Mohammed V University in Rabat

Contributors to part I:
Belaïd Ahiod, Mohammed V University in Rabat
Mohammad Reza Bonyadi, Rio Tinto




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