A study of problems with multiple interdependent components - Part I

TL;DR

This paper explores formal models for problems with multiple interdependent components, focusing on how to define and classify dependencies by modeling components and their connections, with examples from logistics.

Contribution

It introduces a reverse perspective to model interdependent problems, formalizes dependency notions, and classifies multi-component problem dependencies.

Findings

Proposes a formal framework for modeling component dependencies.

Provides classification of dependency types in multi-component problems.

Uses real-world logistics examples to illustrate concepts.

Abstract

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.

Full text

** A study of problems with multiple interdependent components — Part I

 

Mohamed El Yafrani

**

Acknowledgement

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

Abstract

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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.

Keywords: Interdependence, Multi-component problems, Combinatorial optimisation.

part1

part2