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Table of contents
Chapitre 1 State-of-the-Art
1.1 Cloud Computing
1.2 Scheduling problems
1.3 Computational complexity
1.4 Heuristics and meta-heuristics
1.4.1 Heuristics
1.4.2 Metaheuristics
Genetic algorithm
1.5 Graph theory
1.6 Optimization problems
1.6.1 Combinatorial optimization
1.6.2 Linear programming
1.6.3 Integer programming
1.7 Polyhedral approach
1.7.1 Elements of polyhedral theory
1.7.2 Cutting plane methods
1.8 Branch and cut algorithm
Chapitre 2 Heuristics and Meta-heuristics Solutions
2.1 Introduction
2.1.1 Literature Review
2.2 Problem formulation
2.3 An existing algorithm
2.4 Genetic algorithm (GA)
2.4.1 Modeling the problem using Genetic Algorithm
Task Scheduling Genetic Algorithm (GATS)
Genetic Algorithm Based on Cut-point (GACP)
Genetic Algorithm Based on The List of Available Jobs (GAAV)
Genetic Algorithm (GAAV +)
Experimental Results
Integral Linear Programming Solution (ILP)
Transformations Between Genetic Algorithms
Conclusion
Chapitre 3 Mathematical Formulations
3.1 Introduction
3.2 Problem Description
3.3 Mathematical Formulations
3.3.1 Classical Formulation
3.3.2 Flow Formulation
3.3.3 Order Formulation
3.3.4 Interval Graph Formulation
3.4 Valid Inequalities
3.4.1 Separation Algorithm for SPT Inequality
3.4.2 Reformulation of Interval Graph Formulation
3.5 Experimental Results
3.5.1 Conclusion
Chapitre 4 Polyedral study on interval graphs under m-clique free constraints
4.1 Introduction
4.2 The polytopes of interval sub-graphs
4.2.1 Forbidden subgraphs inequalities
Bipartite Claw
Umbrella Inequalities
n-net Inequalities
n-tent Inequalities
Hole inequalities
Clique inequalities
Clique-Hole inequalities
4.3 Cutting plane algorithms
4.3.1 Bipartite claw separation
Exact Separation (ExBC-Sep)
Heuristic1 : Separation (H1BC-Sep)
Heuristic 2 : Separation (H2BC-Sep)
4.3.2 Umbrella separation
Exact separation algorithm
H1U-Sep separation
H2U-Sep Separation
n-net separation
n-tent separation
4.3.3 Hole separation
4.3.4 Clique separation
4.3.5 Lazy constraint approach
4.4 Application to URPMDC problem
4.4.1 Mathematical formulation
4.4.2 Computational Results
4.5 Conclusion
Chapitre 5 Generalized Open Shop, and Open Shop Problems
5.1 Introduction
5.2 Generalized open shop problem with jobs disjunctive constraints
5.2.1 Integer linear programming formulation
5.2.2 Valid inequalities
Sequence inequalities
Previous job inequalities
Line job inequalities
Logical implication inequalities
5.2.3 Experimental results
5.3 Open shop problem
5.3.1 Integer linear programming formulation
5.3.2 Valid inequalities
Sequence inequalities
Previous operations inequalities
Logical implication inequalities
5.3.3 Experimental results
5.4 Conclusion
Chapitre 6 General Conclusion and Perspectives
Bibliographie
