Cover page -- Half-Title page -- Title page -- Copyright page -- Contents -- List of Tables -- List of Figures -- List of Algorithms -- Introduction -- 1: Basic Concepts in Optimization and Graph Theory -- 1.1. Introduction -- 1.2. Notation -- 1.3. Problem structure and variants -- 1.4. Features of an optimization problem -- 1.5. A didactic example -- 1.6. Basic concepts in graph theory -- 1.6.1. Degree of a graph -- 1.6.2. Matrix representation of a graph -- 1.6.3. Connected graphs -- 1.6.4. Itineraries in a graph -- 1.6.5. Tree graphs -- 1.6.6. The bipartite graphs -- 1.7. Conclusion -- 2: Knapsack Problems -- 2.1. Introduction -- 2.2. Graph modeling of the knapsack problem -- 2.3. Notation -- 2.4. 0-1 knapsack problem -- 2.5. An example -- 2.6. Multiple knapsack problem -- 2.6.1. Mathematical model -- 2.6.2. An example -- 2.7. Multidimensional knapsack problem -- 2.7.1. Mathematical model -- 2.7.2. An example -- 2.8. Quadratic knapsack problem -- 2.8.1. Mathematical model -- 2.8.2. An example -- 2.9. Quadratic multidimensional knapsack problem -- 2.9.1. Mathematical model -- 2.9.2. An example -- 2.10. Solution approaches for knapsack problems -- 2.10.1. The greedy algorithm -- 2.10.2. A genetic algorithm for the KP -- 2.10.2.1. Solution encoding -- 2.10.2.2. Crossover -- 2.10.2.3. Mutation -- 2.11. Conclusion -- 3: Packing Problems -- 3.1. Introduction -- 3.2. Graph modeling of the bin packing problem -- 3.3. Notation -- 3.4. Basic bin packing problem -- 3.4.1. Mathematical modeling of the BPP -- 3.4.2. An example -- 3.5. Variable cost and size BPP -- 3.5.1. Mathematical model -- 3.5.2. An example -- 3.6. Vector BPP -- 3.6.1. Mathematical model -- 3.6.2. An example -- 3.7. BPP with conflicts -- 3.7.1. Mathematical model -- 3.7.2. An example -- 3.8. Solution approaches for the BPP -- 3.8.1. The next-fit strategy -- 3.8.2. The first-fit strategy.

3.8.3. The best-fit strategy -- 3.8.4. The minimum bin slack -- 3.8.5. The minimum bin slack' -- 3.8.6. The least loaded heuristic -- 3.8.7. A genetic algorithm for the bin packing problem -- 3.8.7.1. Solution encoding -- 3.8.7.2. Crossover -- 3.8.7.3. Mutation -- 3.9. Conclusion -- 4: Assignment Problem -- 4.1. Introduction -- 4.2. Graph modeling of the assignment problem -- 4.3. Notation -- 4.4. Mathematical formulation of the basic AP -- 4.4.1. An example -- 4.5. Generalized assignment problem -- 4.5.1. An example -- 4.6. The generalized multiassignment problem -- 4.6.1. An example -- 4.7. Weighted assignment problem -- 4.8. Generalized quadratic assignment problem -- 4.9. The bottleneck GAP -- 4.10. The multilevel GAP -- 4.11. The elastic GAP -- 4.12. The multiresource GAP -- 4.13. Solution approaches for solving the AP -- 4.13.1. A greedy algorithm for the AP -- 4.13.2. A genetic algorithm for the AP -- 4.13.2.1. Solution encoding -- 4.13.2.2. Crossover -- 4.13.2.3. Mutation -- 4.14. Conclusion -- 5: The Resource Constrained Project Scheduling Problem -- 5.1. Introduction -- 5.2. Graph modeling of the RCPSP -- 5.3. Notation -- 5.4. Single-mode RCPSP -- 5.4.1. Mathematical modeling of the SM-RCPSP -- 5.4.2. An example of an SM-RCPSP -- 5.5. Multimode RCPSP -- 5.6. RCPSP with time windows -- 5.7. Solution approaches for solving the RCPSP -- 5.7.1. A greedy algorithm for the RCPSP -- 5.7.2. A genetic algorithm for the RCPSP -- 5.7.2.1. Chromosome encoding -- 5.7.2.2. Selection -- 5.7.2.3. Crossover -- 5.7.2.4. Mutation -- 5.8. Conclusion -- 6: Spanning Tree Problems -- 6.1. Introduction -- 6.2. Minimum spanning tree problem -- 6.2.1. Notation -- 6.2.2. Mathematical formulation -- 6.2.3. Algorithms for the MST problem -- 6.2.3.1. The Kruskal algorithm -- 6.2.3.2. The Prim algorithm -- 6.3. Generalized minimum spanning tree problem -- 6.3.1. Notation.

6.3.2. Mathematical formulation -- 6.3.3. Greedy approaches for the GMST problem -- 6.3.4. Genetic algorithm for the GMST problem -- 6.3.4.1. Encoding -- 6.3.4.2. Fitness -- 6.3.4.3. Crossover -- 6.3.4.4. Mutation -- 6.3.4.5. Parameters -- 6.4. k-cardinality tree problem KCT -- 6.4.1. Problem definition -- 6.4.2. An example -- 6.4.3. Notation -- 6.4.4. Mathematical formulation -- 6.4.5. Greedy approaches for the k-cardinality tree problem -- 6.4.5.1. The k-Prim approach and the dual-greedy algorithm -- 6.4.6. Minimum path approach -- 6.4.7. A genetic approach for the k-cardinality problem -- 6.5. The capacitated minimum spanning tree problem -- 6.5.1. Problem definition -- 6.5.2. Notation -- 6.5.3. An example -- 6.5.4. Solution approaches for the CMST problem -- 6.5.4.1. A greedy approach -- 6.5.4.2. Genetic algorithm for the CMST problem -- 6.5.4.2.1. Encoding -- 6.5.4.2.2. Fitness -- 6.5.4.2.3. Mutation -- 6.5.4.2.4. Parameters -- 6.6. Conclusion -- 7: Steiner Problems -- 7.1. Introduction -- 7.2. The Steiner tree problem -- 7.2.1. Problem definition -- 7.2.2. Problem formulation -- 7.2.3. Constructive heuristics for the Steiner tree problem -- 7.2.3.1. Shortest paths heuristic -- 7.2.3.2. Shortest distance heuristic -- 7.2.3.3. Arbitrary node insertion -- 7.2.3.4. Cheapest node insertion -- 7.2.3.5. Cheapest node insertion for all roots -- 7.3. The price collecting Steiner tree problem -- 7.3.1. Problem definition -- 7.3.2. Example -- 7.3.3. Mathematical formulation -- 7.3.4. A greedy approach to solve the PCSTP -- 7.3.5. A genetic algorithm for the PCSTP -- 7.3.5.1. Encoding -- 7.3.5.2. Fitness -- 7.3.5.3. Crossover -- 7.4. Conclusion -- 8: A DSS Design for Optimization Problems -- 8.1. Introduction -- 8.2. Definition of a DSS -- 8.3. Taxonomy of a DSS -- 8.4. Architecture and design of a DSS -- 8.4.1. Architecture of a DSS -- 8.4.2. DSS design.

8.5. A DSS for the knapsack problem -- 8.6. A DSS for the DCVRP -- 8.6.1. Statement and modeling of the CVRP -- 8.6.2. Notation -- 8.6.3. Mathematical formulation of the DCVRP -- 8.6.4. DCVRP-DSS interfaces -- 8.6.5. A real application: the case of Tunisia -- 8.7. Conclusion -- Conclusion -- Glossary -- Bibliography -- Index.