Applications of combinatorial optimization
Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aim to cover a wide range of topics in this area. These to...
Saved in:
| Main Author: | |
|---|---|
| Format: | eBook Book |
| Language: | English |
| Published: |
London
ISTE
2014
Hoboken, N.J John Wiley Wiley John Wiley & Sons, Incorporated Wiley-Blackwell |
| Edition: | 2 |
| Series: | Combinatorial optimization |
| Subjects: | |
| ISBN: | 1848216580, 9781848216587, 9781119015246, 1119015243 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 5.4.1. Service network design -- 5.4.2. Static formulations -- 5.4.3. Dynamic formulations -- 5.4.4. Fleet management -- 5.5. Vehicle routing problems -- 5.5.1. Definitions and complexity -- 5.5.2. Classical extensions -- 5.6. Exact models and methods for the VRP -- 5.6.1. Flow model with three indices -- 5.6.2. Flow model for the symmetric CVRP -- 5.6.3. Set partitioning model -- 5.6.4. Branch-and-cut methods for the CVRP -- 5.6.4.1. Valid inequalities -- 5.6.4.2. Branching methods -- 5.6.5. Column generation methods for the VRPTW -- 5.7. Heuristic methods for the VRP -- 5.7.1. Classical heuristics -- 5.7.1.1. Constructive methods -- 5.7.1.2. Two-phase methods -- 5.7.1.3. Improvement methods -- 5.7.2. Metaheuristics -- 5.7.2.1. Metaheuristics for the CVRP and the CVRPLC -- 5.7.2.1.1. Methods based on Tabu search -- 5.7.2.1.2. Methods based on genetic algorithms -- 5.7.2.2. Metaheuristics for the VRPTW -- 5.7.2.2.1. Methods based on Tabu search -- 5.7.2.2.2. Methods based on evolutionary algorithms -- 5.7.2.2.3. Other approaches -- 5.7.3. The VRP in practice -- 5.8. Conclusion -- 5.9. Appendix: metaheuristics -- 5.9.1. Tabu search -- 5.9.2. Evolutionary algorithms -- 5.10. Bibliography -- Chapter 6: Optimization Models for Transportation Systems Planning -- 6.1. Introduction -- 6.2. Spatial interaction models -- 6.3. Traffic assignment models and methods -- 6.3.1. System optimization and user optimization models -- 6.3.2. Algorithms for traffic assignment for the user optimization model -- 6.3.2.1. Cyclic decomposition of the O-D with path balancing -- 6.3.2.2. Linear approximation method -- 6.3.3. The user problem as variational inequality -- 6.3.3.1. Projection method for FD-UVI -- 6.3.3.2. Simplicial decomposition for FD-UVI -- 6.4. Transit route choice models -- 6.5. Strategic planning of multimodal systems -- 6.5.1. Demand -- 6.5.2. Mode choice
- Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1: Airline Crew Pairing Optimization -- 1.1. Introduction -- 1.2. Definition of the problem -- 1.2.1. Constructing subnetworks -- 1.2.2. Pairing costs -- 1.2.3. Model -- 1.2.4. Case without resource constraints -- 1.3. Solution approaches -- 1.3.1. Decomposition principles -- 1.3.2. Column generation, master problem and subproblem -- 1.3.3. Branching methods for finding integer solutions -- 1.4. Solving the subproblem for column generation -- 1.4.1. Mathematical formulation -- 1.4.2. General principle of effective label generation -- 1.4.3. Case of one single resource: the bucket method -- 1.4.4. Case of many resources: reduction of the resource space -- 1.4.4.1. Reduction principle -- 1.4.4.2. Approach based on the Lagrangian relaxation -- 1.4.4.3. Approach based on the surrogate relaxation -- 1.5. Conclusion -- 1.6. Bibliography -- Chapter 2: The Task Allocation Problem -- 2.1. Presentation -- 2.2. Definitions and modeling -- 2.2.1. Definitions -- 2.2.2. The processors -- 2.2.3. Communications -- 2.2.4. Tasks -- 2.2.5. Allocation types -- 2.2.5.1. Static allocation -- 2.2.5.2. Dynamic allocation -- 2.2.5.3. With or without pre-emption -- 2.2.5.4. Task duplication -- 2.2.6. Allocation/scheduling -- 2.2.7. Modeling -- 2.2.7.1. Modeling costs -- 2.2.7.2. Constraints -- 2.2.7.3. Objectives of the allocation -- 2.2.7.3.1. Minimizing the execution duration -- 2.2.7.3.2. Minimizing the global execution and communication cost -- 2.2.7.3.3. Load balancing -- 2.3. Review of the main works -- 2.3.1. Polynomial cases -- 2.3.1.1. Two-processor cases -- 2.3.1.2. Tree case -- 2.3.1.3. Other structures -- 2.3.1.4. Restrictions on the processors or the tasks -- 2.3.1.5. Minmax objective -- 2.3.2. Approximability -- 2.3.3. Approximate solution -- 2.3.3.1. Heterogenous processors
- 8.1. Impact of parallelism in combinatorial optimization -- 8.2. Parallel metaheuristics -- 8.2.1. Notion of walks -- 8.2.2. Classification of parallel metaheuristics -- 8.2.3. An illustrative example: scatter search for the quadratic assignment or QAP -- 8.3. Parallelizing tree exploration in exact methods -- 8.3.1. Return to two success stories -- 8.3.2. B& -- X model and data structures -- 8.3.3. Different levels of parallelism -- 8.3.4. Critical tree and anomalies -- 8.3.5. Parallel algorithms and granularity -- 8.3.6. The BOB++ library -- 8.3.7. B& -- X on grids of machines -- 8.4. Conclusion -- 8.5. Bibliography -- Chapter 9: Network Design Problems: Fundamental Methods -- 9.1. Introduction -- 9.2. The main mathematical and algorithmic tools for network design -- 9.2.1. Decomposition in linear programming and polyhedra -- 9.2.2. Flows and multiflows -- 9.2.3. Queuing network -- 9.2.4. Game theory models -- 9.3. Models and problems -- 9.3.1. Location problems -- 9.3.2. Steiner trees and variants -- 9.4. The STEINER-EXTENDED problem -- 9.5. Conclusion -- 9.6 Bibliography -- Chapter 10: Network Design Problems: Models and Applications -- 10.1. Introduction -- 10.2. Models and location problems -- 10.2.1. Locating the network access device -- 10.2.2. Locating machines and activities at the core of a production space -- 10.3. Routing models for telecommunications -- 10.3.1. Numerical tests -- 10.4. The design or dimensioning problem in telecommunications -- 10.4.1. Numerical tests -- 10.5. Coupled flows and multiflows for transport and production -- 10.5.1. Analysis of the COUPLED-FLOW-MULTIFLOW (CFM) problem -- 10.6. A mixed network pricing model -- 10.7. Conclusion -- 10.8. Bibliography -- Chapter 11: Multicriteria Task Allocation to Heterogenous Processors with Capacity and Mutual Exclusion Constraints
- 6.5.3. Representing transport supply and assigning demand -- 6.6. Conclusion -- 6.7. Bibliography -- Chapter 7: A Model for the Design of a Minimum-cost Telecommunications Network -- 7.1. Introduction -- 7.2. Minimum cost network construction -- 7.2.1. The difficulties of solving jointly or globally -- 7.2.1.1. Preliminaries: a few telecommunications fundamentals -- 7.2.1.2. Difficulties: integrity and strong non-linearity -- 7.2.1.2.1. Objective function part -- 7.2.1.2.2. Decision variables part -- 7.2.1.2.3. Restrictions -- 7.2.2. Why tackle the global problem? -- 7.2.3. How to circumvent these difficulties -- 7.2.3.1. Separating the problems -- 7.2.3.2. From transmission to switching -- 7.2.3.3. Size of the multiflow problem relative to beams -- 7.3. Mathematical model, general context -- 7.3.1. Hypotheses -- 7.3.1.1. The costs -- 7.3.1.2. Dimensioning -- 7.3.1.3. Constraints -- 7.3.1.4. Distribution of traffic -- 7.3.2. The original problem -- 7.3.3. Solution principle -- 7.3.3.1. The beams network -- 7.3.3.2. Reduction of the problem -- 7.3.3.3. The multiflow problem -- 7.3.3.4. Global solution -- 7.4. Proposed algorithm -- 7.4.1. A bit of sensitivity in an NP-hard world -- 7.4.2. The initial solution -- 7.4.3. Step-by-step exploration -- 7.4.3.1. The idea -- 7.4.3.2. Details of a cycle -- 7.4.3.2.1. First strategy -- 7.4.3.2.2. Second strategy -- 7.4.3.2.3. Evaluation -- 7.4.3.3. Global management of the exploration -- 7.5. Critical points -- 7.5.1. Parametric difficulties -- 7.5.2. Realities not taken into account -- 7.5.2.1. Traffic dispersion -- 7.5.2.2. Distorted dimensioning -- 7.5.3. Complexity in size of the problem -- 7.5.3.1. When beams and edges coincide -- 7.5.3.2. Size of the multiflow problem relative to the edges -- 7.6. Conclusion -- 7.7. Bibliography -- Chapter 8: Parallel Combinatorial Optimization
- 11.1. Introduction and formulation of the problem
- 2.3.3.2. Homogenous processors -- 2.3.4. Exact solution -- 2.3.5. Independent tasks case -- 2.4. A little-studied model -- 2.4.1. Model -- 2.4.2. A heuristic based on graphs -- 2.4.2.1. Transformation of the problem -- 2.4.2.2. Modeling -- 2.4.2.3. Description of the heuristic -- 2.5. Conclusion -- 2.6. Bibliography -- Chapter 3: A Comparison of Some Valid Inequality Generation Methods for General 0-1 Problems -- 3.1. Introduction -- 3.2. Presentation of the various techniques tested -- 3.2.1. Exact separation with respect to a mixed relaxation -- 3.2.2. Approximate separation using a heuristic -- 3.2.3. Restriction + separation + relaxed lifting (RSRL) -- 3.2.4. Disjunctive programming and the lift and project procedure -- 3.2.5. Reformulation-linearization technique (RLT) -- 3.3. Computational results -- 3.3.1. Presentation of test problems -- 3.3.2. Presentation of the results -- 3.3.3. Discussion of the computational results -- 3.4. Bibliography -- Chapter 4: Production Planning -- 4.1. Introduction -- 4.2. Hierarchical planning -- 4.3. Strategic planning and productive system design -- 4.3.1. Group technology -- 4.3.2. Locating equipment -- 4.4. Tactical planning and inventory management -- 4.4.1. A linear programming model for medium-term planning -- 4.4.2. Inventory management -- 4.4.3. Wagner and Whitin model -- 4.4.4. The economic order quantity model (EOQ) -- 4.4.5. The EOQ model with joint replenishments -- 4.5. Operations planning and scheduling -- 4.5.1. Tooling -- 4.5.2. Robotic cells -- 4.6. Conclusion and perspectives -- 4.7. Bibliography -- Chapter 5: Operations Research and Goods Transportation -- 5.1. Introduction -- 5.2. Goods transport systems -- 5.3. Systems design -- 5.3.1. Location with balancing requirements -- 5.3.2. Multiproduct production-distribution -- 5.3.3. Hub location -- 5.4. Long-distance transport