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E-raamat: Graph-related Optimization and Decision Support Systems

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  • Ilmumisaeg: 10-Sep-2014
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118984253
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Graph-related Optimization and Decision Support SystemsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 10-Sep-2014
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781118984253
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Constrained optimization is a challenging branch of operations research that aims to create a model which has a wide range of applications in the supply chain, telecommunications and medical fields. As the problem structure is split into two main components, the objective is to accomplish the feasible set framed by the system constraints. The aim of this book is expose optimization problems that can be expressed as graphs, by detailing, for each studied problem, the set of nodes and the set of edges. This graph modeling is an incentive for designing a platform that integrates all optimization components in order to output the best solution regarding the parameters' tuning. The authors propose in their analysis, for optimization problems, to provide their graphical modeling and mathematical formulation and expose some of their variants. As a solution approaches, an optimizer can be the most promising direction for limited-size instances. For large problem instances, approximate algorithms are the most appropriate way for generating high quality solutions. The authors thus propose, for each studied problem, a greedy algorithm as a problem-specific heuristic and a genetic algorithm as a metaheuristic.

List of Tables
xi
List of Figures
xiii
List of Algorithms
xvii
Introduction xix
Chapter 1 Basic Concepts in Optimization and Graph Theory
1(12)
1.1 Introduction
1(1)
1.2 Notation
2(1)
1.3 Problem structure and variants
2(2)
1.4 Features of an optimization problem
4(1)
1.5 A didactic example
5(1)
1.6 Basic concepts in graph theory
6(6)
1.6.1 Degree of a graph
7(1)
1.6.2 Matrix representation of a graph
7(1)
1.6.3 Connected graphs
8(1)
1.6.4 Itineraries in a graph
8(1)
1.6.5 Tree graphs
9(2)
1.6.6 The bipartite graphs
11(1)
1.7 Conclusion
12(1)
Chapter 2 Knapsack Problems
13(18)
2.1 Introduction
13(1)
2.2 Graph modeling of the knapsack problem
14(1)
2.3 Notation
14(1)
2.4 0-1 knapsack problem
15(1)
2.5 An example
16(1)
2.6 Multiple knapsack problem
17(2)
2.6.1 Mathematical model
17(1)
2.6.2 An example
18(1)
2.7 Multidimensional knapsack problem
19(2)
2.7.1 Mathematical model
19(1)
2.7.2 An example
20(1)
2.8 Quadratic knapsack problem
21(2)
2.8.1 Mathematical model
22(1)
2.8.2 An example
22(1)
2.9 Quadratic multidimensional knapsack problem
23(2)
2.9.1 Mathematical model
24(1)
2.9.2 An example
24(1)
2.10 Solution approaches for knapsack problems
25(3)
2.10.1 The greedy algorithm
25(1)
2.10.2 A genetic algorithm for the KP
26(2)
2.11 Conclusion
28(3)
Chapter 3 Packing Problems
31(20)
3.1 Introduction
31(1)
3.2 Graph modeling of the bin packing problem
32(1)
3.3 Notation
33(1)
3.4 Basic bin packing problem
33(3)
3.4.1 Mathematical modeling of the BPP
34(1)
3.4.2 An example
35(1)
3.5 Variable cost and size BPP
36(1)
3.5.1 Mathematical model
36(1)
3.5.2 An example
37(1)
3.6 Vector BPP
37(3)
3.6.1 Mathematical model
38(1)
3.6.2 An example
39(1)
3.7 BPP with conflicts
40(2)
3.7.1 Mathematical model
40(1)
3.7.2 An example
41(1)
3.8 Solution approaches for the BPP
42(6)
3.8.1 The next-fit strategy
42(1)
3.8.2 The first-fit strategy
43(1)
3.8.3 The best-fit strategy
44(1)
3.8.4 The minimum bin slack
44(2)
3.8.5 The minimum bin slack'
46(1)
3.8.6 The least loaded heuristic
46(1)
3.8.7 A genetic algorithm for the bin packing problem
47(1)
3.9 Conclusion
48(3)
Chapter 4 Assignment Problem
51(18)
4.1 Introduction
51(1)
4.2 Graph modeling of the assignment problem
52(1)
4.3 Notation
52(1)
4.4 Mathematical formulation of the basic AP
53(2)
4.4.1 An example
54(1)
4.5 Generalized assignment problem
55(2)
4.5.1 An example
56(1)
4.6 The generalized multiassignment problem
57(2)
4.6.1 An example
58(1)
4.7 Weighted assignment problem
59(1)
4.8 Generalized quadratic assignment problem
60(1)
4.9 The bottleneck GAP
61(1)
4.10 The multilevel GAP
61(1)
4.11 The elastic GAP
62(1)
4.12 The multiresource GAP
63(1)
4.13 Solution approaches for solving the AP
64(3)
4.13.1 A greedy algorithm for the AP
64(1)
4.13.2 A genetic algorithm for the AP
65(2)
4.14 Conclusion
67(2)
Chapter 5 The Resource Constrained Project Scheduling Problem
69(14)
5.1 Introduction
69(1)
5.2 Graph modeling of the RCPSP
70(1)
5.3 Notation
71(1)
5.4 Single-mode RCPSP
72(3)
5.4.1 Mathematical modeling of the SM-RCPSP
73(1)
5.4.2 An example of an SM-RCPSP
74(1)
5.5 Multimode RCPSP
75(1)
5.6 RCPSP with time windows
75(1)
5.7 Solution approaches for solving the RCPSP
76(6)
5.7.1 A greedy algorithm for the RCPSP
76(1)
5.7.2 A genetic algorithm for the RCPSP
77(5)
5.8 Conclusion
82(1)
Chapter 6 Spanning Tree Problems
83(30)
6.1 Introduction
83(1)
6.2 Minimum spanning tree problem
84(4)
6.2.1 Notation
84(1)
6.2.2 Mathematical formulation
84(1)
6.2.3 Algorithms for the MST problem
85(3)
6.3 Generalized minimum spanning tree problem
88(12)
6.3.1 Notation
90(1)
6.3.2 Mathematical formulation
90(3)
6.3.3 Greedy approaches for the GMST problem
93(3)
6.3.4 Genetic algorithm for the GMST problem
96(4)
6.4 k-cardinality tree problem KCT
100(6)
6.4.1 Problem definition
100(1)
6.4.2 An example
100(2)
6.4.3 Notation
102(1)
6.4.4 Mathematical formulation
103(1)
6.4.5 Greedy approaches for the k-cardinality tree problem
103(1)
6.4.6 Minimum path approach
104(1)
6.4.7 A genetic approach for the k-cardinality problem
105(1)
6.5 The capacitated minimum spanning tree problem
106(6)
6.5.1 Problem definition
106(1)
6.5.2 Notation
107(1)
6.5.3 An example
107(1)
6.5.4 Solution approaches for the CMST problem
108(4)
6.6 Conclusion
112(1)
Chapter 7 Steiner Problems
113(12)
7.1 Introduction
113(1)
7.2 The Steiner tree problem
114(4)
7.2.1 Problem definition
114(1)
7.2.2 Problem formulation
115(1)
7.2.3 Constructive heuristics for the Steiner tree problem
115(3)
7.3 The price collecting Steiner tree problem
118(5)
7.3.1 Problem definition
118(1)
7.3.2 Example
118(1)
7.3.3 Mathematical formulation
118(2)
7.3.4 A greedy approach to solve the PCSTP
120(1)
7.3.5 A genetic algorithm for the PCSTP
121(2)
7.4 Conclusion
123(2)
Chapter 8 A DSS Design for Optimization Problems
125(20)
8.1 Introduction
125(1)
8.2 Definition of a DSS
126(1)
8.3 Taxonomy of a DSS
127(1)
8.4 Architecture and design of a DSS
128(3)
8.4.1 Architecture of a DSS
129(1)
8.4.2 DSS design
130(1)
8.5 A DSS for the knapsack problem
131(2)
8.6 A DSS for the DCVRP
133(10)
8.6.1 Statement and modeling of the CVRP
136(1)
8.6.2 Notation
137(1)
8.6.3 Mathematical formulation of the DCVRP
138(1)
8.6.4 DCVRP-DSS interfaces
139(2)
8.6.5 A real application: the case of Tunisia
141(2)
8.7 Conclusion
143(2)
Conclusion 145(2)
Glossary 147(2)
Bibliography 149(6)
Index 155
Saoussen Krichen, LARODEC Laboratory and Faculty of Law, Economics and Management, University of Jendouba, Tunisia.

Jouhaina Chaouachi, IHEC Carthage, Tunisia.
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