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Chapter 5 The characteristic equation for linear integer programs

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Linear Integer Programming
Ein Kapitel aus dem Buch Linear Integer Programming

Abstract

This chapter develops an innovative relation, called the characteristic equation (CE) for solving a pure integer program (PIP) and illustrates how the characteristic equation not only finds an optimal integer solution to a PIP but it also can find the ordered kth best, k ≥ 2 optimal solution, which is a feature not available to other approaches. The CE approach has been discussed for pure integer, binary integer, and mixed-integer models. A potential application of CE in context of a biobjective and multi-objective models has been pointed out.

Abstract

This chapter develops an innovative relation, called the characteristic equation (CE) for solving a pure integer program (PIP) and illustrates how the characteristic equation not only finds an optimal integer solution to a PIP but it also can find the ordered kth best, k ≥ 2 optimal solution, which is a feature not available to other approaches. The CE approach has been discussed for pure integer, binary integer, and mixed-integer models. A potential application of CE in context of a biobjective and multi-objective models has been pointed out.

Kapitel in diesem Buch

  1. Frontmatter I
  2. Acknowledgements VII
  3. Preface IX
  4. Contents XI
  5. About the authors XVII
  6. Chapter 1 Segment search approach for the general linear integer model 1
  7. Chapter 2 Improved solution method for the 0-1 GAP model 19
  8. Chapter 3 A search for an optimal integer solution over the integer polyhedron – Two iterative approaches 33
  9. Chapter 4 Use of variable sum limits to solve the knapsack problem 53
  10. Chapter 5 The characteristic equation for linear integer programs 65
  11. Chapter 6 Random search method for integer programming 95
  12. Chapter 7 Some special linear integer models and related problems 119
  13. Chapter 8 The travelling salesman problem: Sub-tour elimination approaches and algorithms 155
  14. Index 181
https://doi.org/10.1515/9783110703023-005

Kapitel in diesem Buch

  1. Frontmatter I
  2. Acknowledgements VII
  3. Preface IX
  4. Contents XI
  5. About the authors XVII
  6. Chapter 1 Segment search approach for the general linear integer model 1
  7. Chapter 2 Improved solution method for the 0-1 GAP model 19
  8. Chapter 3 A search for an optimal integer solution over the integer polyhedron – Two iterative approaches 33
  9. Chapter 4 Use of variable sum limits to solve the knapsack problem 53
  10. Chapter 5 The characteristic equation for linear integer programs 65
  11. Chapter 6 Random search method for integer programming 95
  12. Chapter 7 Some special linear integer models and related problems 119
  13. Chapter 8 The travelling salesman problem: Sub-tour elimination approaches and algorithms 155
  14. Index 181
Heruntergeladen am 11.5.2026 von https://www.degruyterbrill.com/document/doi/10.1515/9783110703023-005/html?lang=de
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