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Discrete Optimization with Interval Data

Minmax Regret and Fuzzy Approach

  • Book
  • © 2008

Overview

Authors:
  1. Adam Kasperski
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  • Novel research results in the field of Discrete Optimization with Interval Data
  • Presents a new approach (robust optimization) to modeling incomplete knowledge

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ)

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Table of contents (17 chapters)

  1. Front Matter

    Download chapter PDF

  2. Minmax Regret Combinatorial Optimization Problems with Interval Data

    1. Front Matter

      Pages 1-1
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    2. Problem Formulation

      • Adam Kasperski
      Pages 3-16

    3. Evaluation of Optimality of Solutions and Elements

      • Adam Kasperski
      Pages 17-30

    4. Exact Algorithms

      • Adam Kasperski
      Pages 31-38

    5. Approximation Algorithms

      • Adam Kasperski
      Pages 39-50

    6. Minmax Regret Minimum Selecting Items

      • Adam Kasperski
      Pages 51-60

    7. Minmax Regret Minimum Spanning Tree

      • Adam Kasperski
      Pages 61-79

    8. Minmax Regret Shortest Path

      • Adam Kasperski
      Pages 81-112

    9. Minmax Regret Minimum Assignment

      • Adam Kasperski
      Pages 113-120

    10. Minmax Regret Minimum s − t Cut

      • Adam Kasperski
      Pages 121-135

    11. Fuzzy Combinatorial Optimization Problem

      • Adam Kasperski
      Pages 137-153

    12. Conclusions and Open Problems

      • Adam Kasperski
      Pages 155-157

  3. Minmax Regret Sequencing Problems with Interval Data

    1. Front Matter

      Pages 159-159
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    2. Problem Formulation

      • Adam Kasperski
      Pages 161-165

    3. Sequencing Problem with Maximum Lateness Criterion

      • Adam Kasperski
      Pages 167-173

    4. Sequencing Problem with Weighted Number of Late Jobs

      • Adam Kasperski
      Pages 175-182

    5. Sequencing Problem with the Total Flow Time Criterion

      • Adam Kasperski
      Pages 183-195

    6. Conclusions and Open Problems

      • Adam Kasperski
      Pages 197-198

    7. Discrete Scenario Representation of Uncertainty

      • Adam Kasperski
      Pages 199-207
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Keywords

About this book

Operations research often solves deterministic optimization problems based on elegantand conciserepresentationswhereall parametersarepreciselyknown. In the face of uncertainty, probability theory is the traditional tool to be appealed for, and stochastic optimization is actually a signi?cant sub-area in operations research. However, the systematic use of prescribed probability distributions so as to cope with imperfect data is partially unsatisfactory. First, going from a deterministic to a stochastic formulation, a problem may becomeintractable. Agoodexampleiswhengoingfromdeterministictostoch- tic scheduling problems like PERT. From the inception of the PERT method in the 1950’s, it was acknowledged that data concerning activity duration times is generally not perfectly known and the study of stochastic PERT was launched quite early. Even if the power of today’s computers enables the stochastic PERT to be addressed to a large extent, still its solutions often require simplifying assumptions of some kind. Another di?culty is that stochastic optimization problems produce solutions in the average. For instance, the criterion to be maximized is more often than not expected utility. This is not always a meaningful strategy. In the case when the underlying process is not repeated a lot of times, let alone being one-shot, it is not clear if this criterion is realistic, in particular if probability distributions are subjective. Expected utility was proposed as a rational criterion from ?rst principles by Savage. In his view, the subjective probability distribution was - sically an artefact useful to implement a certain ordering of solutions.

Bibliographic Information

  • Book Title: Discrete Optimization with Interval Data

  • Book Subtitle: Minmax Regret and Fuzzy Approach

  • Authors: Adam Kasperski

  • Series Title: Studies in Fuzziness and Soft Computing

  • DOI: https://doi.org/10.1007/978-3-540-78484-5

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2008

  • Hardcover ISBN: 978-3-540-78483-8Published: 04 June 2008

  • Softcover ISBN: 978-3-642-09720-1Published: 23 November 2010

  • eBook ISBN: 978-3-540-78484-5Published: 06 April 2008

  • Series ISSN: 1434-9922

  • Series E-ISSN: 1860-0808

  • Edition Number: 1

  • Number of Pages: XVI, 220

  • Topics: Optimization, Mathematical and Computational Engineering, Artificial Intelligence

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