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Behnam Malakooti, Ph.D., P.E.
 

Multiple Objective Nonlinear and Artificial Neural Network Optimization

Behnam Malakooti

Brief Table Of Contents Detailed Table Of Contents

  • Part I. Multiple Objective Linear Programming with Nonlinear Multiple Criteria Utility Functions

    • Chapter 1 Exploring Efficient Facets of Multiple Objective Linear Programming: Interactive Quasi-Concave Utility Functions

      • An Exact Interactive Paired Comparison Method for Exploring the Efficient Facets of MOLP Problems with Underlying Quasi-Concave Utility Functions (39)
      • 1. Abstract
      • 2. Introduction
      • 3. Identification of Efficient Trade-Off Vectors for Nonlinear Utility Functions and Interactive Multiple Objective Linear Programming Methods: Exploring Efficient Facets
        • 3.1. MOLP Problems and Efficiency Definition
        • 3.2. Trade-Off Efficiency Definitions
        • 3.3. Identification of Efficient Trade-Off When the Alternative is on an Efficient Facet
        • 3.4. An Algorithm for Identifying Efficient Trade-Off with Respect to a Given Set of Constraints
      • 4. Some Theory for Quasi-Concave Utility Functions and Multiple Objective Linear Programming Problems for Convergence and Reducing the Number of Questions
        • 4.1. Sufficient Conditions for Optimality with Quasi-Concave and Pseudo-Concave Functions
        • 4.2. Optimality with Limited Number of Responses
        • 4.3. Generation of Partial Information Using 1-D Search Information and Trade-Offs
        • 4.4. Generation and Use of Partial Information (Utility Efficiency) for Trade-Offs
      • 5. An Interactive Trade-Off and Paired Comparison Method
        • 5.1. Divisions of Variables into Basic and Nonbasic Variables and Calculations
        • 5.2. Graphical Representation of the 1-D Search
        • 5.3. Notations and the General Strategy for the Interactive Algorithm
        • 5.4. The Interactive Algorithm
      • 6. Experiments with the Method
      • 7. Conclusions
      • 8. Appendix A. An Example for the Interactive Method
      • 9. Appendix B. A Critique of Some Well-Known Interactive Methods
      • 10. Appendix C. A Critique of the Zionts and Wallenius Trade-Off Efficiency Test and Interactive Methods
      • 11. References

    • Chapter 2 A Heuristic Interactive Method and Two Point Cones for Quasi-Concave Utility Functions and Quick Ranking Methods

      • A Decision Support System and a Heuristic Interactive Approach for Solving Discrete Multiple Criteria Problems (40)
      • 1. Introduction
      • 2. Two-Point Cones
        • 2.1. Clustering of Alternatives
        • 2.2. A Projection Approach for Finding Shadow Points
        • 2.3. A Procedure for Selecting Good Candidates
      • 3. Procedures for a Gradient-Based Approach
        • 3.1. Some Theory for the Approximation of the Gradient Through Paired Comparison Questions
        • 3.2. A Heuristic Method for Generating Local Adjacent Points
        • 3.3. A Procedure for Assisting Weights of Gradient by Strength of Preferences
        • 3.4. A Heuristic Method for Gradient Cuts
        • 3.5. A Heuristic Method for Generating Alternatives for the One-Dimensional Search
      • 4. A Gradient-Based Interactive Paired Comparison Approach
      • 5. Computational Experiments with the Method and Comparison to Other Methods
        • 5.1. Computational Experiences
        • 5.2. Comparison to Analytic Hierarchy Process
      • 6. A Decision Support System for Ranking Discrete Alternatives
        • 6.1. Quick Ranking by Lexicographic Ordering (Q-RALO)
        • 6.2. Quick Ranking by Identification of Trial Alternatives (Q-RITA)
        • 6.3. Quick Ranking by Assessment of Weights (Q-RAW)
        • 6.4. Ranking Alternatives with Strength of Preference (RASP)
        • 6.5. Gradient-Based Alternative Selection Procedure (GASP)
        • 6.6. Gradient-Based Unbound Search Technique (GUST)
      • 7. Conclusion
      • 8. Appendix (An Example)
      • 9. References

    • Chapter 3 Decision Support System for Multiple Criteria Decision Making and Hierarchical Problems

      • A Decision Support System for Solving Discrete Multi-Criteria Problems under Certainty and Uncertainty; and Hierarchical Systems (22)
      • 1. Abstract
      • 2. Introduction
      • 3. Data Entry, Assessment, and Summary
        • 3.1. Assessment of Single-Attribute Value Functions by the DM
        • 3.2. Statistics and Matrix of Extreme Values
      • 4. Screening Methods
        • 4.1. Efficiency (Nondominancy)
        • 4.2. Reference Efficiency (Reference Nondominancy)
        • 4.3. Convex Efficiency
        • 4.4. Bounds on Criteria (Objective) Values
        • 4.5. Bounds on Criteria (Objective) Weights
        • 4.6. Ranking of Objective Weights
      • 5. Complete Ranking Methods
        • 5.1. Simple Utility Function Forms for Trial and Error Approach
        • 5.2. Assessment of Additive Utility Functions
        • 5.3. Concave and Convex Quadratic Utility Functions
        • 5.4. Artificial Neural Network Utility Functions
        • 5.5. Consistency and Sensitivity Analysis
      • 6. Finding the Best Alternative (Interactive Methods)
        • 6.1. Quasi-Concave Utility Functions: A Gradient-Based Alternative Selection Procedure
        • 6.2. Quasi-Convex Utility Functions
        • 6.3. Unknown Nonlinear Utility Functions: A Gradient-Based Unbounded Search Technique
      • 7. Extension to Problems under Uncertainty
      • 8. Solving Discrete Pay-Off Matrix (One Criterion)
      • 9. Solving Discrete MCDM Problems Under Uncertainty
      • 10. Hierarchical and Large-Scale Multi-Criteria Problems
      • 11. Results of Some Experiments and a Guide to use the Package
        • 11.1. Experimental Results and Discussions
        • 11.2. A Guide to Choose Appropriate Methods
      • 12. Conclusions
      • 13. References

    • Chapter 4 An Interactive Multiple Objective Linear Programming Paired Comparison Method with Interactive Quasi-Convex Utility Functions

      • Extremist vs. Centrist Decision Behavior: Quasi-Convex Utility Functions for Interactive Multi-Objective Linear Programming Problems (5)
      • 1. Introduction
      • 2. Basic Definitions and Theories
      • 3. The Interactive Branch and Bound algorithm
        • 3.1. Overview
        • 3.2. Steps of the Algorithm and its Convergence
        • 3.3. Implementation issues
      • 4. Some Examples and Computational Experiments
        • 4.1. Example 1
        • 4.2. Implementation and Computational Experiments
      • 5. Conclusions
      • 6. References

    • Chapter 5 Unified Quasi-Concave and Quasi-Convex for Interactive Multiple Objective Linear Programming

      • An Integrated Multiobjective Approach for Quasi Concave/Quasi Convex Utility Functions (21)
      • 1. Abstract
      • 2. Introduction
      • 3. The Interactive Integrated Approach
        • 3.1. The Steps of the Approach
        • 3.2. Utility Class Test
      • 4. The Quasi Concave Utility-Based Interactive Multiobjective Algorithm
        • 4.1. The Steps of the Algorithm
        • 4.2. The Interactive Termination Criterion
      • 5. Example of the Quasi Concave Algorithm
      • 6. Quasi Convex Utility-Based Multi-Objective Algorithms: A Brief Summary
      • 7. Conclusions
      • 8. References

  • Part II. Artificial Neural Networks

    • Chapter 6 Adaptive Feedforward Artificial Neural Network Multiple Criteria Decision Making

      • An Adaptive Feedforward Artificial Neural Network with Application to Multiple Criteria Decision Making (16)
      • 1. Introduction
      • 2. An Adaptive Feedforward Artificial Neural Network Algorithm
        • 2.1. Some Notation and Basic Concepts
        • 2.2. Adaptive Strategy Algorithm to Find the AF-ANN Topology
      • 3. The Basic Properties of Multiple Criteria Decision Making with Adaptive Feedforward Artificial Neural Networks
        • 3.1. Basic Concepts Related to Multiple Criteria Decision Making
        • 3.2. Concave or Convex AF-ANNs
      • 4. An Approach to Training Adaptive Feedforward Artificial Neural Networks and Ranking Discrete Multiple Criteria Alternatives
      • 5. Computational Experiments with Adaptive Feedforward Artificial Neural Networks for Discrete Multiple Criteria Decision Making Problems
      • 6. Conclusions and Discussion
      • 7. Appendix A. Proofs for Propositions
      • 8. Appendix B. A Flexible Learning Algorithm to Assess Parameters of a Given AF-ANN Topology
      • 9. References

    • Chapter 7 Approximating Polynomial Multiple Criteria Utility Functions by Feedforward Artificial Neural Networks

      • Approximating Polynomial Functions by Feedforward Artificial Neural Networks: Capacity, Analysis, and Design (11)
      • 1. Abstract
      • 2. Introduction
      • 3. Capacity of Feedforward Artificial Neural Networks in Approximating Polynomials
      • 4. A Method to Realize Feedforward Artificial Neural Networks in Approximating Polynomial Functions
      • 5. Training Algorithm and Computational Examples
      • 6. Conclusions
      • 7. References

  • Part III. Generalized Polynomial Multiple Criteria Utility Functions

    • Chapter 8 Generalized Decomposable Multiple Attribute Utility Functions

      • A Generalized Decomposable Multi-Attribute Utility Function (29)
      • 1. Abstract
      • 2. Introduction
      • 3. A Generalized Decomposable Multi-Attribute Utility Function
        • 3.1. Organization
      • 4. Some Extensions of the Generalized Decomposable Multi-Attribute Utility Function
        • 4.1. Class A: Additive, Multiplicative, and Multilinear MAUFs
        • 4.2. Class B: A Separable GDMAUF (or Generalized Additive MAUF)
        • 4.3. Class C: A Partitionable GDMAUF
      • 5. Some Properties of the Generalized Decomposable Multi-Attribute Utility Function
        • 5.1. Existence and Assessment of Global Bounds
        • 5.2. Ranking by Assessment of Weights at a Given Alternative
      • 6. Ranking with Partial Information on the Weights: Utility Efficiency
        • 6.1. Definitions for Ranking
        • 6.2. An Inspection Procedure for Ranking for Any Known MAUF Structure
      • 7. Conclusions
      • 8. Appendix A. Multilinear MAUF as a Special Case of the GDMAUF
      • 9. Appendix B. Examples for the Assessment of Global Weights for the Generalized Decomposable MAUF
      • 10. References

    • Chapter 9 Decomposable Polynomial Multiple Criteria Utility Functions

      • Generalized Polynomial Decomposable Multiple Attribute Utility Functions For Ranking and Rating of Alternatives (10)
      • 1. Introduction
      • 2. A Generalized Decomposable Multi-Attribute Utility Function
      • 3. Properties and Types of the Generalized Decomposable Multi-Attribute Utility Function
      • 4. A New Holistic Method to Assess the Gradient of a Utility Function
      • 5. An Interactive Procedure to Assess the Generalized Decomposable Multi-Attribute Utility Function and Rank the Discrete Alternatives
      • 6. Computational Experiments
      • 7. Conclusions
      • 8. Appendix A. Examples for Demonstrating a New Holistic Method to Assess the Gradient of a Utility Function
      • 9. Appendix B. An Example for an Interactive Procedure to Assess the GDMAUF and Rank the Discrete Alternatives
      • 10. Appendix C. List of Utility Functions Used for Computational Experiments
      • 11. References