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Introduction to Multi-objective Optimization and Decision-Making Analysis

  • Mohammad Kiani-Moghaddam
  • Mojtaba Shivaie
  • Philip D. Weinsier
Chapter
Part of the Power Systems book series (POWSYS)

Abstract

In this chapter, the necessity of utilizing a multi-objective optimization process is rigorously elucidated. Afterwards, the fundamental concepts of optimization in multi-objective optimization problems are thoroughly described in five sections: (1) mathematical description of a multi-objective optimization problem; (2) concepts related to efficiency, efficient frontier, and dominance; (3) concepts relevant to Pareto optimality; (4) concepts associated with the vector of ideal objective functions and the vector of nadir objective functions; and (5) concepts pertaining to Pareto optimality investigation. In this chapter, the authors also provide an exhaustive classification of the multi-objective optimization algorithms by concentrating on the role of the decision maker in the solution process, which are then broken down into two approaches: (1) noninteractive and (2) interactive. Noninteractive approaches are further divided into four classes, including basic, no-preference, a priori, and a posteriori approaches. The fuzzy satisfying method is then extensively expressed in order to select the final optimal compromise solution from the Pareto-optimal solution set.

Keywords

A posteriori approaches A priori approaches Basic approaches Efficient frontier Fuzzy satisfying method Interactive approaches Multi-objective optimization problems Noninteractive approaches No-preference approaches Pareto optimality 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mohammad Kiani-Moghaddam
    • 1
  • Mojtaba Shivaie
    • 2
  • Philip D. Weinsier
    • 3
  1. 1.Department of Electrical EngineeringShahid Beheshti UniversityTehranIran
  2. 2.Faculty of Electrical Engineering and RoboticShahrood University of TechnologyShahroodIran
  3. 3.Department of Applied Electrical EngineeringBowling Green State University FirelandsHuronUSA

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