# Introduction to Multi-objective Optimization and Decision-Making Analysis

## 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## References

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