Basic Concepts

Motivation Most problems in nature have several (possibly conflicting) objectives to be satisfied. Many of these problems are frequently treated as single-objective optimization problems by transforming all but one objective into constraints. What is a multiobjective optimization problem? The Multiobjective Optimization Problem (MOP) (also called multicriteria optimization, multiperformance or vector optimization problem) can be defined (in words) as the problem of finding (Osyczka, 1985): a vector of decision variables which satisfies constraints and optimizes a vector function whose elements represent the objective functions. These functions form a mathematical description of performance criteria which are usually in conflict with each other. Hence, the term " optimize " means finding such a solution which would give the values of all the objective functions acceptable to the decision maker. What is the notion of optimum in multiobjective optimization? Having several objective functions, the notion of " optimum " changes, because in MOPs, we are really trying to find good compromises (or " trade-offs ") rather than a single solution as in global optimization. The notion of " optimum " that is most commonly adopted is that originally proposed by Francis Ysidro Edgeworth in 1881.