tutorial-moea

Evolutionary Multiobjective Optimization:Past, Present and FutureCarlos A. Coello CoelloCINVESTAV-IPNDepto. de Ingenier´ıa El´ectricaSecci´ on de Computaci´ onAv. Instituto Polit´ecnico Nacional No. 2508Col. San Pedro ZacatencoM´exico, D. F. 07300, MEXICOccoello@cs.cinvestav.mx1MotivationMost problems in nature have several (possibly conflicting)objectives to be satisfied. Many of these problems are frequentlytreated as single-objective optimization by transformingall but one objective into constraints.2What is a multiobjective optimization problem?The Multiobjective Optimization Problem (MOP) (alsocalled multicriteria optimization, multiperformance or vectoroptimization problem) can be defined (in words) as the problem offinding (Osyczka, 1985):a vector of decision variables which satisfies constraints andoptimizes a vector function whose elements represent theobjective functions. These functions form a mathematicaldescription of performance criteria which are usually inconflict with each other. Hence, the term “optimize” meansfinding such a solution which would give the values of allthe objective functions acceptable to the decision maker.3A Formal DefinitionThe general Multiobjective Optimization Problem (MOP) can beformally defined as:T∗ ∗ ∗ ∗Find the vector~x = [x ,x ,...,x ] which will satisfy the m1 2 ninequality constraints:g (~x)≥ 0 i = 1, 2,...,m (1)ithe p equality constraintsh (~x) = 0 i = 1, 2,...,p (2)iand will optimize the ...