Multi-objective Optimization - A Priori Methods

A Priori Methods

A priori methods require that sufficient preference information is expressed before the solution process. Well-known examples of a priori methods include the utility function method, lexicographic method, and goal programming. In the utility function method, it is assumed that the decision maker's utility function is available. A mapping is a utility function if for all it holds that if the decision maker prefers to, and if the decision maker is indifferent between and . Once is obtained, it suffices to solve

but in practice it is very difficult to construct a utility function that would accurately represent the decision maker's preferences.

Lexicographic method assumes that the objectives can be ranked in the order of importance. We can assume, without loss of generality, that the objective functions are in the order of importance so that is the most important and the least important to the decision maker. The lexicographic method consists of solving a sequence of single objective optimization problems of the form

where is the optimal value of the above problem with . Thus, and each new problem of the form in the above problem in the sequence adds one new constraint as goes from to .