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 .
Read more about this topic: Multi-objective Optimization
Famous quotes containing the words priori and/or methods:
“The so-called law of induction cannot possibly be a law of logic, since it is obviously a proposition with a sense.—Nor, therefore, can it be an a priori law.”
—Ludwig Wittgenstein (1889–1951)
“The comparison between Coleridge and Johnson is obvious in so far as each held sway chiefly by the power of his tongue. The difference between their methods is so marked that it is tempting, but also unnecessary, to judge one to be inferior to the other. Johnson was robust, combative, and concrete; Coleridge was the opposite. The contrast was perhaps in his mind when he said of Johnson: “his bow-wow manner must have had a good deal to do with the effect produced.””
—Virginia Woolf (1882–1941)