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Lexicographic optimization

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Lexicographic optimization is a kind of multi-objective optimization. In general, multi-objective optimization deals with optimization problems with two or more objective functions to be optimized simultaneously. Often, the different objectives can be ranked in order of importance to the decision-maker, so that objective f 1 {\displaystyle f_{1}} is the most important, objective f 2 {\displaystyle f_{2}} is the next most important, and so on. Lexicographic optimization presumes that the decision-maker prefers even a very small increase in f 1 {\displaystyle f_{1}} , to even a very large increase in f 2 , f 3 , f 4 , {\displaystyle f_{2},f_{3},f_{4},} etc. Similarly, the decision-maker prefers even a very small increase in f 2 {\displaystyle f_{2}} , to even a very large increase in f 3 , f 4 , {\displaystyle f_{3},f_{4},} etc. In other words, the decision-maker has lexicographic preferences, ranking the possible solutions according to a lexicographic order of their objective function values. Lexicographic optimization is sometimes called preemptive optimization, since a small increase in one objective value preempts a much larger increase in less important objective values.