2 ND INTERNATIONAL CONFERENCE ON METAHEURISTICS - MIC 97 IContents

It has often been assumed that ordering problems form a special class of problems amenable to a largely uniform treatment. Since successful ordering Genetic Algorithms (gas) have been deened for optimization of some ordering problems, it has become customary to assume that ordering problems are well solved by ordering gas tted with standardd operators. The success of the standard ordering gas on some problems led to an indirect approach to solving numerous combinatorial problems as follows: deene a decoder of a permutation of items that builds a solution to the original problem, and use the ordering ga to nd a permutation that decodes into a good solution to the original problem. Such lavish applications of the standard ordering ga to all sorts of problems have become pervasive. In this paper, we construct a very simple way of transforming a function deened over bitstrings to a function deened over permutations, and conversely. As a result, there is a simple way of transforming any function to an ordering problemm. The implication of this is that should there indeed be a standard way of eeciently solving ordering problems, then the standard ordering ga would be capable of eeciently optimizing all functions. That, however, would contradict the No Free Lunch Theorem for search. Consequently, many ordering problems are not amenable to solution by standard ordering gas, i.e. the lavish use of the standard ordering ga is unwarranted. We support this claim by experiments where we attempt to optimize the easy 32-bit one-max function with an ordering ga, using the simple transformation between permutations and bitstrings. As expected, standard ordering crossover operators perform extremely poorly on that simple function. In order to illustrate how much an ordering crossover for one-max would have to diier from the standard ones, we then construct an exoticc tailored crossover which performs well.