Abstract

Many optimization problems find a natural mapping in permutation spaces where dedicated algorithms can be used during the optimization process. Unfortunately, some of the best and most effective techniques currently used can only be applied to vectors (cartesian) spaces, where a concept of distance between different objects can be easily defined. Examples of such techniques go from simplest deepest descent hill climbers and the more sophisticated conjugate gradient methods used in continuous spaces, to dynanic hill climbers or Genetic algorithms (GAs) used in many large combinatorial problems. This paper describes a general method that allows the best optimization techniques used in vector spaces to be applied to all order based problems whose domain is a permutation space. It will also be shown how this method can be applied to a real world problem, the optimal placement of interconnected cells (modules) on a chip, in order to minimize the total length of their connections. For this p...

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