Formal Search Algorithms + Problem Characterisations = Executable Search Strategies

Abstract

Traditional evolutionary algorithms use a standard, predetermined representation space, often in conjunction with a similarly standard and predetermined set of genetic move operators, themselves defined in terms of the representation space. This approach, while simple, is awkward and—we contend—inappropriate for many classes of problem, especially those in which there are dependencies between problem variables (e.g., problems naturally defined over permutations). For these reasons, over time a much wider variety of representations have come into common use. This paper presents a method for specifying algorithms with respect to abstract or formal representations, making them independent of both problem domain and representation. It also defines a procedure for generating an appropriate problem representation from an explicit characterisation of a problem domain that captures beliefs about its structure. We are then able to apply a formal search algorithm to a given problem domain by providing a suitable characterization of it and using this to generate a formal representation of problems in the domain, resulting in a practical, executable search strategy specific to that domain. This process is illustrated by showing how identical formal algorithms can be applied to both the travelling sales-rep problem (TSP) and real parameter optimisation to yield familiar (but superficially very different) concrete search strategies.