The 'representative' metaheuristic design pattern

1. PROBLEM STATEMENT The ‘Representative’ pattern is applicable when it is desirable to eliminate redundancy in the search process: • It is often the case that some function f of interest in optimization gives a many-to-one mapping, i.e. it induces equivalence classes over the image of f . If f is a fitness function, this can lead to plateaus in the fitness landscape. • It may be that the elimination of redundancy allows search to be performed in a smaller (‘quotient’) space that can be searched using methods (possibly even exact techniques) not applicable to the original space. • In the case of GP-trees, syntactically inequivalent but semantically equivalent representations (e.g. x + x, 2 ∗x) can lead to a lack of gradient in genotype-to-phenotype mappings, which may make the space of programs harder to search effectively.