Overrepresentations in Neutral Genotype-Phenotype Mappings and their Applications

This work presents in a first phase an original solution to the "Worst 1-MAX solver" competition, proposed at the Genetic and Evolutionary Computation Conference - GECCO´ 2007 where the goal was to evolve the solution of the 1-MAX problem as late as possible within 1000 generations. If P_EA,_n (gles1000) is a function which describes the convergence probability of the algorithm EA on the function 1-MAX of size n within g generations, then our proposed generational evolutionary algorithm EA* has P_EA*_n(1000) = 1, always solving the problem within 1000 generations. The interesting particularity of the algorithm is that for generations g < 1000 the convergence probability is exponential in n. We achieve this performance by using a neutral genotype-phenotype mapping with a high degree of overrepresentation. As a second result, we show that deliberated overrepresentations may extended to problems of general interests, having a wide applicability in developing sustainable evolutionary methods.