On Making Problems evolutionarily Friendly Part 1: Evolving the Most Convenient Representations

摘要

The idea of evolutionary friendliness recognizes that problem representations have a significant impact on the performance of evolutionary algorithms. There are two aspects of these representations. Different solution schemes exploit different natural symmetries. Very commonly, problems also possess symmetries that are determined by the coordinate systems used to represent them. Solution symmetries are typically specified by the user and are not allowed to evolve. The problem coordinate system is again typically chosen by the user and not evlved. In this first paper, the most appropriate solution symmetry is evolved. In the second paper, the coordinate system is evolved. In this paper, common detection problems with decision boundaries that possess special symmetries are solved using an evolutionary programming (EP) framework that is capable of exploiting these symmetries to quickly generate solutions. In particular, neural networks possessing appropriate symmetries are evolved by optimizing both their bases and their parameters. Simulation results indicate that the EP procedure is capable of selecting appropiate basis functions for different regions of the input space as well as optimizing the associated set of parameters.