On Making Problems Evolutionarily Friendly Part 2: Evolving the Most Convenient Coordinate Systems Within Which to Pose (and Solve) the Given Problem

摘要

The idea of evolutionary friendliness recognizes that problem representations have a significant impact on the performance of cvolutionary algorithms. There are two aspects of these representations. Diffcrent solution schemes exploit different natural symmetries. Very commonly, problems also possess symmetries that are determined by the coordinate systems used to represent them. Solution symmctries are typically spccified by the user and not evoluved. In the first paper, the most appropriate symmctry was evolved. In this second paper, the coordinate system is evolved. In this paper, comon detection problems are solved by evolving appropriate coordinate systems. These coordinate systems effectively transform the nonlinear detection problem into a linear detection problem, which is then solved using simple gradient descent. These coordinate systems are modeled through a pair of equations and are represented as parse trees. Evolutionary programming (EP) is used to optimize these coordinate systems in light of a fitness function based on the number of corrcct deteetions. Results indicate that such coordinate systems can be efficiently cvolved to solve non-trivial detection poroblems.