On making problems evolutionarily friendly part 2: Evolving the most convenient coordinate systems within which to pose (and solve) the given problem

Abstract

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 arl 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 evolved. In the first paper, the most appropriate symmetry was evolved. In this second paper, the coordinate system is evolved. In this paper, common detection problems arl 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 arl 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 correct detections. Results indicate that such coordinate systems can be efficiently evolved to solve non-trivial detection problems.

Funded in part by the California Institute For Energy Efficiency Project On Diagnostics for Building Commissioning And Operation. The authors are indebted to LeeEng Lock for many hours of very fruitful tutclage and conversation regarding proper ways to visualize detection of anomalous behavior in large classA building HVAC systems.