Riemann mapping based constraint handling for evolutionary search
Dae Gyu Kim · 1998
Evolutionary search (ES) methods encode each parameter within allowed interval. Thus, as a whole, candidate solutions are defined in an n-dimensional hypercube with n independent parameters. Constraints in the search impose complicated feasible solution domain shape from the hypercube. Most of the research on ES on constrained problems use heuristics to handle infeasible solutions, [5]. The performance of the search is dependent on the quality of the heuristics. Such heuristics usually become problem dependent for better performance. If feasible solution domains defined by domains of parameters and constraints can be mapped into a hypercubic domain again, then ES can be easily applied within the mapped domain without the help of any further heuristics. Riemann's mapping theorem proves the existence and the uniqueness of a one-to-one mapping between any simply connected and bounded domain on a plane and a unit circle. Thurston's circle packing, Appendix 2 of [11], is an algorithm doi...