Mapping based constraint handling for evolutionary search; Thurston's circle packing and grid generation

摘要

This paper presents a mapping based constraint handling method for optimisation problems to be used with evolutionary search techniques. Two different mapping techniques are used; Thurston's circle packing algorithm and TTM(Thompson-Thames-Martin) grid generator. Both methods are used to find approximate Riemann mappings between arbitrarily shaped 2D feasible solution spaces and a simple rectangular domain in which evolutionary search can be applied in a straightforwardmanner.The mapping based constraint handling method is compared, on a number of problems, with penalty-based and repair-based constraint handling methods. Discussions on the method's limitations and ways to overcome these, and extension to higher dimensionalproblems are given.