An incremental-approximate-clustering approach for developing dynamic reduced models for design optimization

This paper we describe a method for improving genetic algorithm based optimization using reduced models. The main idea is to maintain a large sample of the points encountered in the course of the optimization divided into clusters. Least squares quadratic approximations are periodically formed of the entire sample as well as the big enough clusters. These approximations are used as a reduced model to compute cheap approximations of the fitness function through a two phase approach in which the point is first classified (into potentially feasible, infeasible or unevaluable) and then its fitness is computed accordingly. We then use the reduced models to speedup the GA optimization by making the genetic operators such as mutation and crossover more informed. The proposed approach is particularly suitable for search spaces with expensive evaluation functions, such as those that arise in engineering design. Empirical results in several engineering design domains demonstrate that the proposed method can significantly speed up the GA optimizer