Response Surface Optimization with Discrete Variables

Abstract

Recent advances in non-gradient based optimization methods (e.g., Genetic Algorithms, Particle Swarm Optimization) enhanced the abilities of discrete, integer, and mixed optimization problems. However, the very nature of non-gradient based algorithms is that the number of analyses required to get to an optimal solution is several orders of magnitude higher than for traditional gradient based optimization methods or response surface optimization methods, when considering continuous problems. Instead of these approaches we propose to use a response surface approximate optimization method modified to work with discrete design variables. In this case whenever it is required to perform the actual analysis of responses for the purpose of fitting a response surface approximation, the design variables will be converted to corresponding discrete values. Two discretization techniques are proposed. We demonstrate that although lacking global search properties like Genetic Algorithms and Particle Swarm Optimization, the discrete response surface optimization provides a computationally efficient way of improving an initial design and getting into a region of an optimum using only discrete points for analysis.