Mysterious Behavior of Optimization Calculation With MOGA

Abstract

Multi-Objective Generic Algorithm (MOGA) is a popular and viable optimization calculation scheme for many practical engineering problems. This is because MOGA provides reliable search results covering wide and multi-variable design spaces. Most importantly when an optimization problem involves using mixed design variables, i.e. continuous and discrete variables, MOGA is still applicable. However, in such a condition MOGA needs to be programmed in a binary mode, which requires a minimum number of bits to represent each real and integer design variable. The accuracy of the prediction of the optimization calculation is expected to depend on the number of bits used. This paper introduces such a problem based on a general turbomachinery design problem. The design variables of the centrifugal impeller design consist of discrete and continuous variables. Some puzzling behavior occurred when the optimization calculation was carried out, related to the prediction accuracy when applying different number of bits to represent the continuous and discrete design variables. It is found that the accuracy is independent of the number of binary bits used. Detailed analyses were performed using simplified analytic formulations for the objective functions to determine why the calculated results show such a behavior. In addition, objective functions are developed and verified that do not show this behavior.