Generating evenly distributed nondominated solutions in dual response surface optimization

Abstract

The dual response surface optimization (DRSO) approach attempts to simultaneously optimize the mean and standard deviation of a response variable. In DRSO, the mean and standard deviation of a response are often in conflict and thus, it is extremely critical to compromise the two conflicting functions. Recently, a posterior preference articulation approach for DRSO (P-DRSO) was proposed. P-DRSO generates a set of nondominated solutions and allows a decision-maker (DM) to select the most preferred solution. P-DRSO has an advantage in that the DM can better understand the trade-offs between the mean and standard deviation. Thus, the most satisfactory compromised solution can be easily obtained. One important issue of P-DRSO is to generate uniformly distributed nondominated solutions for the DM to obtain better understanding of the trade-offs between the mean and standard deviation. P-DRSO employs a conventional ε-constraint method. However, it often generates nondominated solutions that are not uniformly distributed. To address this issue, we propose a new approach to generate the nondominated solutions. We demonstrated that the uniformity of the generated nondominated solutions is better than that of P-DRSO in two well-known DRSO case problems.