Multi-Objective Efficient Global Optimization Method With Truncated Expected Improvement Matrix-Based Infill Criterion for Problems With Prior Knowledge on Objective Bounds
TL;DR
Comparative studies demonstrate that the proposed MOEGO methods could obtain better solutions in terms of convergence and diversity or find solutions in region of interest by making use of the prior knowledge on the objectives.
Abstract
The multi-objective efficient global optimization (MOEGO), an extension of the single-objective efficient global optimization algorithm with the intention to handle multiple objectives, is one of the most frequently studied surrogate-based multi-objective optimization algorithms. The efficiency of MOEGO algorithm mainly depends on the multi-objective expected improvement criterion used. The expected improvement matrix (EIM) based criterion is cheap-to-evaluate and yet efficient compared to the others. The EIM criterion stands on the assumption: for an untested point, the prediction of each objective follows a normal distribution which varies from minus infinity and plus infinity. However, in many practical applications, a prior knowledge about the objective range is available. Such prior knowledge may be the known/estimated objective bounds or come from the designers’ preferences which is the designers want solutions in a region of interest other than those scattered over the whole objective space. But such prior knowledge of the objective functions has not been made use of in the EIM based criterion. To make use of such prior knowledge on objective range, a truncated expected improvement matrix (TEIM) based criterion is proposed and incorporated to MOEGO to develop methods dedicated to use the known lower bounds or prior preference respectively. Comparative studies demonstrate that the proposed MOEGO methods could obtain better solutions in terms of convergence and diversity or find solutions in region of interest by making use of the prior knowledge on the objectives. By integrating the prior preference-inspired MOEGO with TEIM based criterion, the modified Parsec airfoil generation method, and flow solver, a prior-preference inspired airfoil shape optimization method is established and applied to maximize the lift/drag coefficient ratio and minimize the drag coefficient, from which the effectiveness of the proposed method to solve practical problem is demonstrated.