Multi-fidelity optimization approach under prior and posterior constraints and its application to compliance minimization

Abstract

In this paper, we consider a multi-fidelity optimization under two types of constraints: prior constraints and posterior constraints. The prior constraints are prerequisite to execution of the simulation that computes the objective function value and the posterior constraint violation values, and are evaluated independently from the simulation with significantly lower computational time than the simulation. We have several simulators that approximately simulate the objective and constraint violation values with different trade-offs between accuracy and computational time. We propose an approach to solve the described constrained optimization problem with as little computational time as possible by utilizing multiple simulators. Based on a covariance matrix adaptation evolution strategy, we combines three algorithmic components: prior constraint handling technique, posterior constraint handling technique, and adaptive simulator selection technique for multi-fidelity optimization. We apply the proposed approach to a compliance minimization problem and show a promising convergence behavior.