Multi-fidelity constraints in blackbox optimization

TL;DR

This paper introduces IDS and DIDS algorithms that utilize multi-fidelity constraint evaluations to efficiently solve costly blackbox optimization problems, especially in industrial contexts with many discrete fidelity levels and discontinuities.

Contribution

It proposes novel interruptible direct search algorithms that leverage multi-fidelity feasibility assessments to reduce evaluation costs in constrained blackbox optimization.

Findings

Significant performance improvements when combining NOMAD with IDS or DIDS.

Effective handling of highly discontinuous problems with multiple fidelity levels.

Demonstrated efficiency gains in industrial-like optimization scenarios.

Abstract

This work studies constrained blackbox optimization problems that cannot be solved in reasonable time due to prohibitive computational costs. This challenge is especially prevalent in industrial applications, where blackbox evaluations are costly. However, constraints can be evaluated at various fidelities at a lower computational cost. More specifically, this work targets situations in which the infeasibility of each individual constraint can be detected at lower fidelities, and where a large discrete number of fidelities are available. Moreover, highly discontinuous problems which may fail to evaluate are considered, such that direct search methods are preferred to model-based ones. To this effect, the Interruptible Direct Search (IDS) and the Dynamic Interruptible Direct Search (DIDS) algorithms are proposed to leverage feasibility assessments from various fidelity levels to avoid high cost evaluations. The results show highly increased performances from NOMAD when it is paired with IDS or DIDS.