Fidelity and interruption control for expensive constrained multi-fidelity blackbox optimization

TL;DR

This paper presents a new multi-fidelity blackbox optimization algorithm that efficiently handles expensive constrained problems by controlling evaluation fidelity and interruptions, improving solution quality especially with feasible starting points.

Contribution

The paper introduces a fidelity and interruption control mechanism for multi-fidelity optimization, enabling better handling of infeasible points and compatibility with various direct search solvers.

Findings

Significant improvement with feasible starting points

Performance depends on blackbox properties without initial feasibility

Effective management of evaluation costs and feasibility assessments

Abstract

This work introduces a novel blackbox optimization algorithm for computationally expensive constrained multi-fidelity problems. When applying a direct search method to such problems, the scarcity of feasible points may lead to numerous costly evaluations spent on infeasible points. Our proposed fidelity and interruption controlled optimization algorithm addresses this issue by leveraging multi-fidelity information, allowing for premature interruption of an evaluation when a point is estimated to be infeasible. These estimations are controlled by a biadjacency matrix, for which we propose a construction. The proposed method acts as an intermediary component bridging any non multi-fidelity direct search solver and a multi-fidelity blackbox problem, giving the user freedom of choice for the solver. A series of computational tests are conducted to validate the approach. The results show a significant improvement in solution quality when an initial feasible starting point is provided. When this condition is not met, the outcomes are contingent upon specific properties of the blackbox.