Constraint back-offs for safe, sufficient excitation: a general theory with application to experimental optimization

TL;DR

This paper develops a theoretical framework for determining safe perturbation sizes in constrained experimental settings, enabling sufficient excitation without constraint violations, and applies it to optimize experiments effectively.

Contribution

It introduces a method to compute constraint back-offs ensuring safe perturbations and proposes a constrained optimization algorithm based on evolutionary operations.

Findings

Algorithm converges to the neighborhood of the optimum.

Consistently avoids constraint violations in case studies.

Provides a systematic way to set perturbation sizes in constrained experiments.

Abstract

In many experimental settings, one is tasked with obtaining information about certain relationships by applying perturbations to a set of independent variables and noting the changes in the set of dependent ones. While traditional design-of-experiments methods are often well-suited for this, the task becomes significantly more difficult in the presence of constraints, which may make it impossible to sufficiently excite the experimental system without incurring constraint violations. The key contribution of this paper consists in deriving constraint back-off sizes sufficient to guarantee that one can always perturb in a ball of radius $\delta_e$ without leaving the constrained space, with $\delta_e$ set by the user. Additionally, this result is exploited in the context of experimental optimization to propose a constrained version of G. E. P. Box's evolutionary operation technique. The proposed algorithm is applied to three case studies and is shown to consistently converge to the neighborhood of the optimum without violating constraints.