Single-objective robust optimisation in bioprocessing with conformalised quantile regression as interval-based surrogate models

Abstract We present a Monte Carlo-based robust optimisation framework that employs Conformalised Quantile Regression (CQR) as a surrogate model to identify robust operating conditions in various bioprocess single-objective optimisation problems. By generating adaptive and reliable prediction intervals, CQR enables the discovery of solutions that remain near-optimal under worst-case conditions. Through three case studies (upstream glucose feed optimisation, univariate downstream affinity chromatography, and multivariate cation exchange chromatography), we show that CQR-based solutions outperform those obtained with the traditionally used surrogate Gaussian Process Regression (GPR) in both maximin and minimax regret scenarios, particularly when process uncertainty is high. We further validate these robust solutions against mechanistic models, confirming their optimality and underscoring how effective uncertainty estimation leads to robustness. Our results establish this framework as a practical, data-driven decision-support tool for minimising yield losses and mitigating economic risks in biomanufacturing processes.