Bayesian Algorithm for Collaborative Optimization with Application to Aircraft Design

TL;DR

This paper introduces BACO, a Bayesian surrogate-based algorithm for collaborative optimization, significantly reducing expensive evaluations and outperforming existing methods in aircraft design problems.

Contribution

It develops a Bayesian framework replacing black-box evaluations with Gaussian process surrogates, improving efficiency and solution quality in multidisciplinary design optimization.

Findings

BACO achieves lower objective values than state-of-the-art CO variants.

BACO reduces constraint violations and discrepancies to near-zero within evaluation budgets.

BACO successfully solves complex aircraft wing optimization problems with fewer evaluations.

Abstract

Collaborative Optimization (CO) is a multidisciplinary design optimization (MDO) framework that decomposes large-scale engineering problems into parallel, independently solvable subsystems coordinated by a system-level optimizer. Its practical utility is limited by the high frequency of expensive black-box disciplinary evaluations arising from the bi-level consistency constraints. This paper introduces BACO, a Bayesian Algorithm for Collaborative Optimization, which replaces the direct black-box calls at both levels with Gaussian process (GP) surrogates and acquisition function maximization. At the subsystem level, an acquisition function subject to GP-predicted feasibility constraints identifies the next evaluation point. At the system level, the same surrogate framework enforces consistency through predicted discrepancy constraints. This architecture reduces the number of true black-box evaluations required per major iteration. BACO is benchmarked against state-of-the-art CO variants on a Scalable MDO problem over 50 randomized instances. On this problem, BACO consistently achieves lower objective values and drives both constraint violation and interdisciplinary discrepancy to near-zero within the evaluation budget, outperforming all three CO variants across all tested DoE sizes. Further validation is conducted on a coupled aero-structural wing optimization problem based on the Common Research Model (CRM) geometry, where BACO identifies a feasible solution within 886 of 1000 allocated evaluations, recovering results physically consistent with active bending stress and tip deflection constraints. The BACO software, the state-of-the-art CO solvers, as well as standard MDO benchmarking problems are open-source and publicly available at https://moebehfn.github.io/mdotoolbox/.