A methodology for creating multidisciplinary design optimization benchmark problems from optimization ones

Abstract

Benchmark problems with known solutions play a central role in the assessment of optimization algorithms. While mono-disciplinary optimization benefits from a rich collection of such problems, multidisciplinary design optimization (MDO) lacks equivalent resources: existing MDO benchmarks are scarce, rarely scalable, and their solutions are generally not known theoretically. In this paper, we propose a systematic methodology to transform any mono-disciplinary optimization problem with a known solution into a family of parametric MDO problems sharing that same solution. The construction relies on two key ingredients: a set of coupling equations that introduce interdependencies between disciplines, and a link function that eliminates the coupling variables and recovers the original mono-disciplinary problem. Theoretical conditions guaranteeing the equivalence between the two problems are established. The methodology is agnostic to the number of disciplines and variable dimensions, making it naturally suited for scalability studies. As an illustration, we construct a family of scalable MDO Rosenbrock problems and use them to benchmark two MDO coupling algorithms, namely the Jacobi and Gauss-Seidel schemes, across varying problem sizes. The proposed framework opens a systematic route to generating MDO benchmarks of arbitrary scale and complexity from the extensive catalog of existing mono-disciplinary test problems.