Make an optimization problem multidisciplinary

TL;DR

This paper introduces a methodology to transform any known-solution optimization problem into a multidisciplinary design optimization (MDO) problem, creating benchmarks for algorithm comparison and evaluation.

Contribution

It presents a novel link function-based approach that converts single-discipline problems into equivalent MDO problems, including a variant for linear couplings with closed-form solutions.

Findings

Successfully applied to a multidimensional Rosenbrock problem

Enables scalable and configurable MDO benchmark problem generation

Provides a closed-form solution for linear coupling functions

Abstract

Despite the abundance of benchmark problems for optimization algorithms, there is a notable scarcity of such problems in multidisciplinary design optimization (MDO). To address this gap, we introduce a novel methodology that enables the transformation of any optimization problem with a known solution into an equivalent MDO problem. This equivalence holds for a large class of coupling functions, including non-linear ones. The proposed methodology exploits a ''link function'' that effectively eliminates the coupling variables from the MDO problem, without influencing the solution. This approach allows for the creation of benchmark problems with reference solutions, facilitating the comparison and evaluation of various MDO algorithms. Moreover, it is adaptable to scalable optimization problems, where the dimensions of the search and constraint spaces can be configured. We also present a variant tailored to linear coupling functions with constant coefficients sampled independently at random, for which we derive a closed-form solution to the coupling equations. For the sake of illustration, we put our approach into action on a multidimensional Rosenbrock problem, varying the number of disciplines and design variable sizes. This example showcases the versatility and applicability of our methodology in generating benchmark problems for MDO.