Multidisciplinary Design and Optimization (MDAO)

– Model and solve coupled multidisciplinary systems using MDA concepts and SoA software such as GEMSEO. – Formulate numerical optimization problems with design variables, objectives, constraints, and bounds. – Understand the role of gradients in optimization and compare key derivative-computation methods, with emphasis on algorithmic differentiation. – Recognize the main MDO architectures and select an appropriate formulation for a multidisciplinary design problem. – Apply the complete MDAO workflow through guided practical exercises.

Agenda

10:00h-13.30h each day

Day 1 – MDA

1.1 Introduction to MDAO
1.2 From single-discipline analysis to coupled analysis
1.3 MDA: coupling variables, residuals, convergence
1.4 Introduction to GEMSEO for MDA
1.5 Exercise: solve a coupled MDA problem

Day 2 – Optimization

2.1 Introduction to optimization problem formulation
2.2 Design variables, objective functions, constraints and bounds
2.3 Gradient-based optimization
2.4 Non-gradient-based optimization
2.5 Introduction to optimization libraries
2.6 Exercise: solve an optimization problem

Day 3 – Evaluation of Gradients

3.1 Why gradients matter in engineering optimization
3.2 Finite differences and complex step
3.3 Direct and adjoint methods
3.4 Automatic differentiation
3.5 Introduction to JAX
3.6 Exercise: compute and compare gradients

Day 4 – MDO

4.1 Introduction to MDO
4.2 From MDA + optimization to MDO
4.3 MDO architectures: monolithic and distributed architectures
4.4 Coupled derivatives in MDO
4.5 Exercise / capstone: formulate and solve a small MDO problem

Rauno Cavallaro

Rauno Cavallaro is a Researcher at the Barcelona Supercomputing Center, in the Computer Applications in Science and Engineering department. His work focuses on Multidisciplinary Analysis and Design Optimization for aerospace applications. His research addresses the integration of new aircraft technologies, sustainable aviation, aeroelasticity, flight physics, aerostructural design, and unconventional aircraft configurations. He has coordinated and contributed to several national, European, and industrial research projects on low-emission and unconventional aircraft, including hydrogen-powered, hybrid-electric, and electric concepts. His publication record includes peer-reviewed journal articles, conference papers, book chapters, patents, and invited contributions. He also has extensive teaching and professional training experience in aircraft design, structural design, helicopters, and MDO, including activities developed in collaboration with industry.

This course introduces the foundations and practical use of Multidisciplinary Design Analysis and Optimization (MDAO). The course starts with Multidisciplinary Design Analysis (MDA), focusing on coupled disciplines, coupling variables, convergence strategies, and implementation in GEMSEO. It then introduces numerical optimization, including problem formulation, design variables, objectives, constraints, and basic optimization algorithms. The third part focuses on derivative computation techniques, from finite differences to more advanced gradient approaches used in coupled systems. The final part connects these elements into MDO architectures, showing how MDA, optimization, and gradients are integrated to solve multidisciplinary design problems. Practical exercises are included throughout the course to support implementation and interpretation of results.

The course is intended for engineering students, researchers, and practitioners with basic knowledge of calculus, linear algebra, numerical methods, and Python programming. No prior experience with MDAO, GEMSEO, JAX, adjoint methods, or automatic differentiation is required. Familiarity with engineering simulation models and numerical optimization is useful but not mandatory.

Certificate of Attendance

Martins, J. R. R. A., & Ning, A. — Engineering Design Optimization. Main reference textbook for optimization, gradients, numerical models, and MDO. https://mdobook.github.io GEMSEO official documentation. Required for the MDA and MDO practical exercises: https://gemseo.org JAX automatic differentiation documentation. Required for the automatic differentiation practicals. https://docs.jax.dev/en/latest/notebooks/autodiff_cookbook.html Python software environment. Students should have Python installed with NumPy, SciPy, Matplotlib, JupyterLab, GEMSEO, and JAX. Suggested installation: pip install –upgrade pip pip install “gemseo[all]” numpy scipy matplotlib jupyterlab jax

Technical setup or resources needed* Laptop with Python, Jupyter, NumPy, SciPy, Matplotlib, GEMSEO, JAX, and pyXDSM installed. Additional optional optimization libraries may include IPOPT/cyipopt, pyOptSparse, NLopt, pymoo, Nevergrad, PDFO, and UNO for selected demonstration Suggested installation: pip install –upgrade pip pip install numpy scipy matplotlib jupyterlab “gemseo[all]” jax pyxdsm nlopt pymoo nevergrad pdfo