Michigan professor’s new textbook advances design optimization field

Joaquim Martins’ Engineering Design Optimization book to educate students in how design optimization can replace conventional iterative design processes.

A pioneer in multi-disciplinary design optimization (MDO), University of Michigan Aerospace Engineering Professor Joaquim Martins has long touted the benefits that the field brings to aircraft design and the design of other complex engineering systems like automobiles, ships, wind turbines, and spacecraft. 

According to Martins, despite MDO’s usefulness in simultaneously improving design and reducing the time and cost of the design cycle, it is underutilized in industry, in part, due to a lack of engineers well-versed in the field. 

“There was a shortage of MDO courses in undergraduate and graduate curricula,” said Martins, noting that this has begun to change as top aerospace and mechanical engineering departments now include at least one graduate-level course on design optimization. 

In fact, for more than a decade, Martins taught his own MDO course (AE 588) at U-M. During this time, he created and compiled pages of notes to enhance the course and students’ understanding of how MDO can replace conventional iterative design processes.  

More recently, he teamed up with Brigham Young University Mechanical Engineering Associate Professor Andrew Ning, an expert in MDO with applications in aircraft design, to produce a new textbook, Engineering Design Optimization. 

book cover
Engineering Design Optimization book

Already available online for free, Cambridge University Press will release the print edition this fall. 

Targeted toward graduate and senior-level undergraduate students, the book covers fundamental and advanced optimization theory and algorithms, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application.

While other MDO books exist, Martins’ tome strikes a nice balance between numerical methods and engineering applications. 

“If you look at all the books, some are engineering-oriented, so they focus more on applications and are very superficial on the numerical methods,” Martins explained. “On the other extreme, there are books that are more mathy—lots of proofs and theorems but very few figures.”

Engineering Design Optimization contains more than 400 helpful visualizations that Martins and Ning meticulously created themselves to best help students understand fundamental principles. 

“I’m really pleased with the final product,” said Ning. “We put a lot of effort into trying to make the content clear, practical, and visually appealing. Hopefully it becomes a valuable resource to others seeking to learn more in this field. We certainly learned more about optimization during this process.”

If you look at all the books, some are engineering-oriented, so they focus more on applications and are very superficial on the numerical methods. On the other extreme, there are books that are more mathy—lots of proofs and theorems but very few figures.

Joaquim R. R. A. Martins, Professor of aerospace engineering

The book also includes numerous examples that facilitate understanding of the theory, and practical tips—seldom found in existing textbooks—which are the product of the authors’ and their students’ many years of experience. 

There are numerous end-of-chapter homework problems that increase in difficulty as students progressively build their skills and knowledge from chapter to chapter. These homework problems, along with a free, electronic version of the book, enable motivated students to teach themselves the material outside of a formal course. 

According to Martins, MDO became very popular in the 1980s and 1990s and the first applications of this design method was aircraft wing design. 

“There was an explosion in MDO research then,” Martins said. “People thought it would solve all the world’s problems, but then over time, researchers oversold it. However, there’s a resurgence because of the research and educational efforts of my colleagues and me. We also have more computer power so we can do higher fidelity simulations in the optimization loop.”

Martins and his research group are widely recognized for their advances in airplane design optimization based on numerical modeling. For example, they’ve been working with aircraft manufacturers like Airbus and Embraer to use MDO. Both companies are experimenting with the computational framework (MACH) that Martins developed to optimize wing designs. 


Michigan Aerospace logo

Michigan Aerospace Engineering

Communications Team