Groupe d’études et de recherche en analyse des décisions

Utilizing Numerical Optimization in Computational Engineering Design

Michael Kokkolaras Professeur agrégé, Département de génie mécanique, Université McGill, Canada

Mathematical programming is a valuable tool for developing rigorous, quantitative methodologies in simulation-based engineering design. In this talk, we present optimization approaches to address two challenges in systems design and product development.

The first challenge concerns the appropriate formulation and efficient solution of decomposed system design problems. The subproblems are linked by consistency constraints that need to be coordinated to ensure system integration. We use an augmented Lagrangian penalty function approach to formulate the subproblems and the alternating direction method of multipliers to coordinate their solution. After introducing a hierarchical approach, we present non-hierarchical formulations that enable efficient solution of general multidisciplinary design optimization problems. We consider applications in automotive and aerospace engineering and discuss computational tools that facilitate automated implementation of the coordination process.

The second challenge pertains to platform-based design of product families. Product families consist of product variants that share components and/or manufacturing processes (the platform) to save costs and reduce lead times. The challenge is to identify what to share so that commonality benefits are maximized while individual product performance losses are minimized. We use a multi-objective optimization approach that enables the solution of the commonality problem while quantifying tradeoffs among the conflicting design objectives of individual product variants. The proposed methodology is demonstrated using an engine family design problem.