Constraint Management of Reduced Representation Variables in Decomposition-Based Design Optimization

In decomposition-based design optimization strategies, such as Analytical Target Cascading (ATC), it is sometimes necessary to use reduced dimensionality representations to approximate functions of large dimensionality whose values need to be exchanged among subproblems. The reduced representation variables may not be physically meaningful, and it can become challenging to constrain them properly and define the model validity region. For example, in coordination strategies like ATC, representing vector-valued coupling variables with improperly constrained reduced representation variables can lead to poor performance or convergence failure. This paper examines two approaches for constraining effectively the model validity region of reduced representation variables based on proper orthogonal decomposition: a penalty value-based heuristic and a support vector domain description. An ATC application on electric vehicle design helps to illustrate the concepts discussed.