A Study of Aggregation as a Modeling Tool in Optimal Design

In this article we examine the behavior of optimal design models when the parameters are progressively unfixed in a process referred to as design aggregation. While this is a common modeling practice, its consequences on solution properties are not always predictable. Using no special assumptions on problem data, we develop an upper bound result for the aggregation process and highlight the difficulties which arise when even a single parameter is unfixed. When such an aggregated model is in turn parametrically decomposed, we recover the result where sufficiency at the lower level is required for necessary optimality conditions at the upper level. We also present a generalization of the commonly studied “portal frame” problem as a design case study. While aggregation has only benign effects on the solution of this model, interesting new results are obtained when model perturbations more severe than simple aggregation are imposed on this problem. 1corresponding author