A Decomposed Gradient-Based Approach for Generalized Platform Selection and Variant Design in Product Family Optimization

Abstract

A core challenge in product family optimization is to jointly determine (1) the optimal selection of components to be shared across product variants and (2) the optimal values for design variables that define those components. Each of these subtasks depends on the other; however, due to the combinatorial nature and high computational cost of the joint problem, prior methods have forgone optimality of the full problem by fixing the platform a priori, restricting the platform configuration to all-or-none component sharing, or optimizing the joint problem in multiple stages. In this paper, we address these restrictions by (1) introducing an extended metric to account for generalized commonality, (2) relaxing the metric to the continuous space to enable gradient-based optimization, and (3) proposing a decomposed single-stage method for optimizing the joint problem. The approach is demonstrated on a family of ten bathroom scales. Results indicate that generalized commonality dramatically improves the quality of optimal solutions, and the decomposed single-stage approach offers substantial improvement in scalability and tractability of the joint problem, providing a practical tool for optimizing families consisting of many variants.