Optimal Partitioning and Coordination Decisions in Decomposition-based Design Optimization.

Abstract

Successful design of complex modern products is a grand challenge for design organizations. The task is becoming increasingly important due to economic competition and concern over safety, reliability, and energy efficiency. Automotive and aerospace products, for example, are composed of numerous interdependent subsystems with a level of complexity that surpasses the capability of a single design group. A common approach is to partition complex design problems into smaller, more manageable design tasks that can be solved by individual design groups. Effective management of interdependency between these subproblems is critical, and a successful design process ultimately must meet the needs of the overall system. Decomposition-based design optimization techniques provide a mathematical foundation and computational tools for developing such design processes. Two tasks must be performed so that decomposition-based design optimization can be used to solve a system design problem: partitioning the system into subproblems, and determining a coordination method for guiding subproblem solutions toward the optimal system design. System partition and coordination strategy have a profound impact on the design process. The effect of partitioning and coordination decisions have been studied independently, while interaction between these decisions has been largely ignored. It is shown here that these two sets of decisions do interact: how a system is partitioned influences appropriate coordination decisions, and vice versa. Consequently, addressing partitioning and coordination decisions simultaneously leads to improved system design processes. The combined partitioning and coordination decision problem is a difficult combinatorial problem. An evolutionary algorithm that solves this decision problem effectively is presented. The set of all partitioning and coordination options for a specific formulation framework, augmented Lagrangian coordination (ALC), is derived, and a method for choosing Pareto-optimal solutions from amongst these options is described. Concepts and techniques are demonstrated using several engineering example problems. A detailed model for an electric vehicle design problem is presented that considers three vehicle systems: powertrain, chassis, and structure, and partitioning and coordination decisions for this problem are analyzed.