A general decomposition methodology for optimal system design.

Abstract

Recent emphasis on shorter development cycles has effected a need for coordinating simultaneous designs of subsystems to meet overall product development goals. The coordination strategy and independent design problems are often formulated ad hoc or based on domain specific knowledge. The dissertation describes a systematic methodology for the definition and coordination of simultaneous design problems to meet system goals using decomposition methods of mathematical programming problems as a paradigm for coordinated simultaneous design. Mathematical programming decomposition methods formulate independent subproblems in terms of disjoint partitions of original problem functions and variables. These partitions surface when linking functions or variables are temporarily ignored; a master problem accounts for these linking properties and coordinates solution of the subproblems. Specific instances of linking functions, linking variables, separability, linearity, and convexity determine which method is appropriate for a particular problem. The dissertation develops algorithms for systematic identification of linking properties and disjoint partitions. Ranking criteria for linking properties and acceptability metrics for the disjoint partitions are developed. The procedure relies on an undirected graph representation of the primal form of a nonlinear programming problem. Connected components in the graph are equivalent to desired partitions. Algorithms are presented for automated search of linking properties that satisfy acceptability criteria for desired partitions. The algorithms are integrated into a general Decomposition Analysis Methodology that determines suitable decomposition methods for a given problem. Decomposition analysis of selected problems illustrates alternate decomposability of original problems and numerical behavior of specific decomposition methods. The methodology is applied to an optimal powertrain design problem having 87 functions and 128 variables. Decomposition analysis verifies the conventional partitioning of powertrain design according to physical subsystems. A new coordination strategy for this problem is proposed and tested. Convergence in two overall iterations results in an 11% improvement in city-highway fuel economy over a feasible baseline while satisfying all constraints. The coordination strategy represents a new practical approach for accommodating control and geometry variables simultaneously in the important area of automotive powertrain design. This particular application is one of the more comprehensive optimal powertrain design studies available in the open literature.

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