Convergence Properties of Analytical Target Cascading

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77196/1/AIAA-2002-5506-996.pd

A Hypergraph Framework for Optimal Model-Based Decomposition of Design Problems

Decomposition of large engineering system models is desirable sinceincreased model size reduces reliability and speed of numericalsolution algorithms. The article presents a methodology for optimalmodel-based decomposition (OMBD) of design problems, whether or notinitially cast as optimization problems. The overall model isrepresented by a hypergraph and is optimally partitioned into weaklyconnected subgraphs that satisfy decomposition constraints. Spectralgraph-partitioning methods together with iterative improvementtechniques are proposed for hypergraph partitioning. A known spectralK-partitioning formulation, which accounts for partition sizes andedge weights, is extended to graphs with also vertex weights. TheOMBD formulation is robust enough to account for computationaldemands and resources and strength of interdependencies between thecomputational modules contained in the model.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44780/1/10589_2004_Article_136837.pd

Hierarchical overlapping coordination under nonlinear constraints

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76760/1/AIAA-1998-4795-679.pd

Convergence Criteria for Hierarchical Overlapping Coordination of Linearly Constrained Convex Design Problems

Decomposition of multidisciplinary engineering system design problems into smaller subproblems is desirable because it enhances robustness and understanding of the numerical results. Moreover, subproblems can be solved in parallel using the optimization technique most suitable for the underlying mathematical form of the subproblem. Hierarchical overlapping coordination (HOC) is an interesting strategy for solving decomposed problems. It simultaneously uses two or more design problem decompositions, each of them associated with different partitions of the design variables and constraints. Coordination is achieved by the exchange of information between decompositions. This article presents the HOC algorithm and several new sufficient conditions for convergence of the algorithm to the optimum in the case of convex problems with linear constraints. One of these equivalent conditions involves the rank of the constraint matrix that is computationally efficient to verify. Computational results obtained by applying the HOC algorithm to quadratic programming problems of various sizes are included for illustration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44766/1/10589_2004_Article_321085.pd

A Sensitivity-Based Commonality Strategy for Family Products of Mild Variation, with Application to Automotive Body Structures

Identification of the product platform is a key step in designing a family of products. This article presents a methodology for selecting the product platform by using information obtained from the individual optimization of the product variants. Under the assumption that the product variety requires only mild design changes, a performance deviation vector is derived by taking into consideration individual optimal designs and sensitivities of functional requirements. Commonality decisions are based on values of the performance deviation vector, and the product family is designed optimally with respect to the chosen platform. The proposed methodology is applied to the design of a family of automotive body structures. Variants are defined by changing the functional requirements they need to satisfy and/or the geometry of the associated finite element models.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87280/4/Saitou29.pd

A Sensitivity-Based Commonality Strategy for Family Products of Mild Variation, with Application to Automotive Body Structures

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77299/1/AIAA-2002-5610-730.pd

Extension of the target cascading formulation to the design of product families

The target cascading methodology for optimal product development is extended to product families with predefined platforms. The single-product formulation is modified to accommodate the presence of shared systems, subsystems, and/or components and locally introduced targets. Hierarchical optimization problems associated with each product variant are combined to formulate the product family multicriteria design problem, and common subproblems are identified based on the shared elements (i.e. the platform). The solution of the overall design problem is coordinated so that the shared elements are consistent with the performance and behaviour of the product variants. A simple automotive design example is used to demonstrate the proposed methodology.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41910/1/20240293.pd

Model-Based Partitioning in Optimal Design of Large Engineering Systems

The article describes a method to identify weakly-connected structures in design optimization models---an optimization problem in itself. A model is represented by a hypergraph in which nodes represent design relations (i.e., design objectives and constraints) and hyperedges represent design and state/behavior variables. Optimal model-based partitioning of the problem is then solved using graph and hypergraph partitioning techniques, such as spectral and local search methods. The formulation is able to account for computational demands and resources, strength of coupling between design relations, and partitioning constraints of decomposition-by-components and decomposition-by-disciplines. Automotive powertrain system and structural optimization models are used as examples. The method may also be used to organize the design process