Search

Cost and dimensional variation of products are significant attributes in multistation assembly processes. These attributes depend on product/process tolerances and fixture layouts. Typically, tolerance allocation and fixture layout design are conducted separately without considering potential interrelations. In this work, we use multi-objective optimization for integrated tolerance allocation and fixture layout design to address interactions and to quantify tradeoffs among cost, product variation, and assembly process sensitivity. A nested optimization strategy is applied to a vehicle side frame assembly. Results demonstrate the presence and quantification of tradeoffs, based on which we introduce the concept of critical variation and critical budget requirements. [DOI: 10.1115/1.2951951]

Computational models in engineering often use a range of analysis functions within the same optimization problem, from finite element models to analytical expressions. The computational expense of these models often differs by orders of magnitude, and practical optimization algorithms should address this discrepancy. In this article, in an effort to reduce the number of expensive analyses, a technique is discussed for modifying trust region algorithms to utilize the inexpensive functions directly when calculating iterates. The technique is implemented with a trust region algorithm of Yuan and applied to valve event optimization of an internal combustion engine.

Optimal design of large systems is easier if the optimization model can be decomposed and solved as a set of smaller, coordinated subproblems. Casting a given design problem into a particular optimization model by selecting objectives and constraints is generally a subjective task. In system models where hierarchical decomposition is possible, a formal process for selecting objective functions can be made, so that the resulting optimal design model has an appropriate decomposed form and also possesses desirable properties for the scalar substitute functions used in multicriteria optimization. Such a process is often followed intuitively during the development of a system optimization model by summing selected objectives from each subsystem into a single overall system objective. The more formal process presented in this article is simple to implement and amenable to automation.

Global optimization algorithms for generalized polynomial design models using a global feasible search approach was discussed in a previous article. A new convex cutting plane algorithm (CONCUT) based on global feasible search and with improved performance is presented in this sequel article. Computational results of the CONCUT algorithm compared to one using linear cuts (LINCUT) are given for various test problems. A speed reducer design example illustrates the application of the algorithms.

A new design optimization method is described for finding global solutions of models with a nonconvex objective function and nonlinear constraints. All functions are assumed to be generalized polynomials. By introducing new variables, the original model is transformed into one with a linear objective function, one convex and one reversed convex constraint. A two-phase algorithm that includes global feasible search and local optimal search is used for globally optimizing the transformed model. Several examples illustrate the method.

Optimal design of large engineering systems modeled as nonlinear programming problems remains a challenge because increased size reduces reliability and speed of numerical optimization algorithms. Decomposition of the original model into smaller coordinated submodels is desirable or even necessary. The article presents a methodology for optimal model-based decomposition of design problems, whether or not initially cast as optimization models. The overall model is represented by a hypergraph that is optimally partitioned into weakly-connected subgraphs satisfying partitioning constraints. The formulation is robust enough to account for computational demands and resources, and the strength of interdependencies between the design relations contained in the model. This decomposition methodology is applied to a vehicle powertrain system design model consisting of engine, torque converter, transmission, and wheel-tire assemblies, with 87 design relations and 119 design and state/behavior variables.

The capability of mathematical optimization to support the mechanical design process is finally reaching wide recognition, as evidenced by significant applications in industry. The article reviews key issues and challenges for design optimization theorists and practitioners. Large scale system design and topology or configuration design are identified as the most important areas of future design optimization research. Some new approaches for partitioning large design problems and for topology optimization of multi-component structural systems are introduced.

Structural optimization procedures usually Mart from a given design topology and vary proportions or boundary shapes of the design to achieve optimality of an objective under various constraints. This article presents examples of the application of a novel approach for initiating formal structural optimization at an earlier stage, where the design topology is rigorously generated. A three-phase design process is used. In Phase I, an optimal initial topology is created by a homogenization method as a gray-scale image. In Phase II, the image is transformed to a realizable design using computer vision techniques. In Phase III, the design is parameterized and treated in detail by conventional size and shape optimization techniques. Fully-automated procedures for optimization of two-dimensional solid structures are outlined, and several practical design problems for this type of structures are solved using the proposed procedure, including a crane hook and a bicycle frame.

The concept of constraint activity, widely used throughout the optimization literature, is extended and clarified to deal with global optimization problems containing either continuous or discrete variables. The article presents definitions applicable to individual constraints and discusses definitions for groups of constraints. Concepts are reinforced through the use of examples. The definitions are used to investigate the ideas of optimization 'cases' and monotonicity analysis as applied to global and discrete problems. Relationships to local optimization are also noted.

Early preliminary models for optimal design problems in nonlinear programming formulations often have solutions that are constraint-bound points, i.e., the number of active constraints equals the number of design variables. Models leading to such solutions will typically offer little insight to design trade-offs, and it is desirable to identify them early in order to revise the model or to exclude the points from an active set strategy. Application of monotonicity analysis can quickly identify constraint-bound candidate solutions but not always prove their optimality. This article discusses some conditions under which these points are in fact global or local optima.

Byline: K. Hamza, I. Hossoy, J.F. Reyes-Luna, P.Y. Papalambros Designing for improved interior comfort and crashworthiness is an important but competing objective in vehicle development. These objectives are linked by common design decisions on allocating a fixed total amount of space, and so they should be addressed together. Such combined optimisation is hindered by the large computational effort required for crash analysis using full-scale vehicle models and by the lack of adequate interior comfort models. In this paper, a driver and rear passenger seating comfort model is combined with a modest but adequate frontal crashworthiness model into an overall system optimisation problem. Solution of the combined problem allows a quantitative investigation into design tradeoffs between comfort and safety. The results suggest that combined optimisation can lead to superior vehicle designs and they motivate more detailed studies with models of increased fidelity.