Peter Fenyes

Partitioned Quasi-Newton methods for nonlinear equality constrained optimization

We derive new quasi-Newton updates for the (nonlinear) equality constrained minimization problem. The new updates satisfy a quasi-Newton equation, maintain positive definiteness on the null space of the active constraint matrix, and satisfy a minimum change condition. The application of the updates is not restricted to a small neighbourhood of the solution. In addition to derivation and motivational remarks, we discuss various numerical subtleties and provide results of numerical experiments.

A Fast and Efficient Compact Packing Algorithm for Free-Form Objects

In this paper, a compact packing algorithm for the placement of objects inside a container is described. The proposed packing algorithm packs three-dimensional free-form objects inside an arbitrary enclosure such that the packing efficiency is maximized. The proposed packing algorithm can handle objects with holes or cavities and its performance does not degrade significantly with the increase in complexity of the enclosure or the objects. The packing algorithm takes as input the triangulated geometry of the container and all the objects to be packed and outputs the list of objects that can be placed inside the enclosure. The packing algorithm also outputs the location and orientation of all the objects, the packing sequence, and the packed configuration. An improved layout algorithm that works with arbitrary container geometry is also proposed. Several heuristics to improve the performance of the packing algorithm as well as certain aspects that facilitate fast and efficient handling of CAD data are also discussed. A comprehensive benchmarking of the proposed packing algorithm on synthetic and hypothetical problems reflects its superior performance as compared to other similar approaches.Copyright

Three-Dimensional Packing by a Heuristic-based Sequential Genetic Algorithm

This paper presents a hybrid Genetic Algorithm for three-dimensional packing optimization. It is applicable to a class of packing problems where the final number of packed items is unknown. Examples include the bin packing problem and the luggage capacity problem where the compactness or packing efficiency must be maximized by selecting an appropriate subset of items from a predefined set and packing them in a predefined container. Many algorithms, which are reviewed in this paper, have been developed in various engineering fields for specific applications. Packing algorithms can be categorized into two types according to the definition of the design variables. In the first type, the design variables are the spatial coordinates of the packed items. In this case, a constraint specifying zero collision between items must be considered and evaluated for each trial set of design variables. In the second type, the design variables correspond to the sequential order in which the items are considered for packing. In this case, the location of an item is unknown until it is successfully packed inside the container based on a sequence. The advantage of the latter approach is that the zero-collision constraint is implicitly defined in the packing procedure, thereby reducing the need for collision detection and the overall computation effort. The present algorithm is of the second type. The algorithm was developed in two phases. In the first phase, the algorithm was extensively studied and improved using a simplified packing problem where the container and all items are modeled as rectangular prisms with discrete 90-degree rotations. This phase allowed the identification of appropriate values for the problem-dependent genetic parameters such as crossover and mutation rates. In the second phase, sets of heuristic rules were implemented and tested. The use of appropriate heuristics led to an increase in computational efficiency without significant loss in optimality. This paper describes the algorithm and its multiple variants defined by the heuristic rules imbedded in the packing strategy. Several heuristics and packing strategies are presented and the issues related to computational efficiency are discussed. The algorithm is demonstrated on several test problems.

A Fast and Efficient Compact Packing Algorithm for SAE and ISO Luggage Packing Problems

In this paper, a compact packing algorithm for the placement of objects inside a container is described. The proposed packing algorithm is designed to pack three-dimensional free-form objects inside an arbitrary enclosure such that the packing efficiency is maximized. The proposed packing algorithm can handle objects with holes or cavities, and its performance does not degrade significantly with the increase in complexity of the enclosure or the objects. The packing algorithm takes as input the tessellated geometry of the container and all the objects to be packed and outputs the list of objects that can be placed inside the enclosure. The packing algorithm also outputs the location and orientation of all the objects, the packing sequence, and the packed configuration. An improved layout algorithm that works with arbitrary container geometry is also proposed. Separate layout algorithms for the SAE and ISO luggage are developed. Several heuristics to improve the performance of the packing algorithm are also incorporated. Certain aspects that facilitate fast and efficient handling of the computer aided design (CAD) data are also discussed. A comprehensive benchmarking of the proposed packing algorithm on synthetic and hypothetical problems reflects its superior performance as compared with other similar approaches.

Application of Math-Based Marketing and Financial Tools in an Automated Parametric Design Framework

A suite of math-based marketing and financial tools has been deployed and exercised within an automated, multidisciplinary parametric design framework. This suite of tools includes a market share estimator based on Cook’s S-Model, a Technical Cost Model for estimating the variable and fixed costs of the vehicle’s body system, a database of cost estimates for other vehicle systems, and a profit estimator developed from a standard accounting template. Development of the S-Model market share estimator included completion of a Demand-Price analysis for the midsize sedan segment and collection of publicly available value curves predominantly covering the powertrain performance and interior roominess disciplines. A flexible input-output interface was developed for the Technical Cost Model to provide a means of propagating changes in body design parameters throughout the framework. A series of exercises including analysis of a baseline vehicle, optimization of a hypothetical vehicle concept for net income, and a hypothetical architectural parameter study were conducted to demonstrate the capabilities of a multidisciplinary parametric design framework enabled with marketing and financial tools. These exercises demonstrate that existing engineering and business discipline tools can effectively interoperate to design for profitability in a multidisciplinary parametric design environment. They also illustrate several key challenges in automated design for profitability, such as those encountered in defining the role of price as a design variable in a tightly coupled design-for-profit system and in generating cost estimates using a continuously variable design representation.Copyright

An Example Performance Trade-Off Evaluation Using the Integration Framework for Architecture Development (IFAD) for Conceptual Vehicle Design

The Integration Framework for Architecture Development (IFAD) is an integrated framework that provides fast and consistent discipline analysis results and identifies discipline consequences corresponding to vehicle design changes. This information is valuable for balancing and integration in the early design phase. In this paper, the IFAD framework is utilized to conduct an example multi-objective multi-disciplinary optimization to evaluate vehicle performance trade-offs for a hypothetical vehicle. We consider design changes on high-level geometrical dimensions including front overhang, rear overhang and vehicle width at rocker. We also study vehicle configurations including choice of materials and tires and choice of powertrains. A commonly used multi-objective genetic algorithm (MOGA) technique, Non-dominated Sorting Genetic Algorithm (NSGAII [1]) is chosen because of the mixed types of design variables involved (i.e., continuous design variables representing high-level geometrical dimensions and discrete design variables representing vehicle configurations such as powertrain selection and material choice). Vehicle performance analyses in a range of disciplines such as geometry, aerodynamics and energy are carried out automatically through IFAD. The use of response surface modeling (RSM) is desired due to the large number of evaluations typical for a MOGA application. A comparison of the engineering performance trade-offs based on two different sets of performance objectives is presented.Copyright

Propagation and Merging of Uncertain Expert Opinions in a Hierarchical Multilevel System

A procedure for propagating and merging uncertain experts’ opinions provided as intervals and subjective beliefs is presented in this paper. The proposed approach can be applied to hierarchical multilevel models with functional relations linking the characteristics of the multilevel model nodes. When experts’ opinions are provided at the leaf nodes, it is necessary to propagate intervals towards the top level to determine belief and plausibility curves that capture the overall uncertainties in experts’ opinions using the Evidence theory. The propagation of intervals can result in a possibly overwhelming number of intervals to be handled. Hence, a propagation and merging procedure is proposed to reduce the number of intervals. A test case example is used to illustrate the eciency of the procedure.