A Sensitivity-Based Pattern Search Algorithm for 3D Component Layout

2002 ◽  
Author(s):  
Chandankumar Aladahalli ◽  
Jonathan Cagan ◽  
Kenji Shimada
Keyword(s):  
Objective Function ◽  
Search Algorithm ◽  
Search Space ◽  
Pattern Search ◽  
Step Size ◽  
Simple Method ◽  
Pattern Search Algorithm ◽  
Component Layout ◽  
Extended Pattern Search ◽  
Better Than

This paper introduces the Sensitivity-based Pattern Search (SPS) algorithm for 3D component layout. Although based on the pattern search algorithm, SPS differs in that at any given step size the algorithm does not necessarily perturb the search space along all possible search dimensions. Instead all possible perturbations, or moves are ranked in decreasing order of their effect on the objective function and are applied in that order. The philosophy behind this algorithm is that moves that affect the objective function more must be applied before the moves that affect the objective function less. We call this effect on the objective function the sensitivity of the objective function to a particular move and present a simple method to quantify it. This algorithm performs better than the previous Extended Pattern Search algorithm with decrease in run time of up to 28%.

Objective Function Effect Based Pattern Search—An Implementation for 3D Component Layout

2005 ◽  
Vol 129 (3) ◽  
pp. 255-265 ◽  
Author(s):  
Chandankumar Aladahalli ◽  
Jonathan Cagan ◽  
Kenji Shimada
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Search Algorithm ◽  
A Priori ◽  
Search Space ◽  
Pattern Search ◽  
Pattern Search Algorithm ◽  
Function Change ◽  
Component Layout ◽  
Geometric Layout

Generalized pattern search (GPS) algorithms have been used successfully to solve three-dimensional (3D) component layout problems. These algorithms use a set of patterns and successively decreasing step sizes of these patterns to explore the search space before converging to good local minima. A shortcoming of conventional GPS algorithms is the lack of recognition of the fact that patterns affect the objective function by different amounts and hence it might be efficient to introduce them into the search in a certain order rather than introduce all of them at the beginning of the search. To address this shortcoming, it has been shown by the authors in previous work that it is more efficient to schedule patterns in decreasing order of their effect on the objective function. The effect of the patterns on the objective function was estimated by the a priori expectation of the objective function change due to the patterns. However, computing the a priori expectation is expensive, and to practically implement the scheduling of patterns, an inexpensive estimate of the effect on the objective function is necessary. This paper introduces a metric for geometric layout called the sensitivity metric that is computationally inexpensive, to estimate the effect of pattern moves on the objective function. A new pattern search algorithm that uses the sensitivity metric to schedule patterns is shown to perform as well as the pattern search algorithm that used the a priori expectation of the objective function change. Though the sensitivity metric applies to the class of geometric layout or placement problems, the foundation and approach is useful for developing metrics for other optimization problems.

Minimum Height Packing for Layered Manufacturing Using an Extended Pattern Search Algorithm

2003 ◽  
Author(s):  
Chandankumar Aladahalli ◽  
Jonathan Cagan ◽  
Kenji Shimada
Keyword(s):  
Search Algorithm ◽  
3D Models ◽  
Layered Manufacturing ◽  
Pattern Search ◽  
Maximum Height ◽  
Pattern Search Algorithm ◽  
Time To Build ◽  
Component Layout ◽  
Minimum Height ◽  
Extended Pattern Search

This paper introduces an approach to solve the minimum height layout problem for layered manufacturing using a pattern search based algorithm called Extended Pattern Search. In the batch processing of several components in a typical layered manufacturing run, it is efficient in terms of cost and time to build the components after packing their 3D models such that the maximum height of the components is minimized. 3D component layout based on a pattern search algorithm provides a framework to accomplish such minimum height packing. A method to determine the objective function weights for a class of problems is also provided. Finally error minimizing build directions are incorporated in the 3D layout framework by imposing suitable spatial orientation constraints on individual components.

An Extended Pattern Search Algorithm for Three-Dimensional Component Layout

2000 ◽  
Vol 122 (1) ◽  
pp. 102-108 ◽  
Author(s):  
Su Yin ◽  
Jonathan Cagan
Keyword(s):  
Search Algorithm ◽  
Three Dimensional ◽  
Pattern Search ◽  
Test Problems ◽  
Spatial Constraint ◽  
Routing Problem ◽  
Pattern Search Algorithm ◽  
Component Layout ◽  
Different Types ◽  
Extended Pattern Search

An extended pattern search algorithm is introduced for efficient component layout optimization. The algorithm is applicable to general layout problems, where component geometry can be arbitrary, design goals can be multiple and spatial constraint satisfactions can be of different types. Extensions to pattern search are introduced to help the algorithm to converge to optimal solutions by escaping inferior local minima. The performance on all of the test problems shows that the algorithm runs one-to-two orders of magnitude faster than a robust simulated annealing-based algorithm for results with the same quality. The algorithm is further extended to solve a concurrent layout and routing problem, which demonstrates the ability of the algorithm to apply new pattern strategies in search and to include different objective functions in optimization. [S1050-0472(00)01901-2]

Layout Optimization of Shapeable Components With Extended Pattern Search Applied to Transmission Design

2004 ◽  
Vol 126 (1) ◽  
pp. 188-191 ◽  
Author(s):  
Su Yin ◽  
Jonathan Cagan ◽  
Peter Hodges
Keyword(s):  
Cross Section ◽  
Search Algorithm ◽  
Automatic Transmission ◽  
Layout Optimization ◽  
Pattern Search ◽  
Fixed Size ◽  
Pattern Search Algorithm ◽  
Transmission Design ◽  
Product Layout ◽  
Extended Pattern Search

An extended pattern search algorithm is presented for the placement of shapeable components within a product layout. Shapeable octrees are used to evaluate the amount of overlap between pairs of components, extending previous technology that requires fixed-size components. The method is used to conceptualize the layout of the cross-section of an automatic transmission.

An Extended Pattern Search Approach to Wind Farm Layout Optimization

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Bryony L. Du Pont ◽  
Jonathan Cagan
Keyword(s):  
Wind Speed ◽  
Wind Farm ◽  
Search Algorithm ◽  
Pattern Search ◽  
Global Evaluation ◽  
Layout Problem ◽  
Pattern Search Algorithm ◽  
Wind Farm Layout ◽  
Search Approach ◽  
Extended Pattern Search

An extended pattern search approach is presented for the optimization of the placement of wind turbines on a wind farm. Problem-specific extensions infuse stochastic characteristics into the deterministic pattern search, inhibiting convergence on local optima and yielding better results than pattern search alone. The optimal layout for a wind farm is considered here to be one that maximizes the power generation of the farm while minimizing the farm cost. To estimate the power output, an established wake model is used to account for the aerodynamic effects of turbine blades on downstream wind speed, as the oncoming wind speed for any turbine is proportional to the amount of power the turbine can produce. As turbines on a wind farm are in close proximity, the interaction of turbulent wakes developed by the turbines can have a significant effect on the power development capability of the farm. The farm cost is estimated using an accepted simplified model that is a function of the number of turbines. The algorithm develops a two-dimensional layout for a given number of turbines, performing local turbine movement while applying global evaluation. Three test cases are presented: (a) constant, unidirectional wind, (b) constant, multidirectional wind, and (c) varying, multidirectional wind. The purpose of this work is to explore the ability of an extended pattern search (EPS) algorithm to solve the wind farm layout problem, as EPS has been shown to be particularly effective in solving multimodal layout problems. It is also intended to show that the inclusion of extensions into the algorithm can better inform the search than algorithms that have been previously presented in the literature. Resulting layouts created by this extended pattern search algorithm develop more power than previously explored algorithms using the same evaluation models and objective functions. In addition, the algorithm’s resulting layouts motivate a heuristic that aids in the manual development of the best layout found to date. The results of this work validate the application of an extended pattern search algorithm to the wind farm layout problem, and that its performance is enhanced by the use of problem-specific extensions that aid in developing results that are superior to those developed by previous algorithms.

Layout of an Automobile Transmission Using Three-Dimensional Shapeable Components

1999 ◽  
Author(s):  
Su Yin ◽  
Jonathan Cagan ◽  
Peter Hodges ◽  
Xianren Li
Keyword(s):  
Search Algorithm ◽  
Three Dimensional ◽  
Pattern Search ◽  
Optimization Process ◽  
Functional Requirements ◽  
Pattern Search Algorithm ◽  
Torque Capacity ◽  
Product Layout ◽  
Extended Pattern Search ◽  
Connection Cost

Abstract An extended pattern search algorithm is presented for the placement of shapeable components within a product layout. The algorithm is applied to an automobile transmission layout taking into account the shapeability of the components. Overlap between components is allowed and penalized during the optimization process. Shapeable octrees are used to evaluate the amount of overlap between pairs of components. The algorithm minimizes the connection cost in addition to optimizing the position and size of the components. A shapeable component has a defined geometry, but its size may vary within limits. The size of clutches in a transmission is determined by the torque capacity requirement, thermal requirement, and gain requirement. Under a given load, the size of a clutch satisfying a set of functional requirements is related to its location in the transmission assembly, making it necessary to design the clutches on the fly while laying out the components.

Objective Function Based Pattern Search: A Computationally Efficient Algorithm for 3D Component Layout

2004 ◽  
Author(s):  
Chandankumar Aladahalli ◽  
Jonathan Cagan ◽  
Kenji Shimada
Keyword(s):  
Objective Function ◽  
Objective Function Value ◽  
Search Algorithms ◽  
Pattern Search ◽  
Computationally Efficient ◽  
Step Size ◽  
Current Pattern ◽  
New Class ◽  
Component Layout ◽  
3D Layout

A new class of pattern search algorithms called Objective Function-based Pattern Search is proposed for 3D Layout. These algorithms are driven by decreasing expected change in objective function rather than by decreasing step size. Current pattern search algorithms rely on decreasing step size of all patterns at the same rate. Also, all translation and rotation patterns are active at all step sizes of patterns. The new class of algorithms decreases the step sizes of the patterns based on the expected change in objective function value due to that pattern. Also, whether a pattern is active or inactive at a particular step size is decided by the expected change in objective function due to that pattern at that step size. The new algorithm is found to be up to 50% faster in runtime compared to previous pattern search based algorithms.

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