Objective Function Effect Based Pattern Search—Theoretical Framework Inspired by 3D Component Layout

2006 ◽  
Vol 129 (3) ◽  
pp. 243-254 ◽  
Author(s):  
Chandankumar Aladahalli ◽  
Jonathan Cagan ◽  
Kenji Shimada
Keyword(s):  
Objective Function ◽  
A Priori ◽  
Three Dimensional ◽  
Parameter Tuning ◽  
Search Algorithms ◽  
Pattern Search ◽  
Function Change ◽  
Component Layout ◽  
Novel Method ◽  
Treat All

Though pattern search algorithms have been successfully applied to three-dimensional (3D) component layout problems, a number of unanswered questions remain regarding their parameter tuning. One such question is the scheduling of patterns in the search. Current pattern search methods treat all patterns similarly and all of them are active from the beginning to the end of the search. Observations from 3D component layout motivate the question whether patterns should be introduced in some different order during the search. This paper presents a novel method for scheduling patterns that is inspired by observations from 3D component layout problems. The new method introduces patterns into the search in the decreasing order of a priori expectation of the objective function change due to the patterns. Pattern search algorithms based on the new pattern schedule run 30% faster on average than conventional pattern search based algorithms on 3D component layout problems and general 2D multimodal surface minimization problems. However since determining the expected change in objective function value due to the patterns is expensive, we explore approximations using domain information.

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.

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.

Multivariate Constrained GNSS Real-time Full Attitude Determination Based on Attitude Domain Search

2018 ◽  
Vol 72 (2) ◽  
pp. 483-502
Author(s):  
Hongtao Wu ◽  
Xiubin Zhao ◽  
Chunlei Pang ◽  
Liang Zhang ◽  
Bo Feng
Keyword(s):  
Objective Function ◽  
Success Rate ◽  
High Efficiency ◽  
Attitude Determination ◽  
A Priori ◽  
Three Dimensional ◽  
Satellite System ◽  
New Method ◽  
Lambda Method ◽  
Attitude Angle

A priori attitude information can improve the success rate and reliability of Global Navigation Satellite System (GNSS) multi-antennae attitude determination. However, a priori attitude information is nonlinear, and integrating a priori information into the objective function rigorously will increase the complexity of an ambiguity domain search, such as the Multivariate Constrained-Least-squares Ambiguity Decorrelation Adjustment (MC-LAMBDA) method. In this paper, a new method based on attitude domain search is presented to make use of the a priori attitude angle information with high efficiency. First, the a priori information of pitch and roll is integrated into the search process to derive the analytic search step for attitude angle, and the integer candidates are determined by traversal search in the three-dimensional attitude domain. Then, the objective function is parameterised with Euler angles, and a non-iterative approximate method is utilised to simplify the iterative computation in calculating objective function values. Experimental results reveal that compared to the MC-LAMBDA method, our new method has the same success rate and reliability, but higher efficiency in making use of a priori attitude information.

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%.

Automated Generation of Optimally Directed Three Dimensional Component Layouts

1993 ◽  
Author(s):  
Simon Szykman ◽  
Jonathan Cagan
Keyword(s):  
Objective Function ◽  
Three Dimensional ◽  
Function Spaces ◽  
Global Optimality ◽  
Layout Problem ◽  
Automated Generation ◽  
Generation Technique ◽  
Novel Approach ◽  
Component Layout ◽  
Design Generation

Abstract This research introduces a novel approach towards automating the generation of three dimensional component layouts. Three dimensional component layout tasks are typically highly combinatorial, and exhibit objective function spaces that can be nonlinear and/or discontinuous due to discrete allowable locations for component placement. We present an approach to the three dimensional component layout problem that employs shape annealing, a design generation technique combining concepts from shape grammars and simulated annealing, to produce optimally directed designs. The shape annealing paradigm sacrifices global optimality in exchange for the ability to find good designs in a reasonable amount of time, given very large, ill-behaved objective function spaces.

scholarly journals Contextual Covariance Matrix Adaptation Evolutionary Strategies

2017 ◽  
Author(s):  
Abbas Abdolmaleki ◽  
Bob Price ◽  
Nuno Lau ◽  
Luis Paulo Reis ◽  
Gerhard Neumann
Keyword(s):  
Objective Function ◽  
Size Control ◽  
Parameter Tuning ◽  
Search Algorithms ◽  
Stochastic Search ◽  
Premature Convergence ◽  
Evolutionary Strategies ◽  
Minimal Amount ◽  
Step Size ◽  
Covariance Matrix Adaptation

Many stochastic search algorithms are designed to optimize a fixed objective function to learn a task, i.e., if the objective function changes slightly, for example, due to a change in the situation or context of the task, relearning is required to adapt to the new context. For instance, if we want to learn a kicking movement for a soccer robot, we have to relearn the movement for different ball locations. Such relearning is undesired as it is highly inefficient and many applications require a fast adaptation to a new context/situation. Therefore, we investigate contextual stochastic search algorithms that can learn multiple, similar tasks simultaneously. Current contextual stochastic search methods are based on policy search algorithms and suffer from premature convergence and the need for parameter tuning. In this paper, we extend the well known CMA-ES algorithm to the contextual setting and illustrate its performance on several contextual tasks. Our new algorithm, called contextual CMA-ES, leverages from contextual learning while it preserves all the features of standard CMA-ES such as stability, avoidance of premature convergence, step size control and a minimal amount of parameter tuning.

A Pattern Search-Based Algorithm for Three-Dimensional Component Layout

1998 ◽  
Author(s):  
Su Yin ◽  
Jonathan Cagan
Keyword(s):  
Three Dimensional ◽  
Pattern Search ◽  
Test Problems ◽  
Optimal Solutions ◽  
Local Minima ◽  
Objective Functions ◽  
Spatial Constraint ◽  
Routing Problem ◽  
Component Layout ◽  
Different Types

Abstract A pattern search-based 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.

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]

Shape Optimization of Hydraulic Structures: an Example of an Optimum Design of a Fish Passage

10.29007/2k64 ◽  
2018 ◽  
Author(s):  
Pat Prodanovic ◽  
Cedric Goeury ◽  
Fabrice Zaoui ◽  
Riadh Ata ◽  
Jacques Fontaine ◽  
...  
Keyword(s):  
Numerical Model ◽  
Shape Optimization ◽  
Objective Function ◽  
Optimum Design ◽  
Optimization Problem ◽  
A Priori ◽  
Coupled System ◽  
Fish Passage ◽  
Hydraulic Structures ◽  
Design Variables

This paper presents a practical methodology developed for shape optimization studies of hydraulic structures using environmental numerical modelling codes. The methodology starts by defining the optimization problem and identifying relevant problem constraints. Design variables in shape optimization studies are configuration of structures (such as length or spacing of groins, orientation and layout of breakwaters, etc.) whose optimal orientation is not known a priori. The optimization problem is solved numerically by coupling an optimization algorithm to a numerical model. The coupled system is able to define, test and evaluate a multitude of new shapes, which are internally generated and then simulated using a numerical model. The developed methodology is tested using an example of an optimum design of a fish passage, where the design variables are the length and the position of slots. In this paper an objective function is defined where a target is specified and the numerical optimizer is asked to retrieve the target solution. Such a definition of the objective function is used to validate the developed tool chain. This work uses the numerical model TELEMAC- 2Dfrom the TELEMAC-MASCARET suite of numerical solvers for the solution of shallow water equations, coupled with various numerical optimization algorithms available in the literature.

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