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.

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—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.

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.

scholarly journals A Convergence Analysis of Unconstrained and Bound Constrained Evolutionary Pattern Search

2001 ◽  
Vol 9 (1) ◽  
pp. 1-23 ◽  
Author(s):  
William E. Hart
Keyword(s):  
Search Algorithms ◽  
Pattern Search ◽  
Convergence Theory ◽  
Mutation Operator ◽  
Convergence Properties ◽  
Step Size ◽  
Search Methods ◽  
Evolutionary Pattern ◽  
Bound Constrained Optimization ◽  
Pattern Search Methods

We present and analyze a class of evolutionary algorithms for unconstrained and bound constrained optimization on Rn: evolutionary pattern search algorithms (EPSAs). EPSAs adaptively modify the step size of the mutation operator in response to the success of previous optimization steps. The design of EPSAs is inspired by recent analyses of pattern search methods. We show that EPSAs can be cast as stochastic pattern search methods, and we use this observation to prove that EPSAs have a probabilistic, weak stationary point convergence theory. This convergence theory is distinguished by the fact that the analysis does not approximate the stochastic process of EP-SAs, and hence it exactly characterizes their convergence properties.

scholarly journals Chip Attach Scheduling in Semiconductor Assembly

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zhicong Zhang ◽  
Kaishun Hu ◽  
Shuai Li ◽  
Huiyu Huang ◽  
Shaoyong Zhao
Keyword(s):  
Objective Function ◽  
Objective Function Value ◽  
Learning Algorithm ◽  
Parallel Machine Scheduling ◽  
Volume Index ◽  
Production Volume ◽  
Learning Problem ◽  
Reward Function ◽  
Unrelated Parallel Machine Scheduling ◽  
Target Production

Chip attach is the bottleneck operation in semiconductor assembly. Chip attach scheduling is in nature unrelated parallel machine scheduling considering practical issues, for example, machine-job qualification, sequence-dependant setup times, initial machine status, and engineering time. The major scheduling objective is to minimize the total weighted unsatisfied Target Production Volume in the schedule horizon. To apply Q-learning algorithm, the scheduling problem is converted into reinforcement learning problem by constructing elaborate system state representation, actions, and reward function. We select five heuristics as actions and prove the equivalence of reward function and the scheduling objective function. We also conduct experiments with industrial datasets to compare the Q-learning algorithm, five action heuristics, and Largest Weight First (LWF) heuristics used in industry. Experiment results show that Q-learning is remarkably superior to the six heuristics. Compared with LWF, Q-learning reduces three performance measures, objective function value, unsatisfied Target Production Volume index, and unsatisfied job type index, by considerable amounts of 80.92%, 52.20%, and 31.81%, respectively.

Geometric Optimization of Concentrating Solar Collectors using Monte Carlo Simulation

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
A. J. Marston ◽  
K. J. Daun ◽  
M. R. Collins
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Programming ◽  
Objective Function ◽  
Sample Size ◽  
Optimization Algorithm ◽  
Geometric Optimization ◽  
Trial And Error ◽  
Solar Collectors ◽  
Step Size

This paper presents an optimization algorithm for designing linear concentrating solar collectors using stochastic programming. A Monte Carlo technique is used to quantify the performance of the collector design in terms of an objective function, which is then minimized using a modified Kiefer–Wolfowitz algorithm that uses sample size and step size controls. This process is more efficient than traditional “trial-and-error” methods and can be applied more generally than techniques based on geometric optics. The method is validated through application to the design of three different configurations of linear concentrating collector.

scholarly journals Joint admission control and power allocation in hospital networks based on cognitive radios.

2021 ◽  
Author(s):  
Yicong Liu
Keyword(s):  
Objective Function ◽  
Admission Control ◽  
Objective Function Value ◽  
Cognitive Radios ◽  
Hospital Environment ◽  
Mixed Integer ◽  
Total System ◽  
Secondary Users ◽  
Source Power ◽  
Minlp Problem

In this thesis, we present an approach to solve the joint call admission control and power allo- cation problem in a hospital environment based on cognitive radio. Specifically, a multi-objective non-convex mixed integer non-linear programming (MINLP) problem with weighted-sum method for wireless access in an indoor hospital environment has been formulated in order to maximize the number of admitted secondary users and minimize transmit power while guaranteeing the through- put of all secondary users and satisfying the interference constraints for the protected and primary users. To solve this MINLP problem with different weights given to different objectives, we pro- pose to use the standard branch and bound algorithm as appropriately modified to find the optimal solution. We also coded a specific program using OPTI Toolbox to find the minimum objective function value, number of admitted secondary users and all related values such as total system power and throughput. To analyze the numerical results, we considered three cases with equal and non-equal weights. We also changed the values of interference and maximum source power to obtain and analyze different results comparing with the normal one. Our results indicate that more power is allocated and better throughput is guaranteed while the number of admitted users is increasing. However, as they increase, the objective function value increases steadily as well, which means that it is more difficult to reach our minimizing objective.

Gate location optimization scheme for plastic injection molding

e-Polymers ◽  
2009 ◽  
Vol 9 (1) ◽  
Author(s):  
Ming Zhai ◽  
Yeecheong Lam ◽  
Chikit Au
Keyword(s):  
Injection Molding ◽  
Objective Function ◽  
Flow Path ◽  
Computationally Efficient ◽  
Gate Location ◽  
Adjacent Node ◽  
Filling Time ◽  
Efficient Scheme ◽  
Balanced Flow ◽  
Search Routine

AbstractGate location of injection molding is vital to achieve high quality plastic part. The determination of gate location is an important issue in mold design. A computationally efficient scheme based on flow path is proposed to locate the optimum gate for achieving balanced flow. The range of filling time is employed as objective function. Comparisons were made between the flow path search scheme and the existing adjacent node evaluation scheme, and between the objective function of the range of filling time and the existing standard deviation of filling time. The two examples investigated indicated that the search routine based on the concept of flow path is more efficient computationally and the range of filling time is a better objective function to reflect the uniformity of fill.

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