Continuous Global Minimization Method Based on Special Mathematical Structure of Objective Functions and Adjacent Local Minima Search

2014 ◽  
Vol 1 ◽  
pp. 215-218
Author(s):  
Hideo KANEMITSU
Keyword(s):  
Mathematical Structure ◽  
Global Minimization ◽  
Local Minima ◽  
Objective Functions ◽  
Minimization Method

A Global Minimization Method for Image Segmentation

2014 ◽  
Vol 35 (4) ◽  
pp. 791-796
Author(s):  
Wei-bin Li ◽  
Er Gao ◽  
Song-he Song
Keyword(s):  
Image Segmentation ◽  
Global Minimization ◽  
Minimization Method

scholarly journals Hybrid Neural-global Minimization Method of Logical Rule Extraction

1999 ◽  
Vol 3 (5) ◽  
pp. 348-356 ◽  
Author(s):  
Wlodzislaw Duch ◽  
◽  
Rafal Adamczak ◽  
KrzysAof Grabczewski ◽  
Grzegorz Zal
Keyword(s):  
Neural Networks ◽  
Hybrid Approach ◽  
Real Life ◽  
Rule Extraction ◽  
Global Minimization ◽  
Minimization Method ◽  
Life Problems ◽  
Multilayered Perceptron ◽  
Logical Functions ◽  
Logical Rules

Methodology of extraction of optimal sets of logical rules using neural networks and global minimization procedures has been developed. Initial rules are extracted using density estimation neural networks with rectangular functions or multilayered perceptron (MLP) networks trained with constrained backpropagation algorithm, transforming MLPs into simpler networks performing logical functions. A constructive algorithm called CMLP2LN is proposed, in which rules of increasing specificity are generated consecutively by adding more nodes to the network. Neural rule extraction is followed by optimization of rules using global minimization techniques. Estimation of confidence of various sets of rules is discussed. The hybrid approach to rule extraction has been applied to a number of benchmark and real life problems with very good results.

scholarly journals Global minimization for problems with multiple local minima

1993 ◽  
Vol 6 (2) ◽  
pp. 89-90
Author(s):  
Yuefan Deng ◽  
James Glimm ◽  
Qiqing Yu ◽  
Moshe Eisenberg
Keyword(s):  
Global Minimization ◽  
Local Minima

scholarly journals Contaminant source localization via Bayesian global optimization

2019 ◽  
Vol 23 (1) ◽  
pp. 351-369 ◽  
Author(s):  
Guillaume Pirot ◽  
Tipaluck Krityakierne ◽  
David Ginsbourger ◽  
Philippe Renard
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Source Localization ◽  
Source Location ◽  
Bayesian Optimization ◽  
Test Cases ◽  
Local Minima ◽  
Objective Functions ◽  
Contaminant Source ◽  
Highly Nonlinear

Abstract. Contaminant source localization problems require efficient and robust methods that can account for geological heterogeneities and accommodate relatively small data sets of noisy observations. As realism commands hi-fidelity simulations, computation costs call for global optimization algorithms under parsimonious evaluation budgets. Bayesian optimization approaches are well adapted to such settings as they allow the exploration of parameter spaces in a principled way so as to iteratively locate the point(s) of global optimum while maintaining an approximation of the objective function with an instrumental quantification of prediction uncertainty. Here, we adapt a Bayesian optimization approach to localize a contaminant source in a discretized spatial domain. We thus demonstrate the potential of such a method for hydrogeological applications and also provide test cases for the optimization community. The localization problem is illustrated for cases where the geology is assumed to be perfectly known. Two 2-D synthetic cases that display sharp hydraulic conductivity contrasts and specific connectivity patterns are investigated. These cases generate highly nonlinear objective functions that present multiple local minima. A derivative-free global optimization algorithm relying on a Gaussian process model and on the expected improvement criterion is used to efficiently localize the point of minimum of the objective functions, which corresponds to the contaminant source location. Even though concentration measurements contain a significant level of proportional noise, the algorithm efficiently localizes the contaminant source location. The variations of the objective function are essentially driven by the geology, followed by the design of the monitoring well network. The data and scripts used to generate objective functions are shared to favor reproducible research. This contribution is important because the functions present multiple local minima and are inspired from a practical field application. Sharing these complex objective functions provides a source of test cases for global optimization benchmarks and should help with designing new and efficient methods to solve this type of problem.

scholarly journals Common best proximity points for proximity commuting mapping with Geraghty’s functions

2015 ◽  
Vol 31 (3) ◽  
pp. 359-364
Author(s):  
POOM KUMAM ◽  
◽  
CHIRASAK MONGKOLKEHA ◽  
Keyword(s):  
Recent Result ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Global Minimization ◽  
Objective Functions ◽  
Best Proximity Points ◽  
Complete Metric Spaces ◽  
Multi Objective ◽  
Common Best Proximity Point ◽  
Commuting Mapping

In this paper, we prove new common best proximity point theorems for proximity commuting mapping by using concept of Geraghty’s theorem in complete metric spaces. Our results improve and extend recent result of Sadiq Basha [Basha, S. S., Common best proximity points: global minimization of multi-objective functions, J. Glob Optim, 54 (2012), No. 2, 367-373] and some results in the literature.

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.

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