Global optimization based on TT-decomposition

2020 ◽  
Vol 35 (4) ◽  
pp. 247-261
Author(s):  
Dmitry Zheltkov ◽  
Eugene Tyrtyshnikov
Keyword(s):  
Global Optimization ◽  
High Accuracy ◽  
Global Optimum ◽  
Stochastic Methods ◽  
The Matrix ◽  
Matrix Case

AbstractIn contrast to many other heuristic and stochastic methods, the global optimization based on TT-decomposition uses the structure of the optimized functional and hence allows one to obtain the global optimum in some problem faster and more reliable. The method is based on the TT-cross method of interpolation of tensors. In this case, the global optimum can be found in practice even in the case when the approximation of the tensor does not possess a high accuracy. We present a detailed description of the method and its justification for the matrix case and rank-1 approximation.

Enhanced Multi-Agent Normal Sampling Technique for Global Optimization

2008 ◽  
Author(s):  
Alireza Saremi ◽  
Amir H. Birjandi ◽  
G. Gary Wang ◽  
Tarek ElMekkawy ◽  
Eric Bibeau
Keyword(s):  
Global Optimization ◽  
Optimization Technique ◽  
Sampling Technique ◽  
Optimization Methods ◽  
Optimization Method ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Multi Agent ◽  
Mean Function ◽  
Specific Number

This paper describes an enhanced version of a new global optimization method, Multi-Agent Normal Sampling Technique (MANST) described in reference [1]. Each agent in MANST includes a number of points that sample around the mean point with a certain standard deviation. In each step the point with the minimum value in the agent is chosen as the center point for the next step normal sampling. Then the chosen points of all agents are compared to each other and agents receive a certain share of the resources for the next step according to their lowest mean function value at the current step. The performance of all agents is periodically evaluated and a specific number of agents who show no promising achievements are deleted; new agents are generated in the proximity of those promising agents. This process continues until the agents converge to the global optimum. MANST is a standalone global optimization technique and does not require equations or knowledge about the objective function. The unique feature of this method in comparison with other global optimization methods is its dynamic normal distribution search. This work presents our recent research in enhancing MANST to handle variable boundaries and constraints. Moreover, a lean group sampling approach is implemented to prevent sampling in the same region for different agents. The overall capability and efficiency of the MANST has been improved as a result in the newer version. The enhanced MANST is highly competitive with other stochastic methods such as Genetic Algorithm (GA). In most of the test cases, the performance of the MANST is significantly higher than the Matlab™ GA Toolbox.

scholarly journals Global optimization based on active preference learning with radial basis functions

2020 ◽  
Author(s):  
Alberto Bemporad ◽  
Dario Piga
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Decision Maker ◽  
Optimization Problems ◽  
Global Optimum ◽  
Bayesian Optimization ◽  
Preference Learning ◽  
Global Optimizer ◽  
Radial Basis ◽  
Decision Vector

AbstractThis paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as “this is better than that” between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. A radial-basis function surrogate is fit via linear or quadratic programming, satisfying if possible the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is competitive in that, within the same number of comparisons, it usually approaches the global optimum more closely and is computationally lighter. Applications of the proposed algorithm to solve a set of benchmark global optimization problems, for multi-objective optimization, and for optimal tuning of a cost-sensitive neural network classifier for object recognition from images are described in the paper. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/glis.

scholarly journals An Algorithm for Global Optimization Inspired by Collective Animal Behavior

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Erik Cuevas ◽  
Mauricio González ◽  
Daniel Zaldivar ◽  
Marco Pérez-Cisneros ◽  
Guillermo García
Keyword(s):  
Global Optimization ◽  
Animal Behavior ◽  
Food Source ◽  
Collective Motion ◽  
Global Optimum ◽  
Migration Routes ◽  
Collective Behaviors ◽  
Biological Laws ◽  
Harvesting Efficiency ◽  
Collective Animal Behavior

A metaheuristic algorithm for global optimization called the collective animal behavior (CAB) is introduced. Animal groups, such as schools of fish, flocks of birds, swarms of locusts, and herds of wildebeest, exhibit a variety of behaviors including swarming about a food source, milling around a central locations, or migrating over large distances in aligned groups. These collective behaviors are often advantageous to groups, allowing them to increase their harvesting efficiency, to follow better migration routes, to improve their aerodynamic, and to avoid predation. In the proposed algorithm, the searcher agents emulate a group of animals which interact with each other based on the biological laws of collective motion. The proposed method has been compared to other well-known optimization algorithms. The results show good performance of the proposed method when searching for a global optimum of several benchmark functions.

scholarly journals Concurrent stochastic methods for global optimization

1990 ◽  
Vol 46 (1-3) ◽  
pp. 1-29 ◽  
Author(s):  
Richard H. Byrd ◽  
Cornelius L. Dert ◽  
Alexander H. G. Rinnooy Kan ◽  
Robert B. Schnabel
Keyword(s):  
Global Optimization ◽  
Stochastic Methods

Solving Mono- and Multi-Objective Problems Using Hybrid Evolutionary Algorithms and Nelder-Mead Method

2021 ◽  
Vol 12 (4) ◽  
pp. 98-116
Author(s):  
Noureddine Boukhari ◽  
Fatima Debbat ◽  
Nicolas Monmarché ◽  
Mohamed Slimane
Keyword(s):  
Convergence Rate ◽  
Optimization Problem ◽  
Optimization Problems ◽  
State Of The Art ◽  
Hybrid Approach ◽  
Optimization Methods ◽  
Global Optimum ◽  
Stochastic Methods ◽  
Local Optima ◽  
Portfolio Optimization Problem

Evolution strategies (ES) are a family of strong stochastic methods for global optimization and have proved their capability in avoiding local optima more than other optimization methods. Many researchers have investigated different versions of the original evolution strategy with good results in a variety of optimization problems. However, the convergence rate of the algorithm to the global optimum stays asymptotic. In order to accelerate the convergence rate, a hybrid approach is proposed using the nonlinear simplex method (Nelder-Mead) and an adaptive scheme to control the local search application, and the authors demonstrate that such combination yields significantly better convergence. The new proposed method has been tested on 15 complex benchmark functions and applied to the bi-objective portfolio optimization problem and compared with other state-of-the-art techniques. Experimental results show that the performance is improved by this hybridization in terms of solution eminence and strong convergence.

Stochastic Methods Applied to Structural Mechanics

2018 ◽  
pp. 199-220
Author(s):  
Siham Ouhimmou
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Global Optimization ◽  
Transformation Method ◽  
Stochastic Methods ◽  
Element Analysis ◽  
Local Method ◽  
Structural Problem ◽  
Finite Element Software ◽  
The Finite Element Analysis

Uncertainty modelling with random variables motivates the adoption of advanced PTM for reliability analysis to solve problems of mechanical systems. Probabilistic transformation method (PTM) is readily applicable when the function between the input and the output of the system is explicit. When these functions are implicit, a technique is proposed that combines finite element analysis (FEA) and probabilistic transformation method (PTM) that is based on the numerical simulations of the finite element analysis (FEA) and the probabilistic transformation method (PTM) using an interface between finite element software and Matlab. Structure problems are treated with the proposed technique, and the obtained results are compared to those obtained by the reference Monte Carlo method. A second aim of this work is to develop an algorithm of global optimization using the local method SQP. The proposed approach MSQP is tested on test functions comparing with other methods, and it is used to resolve a structural problem under reliability constraints.

Comprehensive Evaluation of Wind Turbine Type Selection Based on GA-SVR Model

2012 ◽  
Vol 468-471 ◽  
pp. 579-582
Author(s):  
Wei Sun ◽  
Le Shen
Keyword(s):  
Genetic Algorithm ◽  
Global Optimization ◽  
Wind Turbine ◽  
Support Vector Regression ◽  
Empirical Analysis ◽  
Comprehensive Evaluation ◽  
Evaluation Model ◽  
High Accuracy ◽  
Support Vector ◽  
Type Selection

Aiming at the current situation of wind turbine type selection in China, this paper has built a more scientific and systematic index system for comprehensive evaluation of wind turbine type selection, and also applied the Support Vector Regression machine evaluation model with parameters optimized by Genetic Algorithm. Through automatic global optimization for parameters, this model has reached an extremely high accuracy required for evaluation of type selection. Empirical analysis shows that the application of this model has a realistic popularized significance for improving the method of the wind turbine type selection and enhancing its efficiency.

Matrix Based Feature Measurement and Extraction for Face Recognition

2015 ◽  
Vol 738-739 ◽  
pp. 643-647
Author(s):  
Qi Zhu ◽  
Jin Rong Cui ◽  
Zi Zhu Fan
Keyword(s):  
Principal Component Analysis ◽  
Feature Extraction ◽  
Face Recognition ◽  
Measurement Method ◽  
Principal Component ◽  
Component Analysis ◽  
High Accuracy ◽  
Face Image ◽  
Two Dimensional ◽  
The Matrix

In this paper, a matrix based feature extraction and measurement method, i.e.: multi-column principle component analysis (MCPCA) is used to directly and effectively extract features from the matrix. We analyze the advantages of MCPCA over the conventional principal component analysis (PCA) and two-dimensional PCA (2DPCA), and we have successfully applied it into face image recognition. Extensive face recognition experiments illustrate that the proposed method obtains high accuracy, and it is more robust than previous conventional face recognition methods.

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