scholarly journals An analytical framework for consensus-based global optimization method

2018 ◽  
Vol 28 (06) ◽  
pp. 1037-1066 ◽  
Author(s):  
José A. Carrillo ◽  
Young-Pil Choi ◽  
Claudia Totzeck ◽  
Oliver Tse
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Mean Field ◽  
Optimization Method ◽  
Analytical Framework ◽  
Global Minimizer ◽  
Global Optimization Method ◽  
The Mean ◽  
Class Of Functions ◽  
Theoretical Results

In this paper, we provide an analytical framework for investigating the efficiency of a consensus-based model for tackling global optimization problems. This work justifies the optimization algorithm in the mean-field sense showing the convergence to the global minimizer for a large class of functions. Theoretical results on consensus estimates are then illustrated by numerical simulations where variants of the method including nonlinear diffusion are introduced.

scholarly journals Design of dimensionally stable composites using efficient global optimization method

2016 ◽  
Vol 233 (2) ◽  
pp. 156-168 ◽  
Author(s):  
Levent Aydin ◽  
Olgun Aydin ◽  
H Seçil Artem ◽  
Ali Mert
Keyword(s):  
Global Optimization ◽  
Communication Systems ◽  
Optimization Problems ◽  
Material Design ◽  
Optimization Method ◽  
Pattern Search ◽  
Efficient Global Optimization ◽  
Global Optimization Method ◽  
Moisture Expansion ◽  
Design And Optimization

Dimensionally stable material design is an important issue for space structures such as space laser communication systems, telescopes, and satellites. Suitably designed composite materials for this purpose can meet the functional and structural requirements. In this paper, it is aimed to design the dimensionally stable laminated composites by using efficient global optimization method. For this purpose, the composite plate optimization problems have been solved for high stiffness and low coefficients of thermal and moisture expansion. Some of the results based on efficient global optimization solution have been verified by genetic algorithm, simulated annealing, and generalized pattern search solutions from the previous studies. The proposed optimization algorithm is also validated experimentally. After completing the design and optimization process, failure analysis of the optimized composites has been performed based on Tsai–Hill, Tsai–Wu, Hoffman, and Hashin–Rotem criteria.

A New Global Optimization Method for Simultaneous Computation on Expensive Black-Box Functions

2003 ◽  
Author(s):  
Liqun Wang ◽  
Songqing Shan ◽  
G. Gary Wang
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Search Space ◽  
Optimization Method ◽  
Global Optimum ◽  
Black Box ◽  
Efficient Global Optimization ◽  
Global Optimization Method ◽  
Global Optimization Methods

The presence of black-box functions in engineering design, which are usually computation-intensive, demands efficient global optimization methods. This work proposes a new global optimization method for black-box functions. The global optimization method is based on a novel mode-pursuing sampling (MPS) method which systematically generates more sample points in the neighborhood of the function mode while statistically covers the entire search space. Quadratic regression is performed to detect the region containing the global optimum. The sampling and detection process iterates until the global optimum is obtained. Through intensive testing, this method is found to be effective, efficient, robust, and applicable to both continuous and discontinuous functions. It supports simultaneous computation and applies to both unconstrained and constrained optimization problems. Because it does not call any existing global optimization tool, it can be used as a standalone global optimization method for inexpensive problems as well. Limitation of the method is also identified and discussed.

Generalized Random Tunneling Algorithm for Continuous Design Variables

2003 ◽  
Author(s):  
Satoshi Kitayama ◽  
Koetsu Yamazaki
Keyword(s):  
Global Optimization ◽  
Mathematical Programming ◽  
Structural Optimization ◽  
Global Minimum ◽  
Optimization Problems ◽  
Optimization Method ◽  
Global Optimization Method ◽  
Numerical Examples ◽  
Design Variables ◽  
Side Constraints

A global optimization method for continuous design variables called as Generalized Random Tunneling Algorithm is proposed. Proposed method is called as “Generalized” random tunneling algorithm because this method can treat the behavior constraints as well as the side constraints. This method consists of three phases, that is, the minimization phase, the tunneling phase, and the constraints phase. In the minimization phase, mathematical programming is used, and heuristic approach is introduced in the tunneling and constraint phases. By iterating these phases, global minimum is found. The characteristics of mathematical programming and heuristic approaches are included in the proposed method. Global minimum which may lie on the boundary of constraints is easily found by proposed method. Proposed method is applied to mathematical and structural optimization problems. Through numerical examples, the effectiveness and validity of proposed method have been confirmed.

scholarly journals A Hybrid Global Optimization Method Based on Genetic Algorithm and Shrinking Box

2016 ◽  
Vol 10 (2) ◽  
pp. 67 ◽  
Author(s):  
Saleem Z. Ramadan
Keyword(s):  
Genetic Algorithm ◽  
Global Optimization ◽  
Constrained Optimization ◽  
Penalty Function ◽  
Optimization Problems ◽  
Fitness Function ◽  
Hybrid Genetic Algorithm ◽  
Optimization Method ◽  
Efficient Global Optimization ◽  
Global Optimization Method

<p class="zhengwen">This paper proposes a hybrid genetic algorithm method for optimizing constrained black box functions utilizing shrinking box and exterior penalty function methods (SBPGA). The constraints of the problem were incorporated in the fitness function of the genetic algorithm through the penalty function. The hybrid method used the proposed Variance-based crossover (VBC) and Arithmetic-based mutation (ABM) operators; moreover, immigration operator was also used. The box constraints constituted a hyperrectangle that kept shrinking adaptively in the light of the revealed information from the genetic algorithm about the optimal solution. The performance of the proposed algorithm was assessed using 11 problems which are used as benchmark problems in constrained optimization literatures. ANOVA along with a success rate performance index were used to analyze the model.</p>Based on the results, we believe that the proposed method is fairly robust and efficient global optimization method for Constrained Optimization Problems whether they are continuous or discrete.

scholarly journals Convergence of a first-order consensus-based global optimization algorithm

2020 ◽  
Vol 30 (12) ◽  
pp. 2417-2444
Author(s):  
Seung-Yeal Ha ◽  
Shi Jin ◽  
Doheon Kim
Keyword(s):  
Machine Learning ◽  
Global Optimization ◽  
Initial Data ◽  
Convergence Analysis ◽  
Mean Field ◽  
Optimization Method ◽  
Learning Problems ◽  
High Dimensional ◽  
Global Optimization Method ◽  
First Order

Global optimization of a non-convex objective function often appears in large-scale machine learning and artificial intelligence applications. Recently, consensus-based optimization (CBO) methods have been introduced as one of the gradient-free optimization methods. In this paper, we provide a convergence analysis for the first-order CBO method in [J. A. Carrillo, S. Jin, L. Li and Y. Zhu, A consensus-based global optimization method for high dimensional machine learning problems, https://arxiv.org/abs/1909.09249v1 ]. Prior to this work, the convergence study was carried out for CBO methods on corresponding mean-field limit, a Fokker–Planck equation, which does not imply the convergence of the CBO method per se. Based on the consensus estimate directly on the first-order CBO model, we provide a convergence analysis of the first-order CBO method [J. A. Carrillo, S. Jin, L. Li and Y. Zhu, A consensus-based global optimization method for high dimensional machine learning problems, https://arxiv.org/abs/1909.09249v1 ] without resorting to the corresponding mean-field model. Our convergence analysis consists of two steps. In the first step, we show that the CBO model exhibits a global consensus time asymptotically for any initial data, and in the second step, we provide a sufficient condition on system parameters — which is dimension independent — and initial data which guarantee that the converged consensus state lies in a small neighborhood of the global minimum almost surely.

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