scholarly journals Small Populations, High-Dimensional Spaces: Sparse Covariance Matrix Adaptation

2015 ◽  
Author(s):  
Silja Meyer-Nieberg ◽  
Erik Kropat
Keyword(s):  
Covariance Matrix ◽  
High Dimensional ◽  
Small Populations ◽  
Covariance Matrix Adaptation

scholarly journals Mirrored Orthogonal Sampling for Covariance Matrix Adaptation Evolution Strategies

2019 ◽  
Vol 27 (4) ◽  
pp. 699-725 ◽  
Author(s):  
Hao Wang ◽  
Michael Emmerich ◽  
Thomas Bäck
Keyword(s):  
Convergence Rate ◽  
Covariance Matrix ◽  
Sampling Technique ◽  
Black Box ◽  
Evolution Strategies ◽  
High Dimensional ◽  
Major Purpose ◽  
Search Spaces ◽  
Covariance Matrix Adaptation ◽  
Adaptation Evolution

Generating more evenly distributed samples in high dimensional search spaces is the major purpose of the recently proposed mirrored sampling technique for evolution strategies. The diversity of the mutation samples is enlarged and the convergence rate is therefore improved by the mirrored sampling. Motivated by the mirrored sampling technique, this article introduces a new derandomized sampling technique called mirrored orthogonal sampling. The performance of this new technique is both theoretically analyzed and empirically studied on the sphere function. In particular, the mirrored orthogonal sampling technique is applied to the well-known Covariance Matrix Adaptation Evolution Strategy (CMA-ES). The resulting algorithm is experimentally tested on the well-known Black-Box Optimization Benchmark (BBOB). By comparing the results from the benchmark, mirrored orthogonal sampling is found to outperform both the standard CMA-ES and its variant using mirrored sampling.

Adaptive Niche Radii and Niche Shapes Approaches for Niching with the CMA-ES

2010 ◽  
Vol 18 (1) ◽  
pp. 97-126 ◽  
Author(s):  
Ofer M. Shir ◽  
Michael Emmerich ◽  
Thomas Bäck
Keyword(s):  
Covariance Matrix ◽  
High Dimensional ◽  
Step Size ◽  
Distance Calculation ◽  
Covariance Matrix Adaptation ◽  
Niching Methods ◽  
Geometrical Shapes ◽  
Matrix Mechanism ◽  
Adaptation Evolution ◽  
Radius Problem

While the motivation and usefulness of niching methods is beyond doubt, the relaxation of assumptions and limitations concerning the hypothetical search landscape is much needed if niching is to be valid in a broader range of applications. Upon the introduction of radii-based niching methods with derandomized evolution strategies (ES), the purpose of this study is to address the so-called niche radius problem. A new concept of an adaptive individual niche radius is applied to niching with the covariance matrix adaptation evolution strategy (CMA-ES). Two approaches are considered. The first approach couples the radius to the step size mechanism, while the second approach employs the Mahalanobis distance metric with the covariance matrix mechanism for the distance calculation, for obtaining niches with more complex geometrical shapes. The proposed approaches are described in detail, and then tested on high-dimensional artificial landscapes at several levels of difficulty. They are shown to be robust and to achieve satisfying results.

Optimization Design of Trusses Based on Covariance Matrix Adaptation Evolution Strategy Algorithm

2012 ◽  
Vol 215-216 ◽  
pp. 133-137
Author(s):  
Guo Shao Su ◽  
Yan Zhang ◽  
Zhen Xing Wu ◽  
Liu Bin Yan
Keyword(s):  
Stochastic Optimization ◽  
Covariance Matrix ◽  
Optimization Problems ◽  
Fitness Function ◽  
Optimization Methods ◽  
Evolution Strategy ◽  
Covariance Matrix Adaptation ◽  
Study Results ◽  
Highly Nonlinear ◽  
Adaptation Evolution

Covariance matrix adaptation evolution strategy algorithm (CMA-ES) is a newly evolution algorithm. It has become a powerful tool for solving highly nonlinear multi-peak optimization problems. In many real-world optimization problems, the location of multiple optima is often required in a search space. In order to evaluate the solution, thousands of fitness function evaluations are involved that is a time consuming or expensive processes. Therefore, conventional stochastic optimization methods meet a special challenge for a very large number of problem function evaluations. Aiming to overcome the shortcoming of stochastic optimization methods in the high calculation cost, a truss optimal method based on CMA-ES algorithm is proposed and applied to solve the section and shape optimization problems of trusses. The study results show that the method is feasible and has the advantages of high accuracy, high efficiency and easy implementation.

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