scholarly journals Convergence Analysis of the Hessian Estimation Evolution Strategy

2021 ◽  
pp. 1-25
Author(s):  
Tobias Glasmachers ◽  
Oswin Krause
Keyword(s):  
Objective Function ◽  
Convergence Analysis ◽  
Covariance Matrix ◽  
Linear Convergence ◽  
Evolution Strategy ◽  
Sampling Distribution ◽  
Evolution Strategies ◽  
Problem Instance ◽  
Family Stability ◽  
The Family

Abstract The class of algorithms called Hessian Estimation Evolution Strategies (HE-ESs) update the covariance matrix of their sampling distribution by directly estimating the curvature of the objective function. The approach is practically efficient, as attested by respectable performance on the BBOB testbed, even on rather irregular functions. In this paper we formally prove two strong guarantees for the (1+4)-HE-ES, a minimal elitist member of the family: stability of the covariance matrix update, and as a consequence, linear convergence on all convex quadratic problems at a rate that is independent of the problem instance.

Adaptive Parent Population Sizing in Evolution Strategies

2015 ◽  
Vol 23 (3) ◽  
pp. 397-420 ◽  
Author(s):  
G. Jake LaPorte ◽  
Juergen Branke ◽  
Chun-Hung Chen
Keyword(s):  
Population Size ◽  
Covariance Matrix ◽  
Evolutionary Process ◽  
Evolution Strategy ◽  
Evolution Strategies ◽  
Parental Population ◽  
Sphere Model ◽  
Parent Population ◽  
Fixed Population

Adaptive population sizing aims at improving the overall progress of an evolution strategy. At each generation, it determines the parental population size that promises the largest fitness gain, based on the information collected during the evolutionary process. In this paper, we develop an adaptive variant of a [Formula: see text] evolution strategy. Based on considerations on the sphere, we derive two approaches for adaptive population sizing. We then test these approaches empirically on the sphere model using a normalized mutation strength and cumulative mutation strength adaption. Finally, we compare the methodology on more general functions with a fixed population, covariance matrix adaption evolution strategy (CMA-ES). The results confirm that our adaptive population sizing methods yield better results than even the best fixed population size.

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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