各向异性自适应方差缩放提升GA性能：解决高斯估计算法的早熟收敛问题

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高斯分布估计的各向异性自适应方差缩放是一项针对传统高斯估计分布算法（Gaussian Estimation of Distribution Algorithm, GEDA）的重要改进策略。GEDA在优化过程中常常面临两个主要问题：一是变量方差过快减小，导致搜索空间的有效探索不足；二是搜索方向容易趋向于局部最优，影响全局搜索能力。为解决这些问题，本文提出了一种创新的方法，即引入各向异性自适应方差缩放机制。在传统的GEDA中，方差通常假设在整个搜索空间内是均匀的，但这并不总是最有效的。各向异性自适应方差缩放允许不同方向的方差根据当前搜索状况动态调整，对于那些搜索进展缓慢或遇到局部最优区域的方向，算法会自动增大其方差，增加随机性，从而促使搜索跳出当前的局部最优陷阱。反之，对于搜索进展较快的方向，较小的方差可以保持收敛性，确保算法在已知的优良解附近进行精细化搜索。作者Zhigang Ren、Yongsheng Liang、Lin Wang、Aimin Zhang、Bei Pang和Biying Li来自西安交通大学自动化科学与技术学院以及西北大学信息科学技术学院，他们合作的研究工作于2018年发表在《知识基于系统》(Knowledge-Based Systems)期刊上，该论文的接收日期为2017年9月12日，修订日期为2018年1月25日，最终接受并在线发布于2018年2月1日。关键词包括高斯分布估计算法、过早收敛、搜索方向和各向异性自适应方差缩放。通过这种新型的方差调整策略，该论文旨在提升GEDA的全局搜索效率和避免陷入局部最优，从而在优化复杂问题时表现出更好的性能。论文的核心贡献在于提出一种实用且有效的策略，将理论分析与实际应用相结合，以期推动高斯分布算法在机器学习、优化算法等领域的发展。这一研究对于理解和改进进化计算方法，特别是在处理多模态和非凸优化问题时，具有重要意义。

Knowledge-Based Systems 146 (2018) 142–151

Contents lists available at ScienceDirect

Knowle dge-Base d Systems

journal homepage: www.elsevier.com/locate/knosys

Anisotropic adaptive variance scaling for Gaussian estimation of

distribution algorithm

Zhigang Ren

a , ∗

, Yongsheng Liang

, Lin Wang

, Aimin Zhang

, Bei Pang

, Biying Li

Department of Automation Science and Technology, School of Electronic and Information Engineering, Xi’an Jiaotong University, No.28 Xianning West Road,

Xi’an, Shaanxi 710049, China

School of Information Science and Technology, Northwest University, Xi’an, China

a r t i c l e i n f o

Article history:

Received 12 September 2017

Revised 25 January 2018

Accepted 1 February 2018

Available online 2 February 2018

Keywords:

Gaussian estimation of distribution

algorithm

Premature convergence

Search direction

Anisotropic adaptive variance scaling

a b s t r a c t

Traditional Gaussian estimation of distribution algorithms (EDAs) are confronted with issues that the vari-

able variances decrease fast and the main search direction tends to become perpendicular to the improve-

ment direction of the ﬁtness function, which reduces the search eﬃciency of Gaussian EDAs (GEDAs) and

makes them subject to premature convergence. In this paper, a novel anisotropic adaptive variance scal-

ing (AAVS) technique is proposed to improve the performance of traditional GEDAs and a new GEDA

variant named AAVS-EDA is developed. The advantages of AAVS over the existing variance scaling strate-

gies lie in its ability for tuning the variances and main search direction of GEDA simultaneously, which

are achieved by anisotropically scaling the variances along different eigendirections based on correspond-

ing landscape characteristics captured by a simple topology-based detection method. Besides, AAVS-EDA

also adopts an auxiliary global monitor to ensure its convergence by shrinking all the variances if no

improvement is achieved in a generation. The evaluation results on 30 benchmark functions of CEC2014

test suite demonstrate that AAVS-EDA possesses stronger global optimization eﬃciency than traditional

GEDAs. The comparison with other state-of-the-art evolutionary algorithms also shows that AAVS-EDA is

eﬃcient and competitive.

Introduction

As a special class of evolutionary algorithm (EA) [1] , estima-

tion of distribution algorithm (EDA) [2–4] is characterized by the

way of generating new solutions, i.e., sampling solutions according

to a probability distribution, but not through crossover and muta-

tion operators as other kinds of EAs. The probability distribution

employed in each generation is generally estimated from the rel-

atively high-quality solutions obtained in previous generations. It

can capture the structure of the problem being solved to a cer-

tain extent and consequently guide the algorithm to more promis-

ing solution regions. During the past few decades, EDAs attracted

much research effort and achieved great success in both combina-

torial and continuous domains [5,6] . In this paper, EDAs for contin-

uous domain are studied.

Continuous EDAs usually adopt Gaussian probability model

[3,4] and histogram model [7] as the basic probability model. Ac-

cording to the way in representing variable dependencies, Gaussian

models for EDAs can be further categorized into three kinds. The

∗

Corresponding author.

E-mail address: renzg@mail.xjtu.edu.cn (Z. Ren).

simplest one is the univariate model which neglects all the variable

dependencies. A representative algorithm with this type of model

is the univariate marginal distribution algorithm (UMDA

) [3,4] . A

slightly more sophisticated model is the one that just considers

some important variable dependencies. To identify these depen-

dencies, Bayesian factorization is usually employed [3,8] . The mul-

tivariate model takes all the variable dependencies into account. A

representative algorithm of this type is estimation of multivariate

normal density algorithm (EMNA

) [4] .

Although possessing clear physical concept, traditional Gaus-

sian EDAs (GEDAs) often suffer from premature convergence [8,11–

15]

. Early improvement studies attributed this defect to the rapid

shrink of variances and developed many variance scaling strate-

gies. Ocenasek et al. [8] proposed a variance adaption operator for

the mixed Bayesian optimization algorithm [9] based on the well-

known 1/5-success-rule [10] . Yuan and Gallagher [11] claimed that

the performance of GEDA could be improved on certain problems

by compulsively keeping the variances at a value of at least 1. Pošík

[12] suggested enlarging variances by a constant factor. Grahl et al.

[13] proposed an adaptive variance scaling (AVS) strategy which in-

creases the variances when the best solution improves, otherwise

reduces them. Nevertheless, AVS does not directly tune variances

in each generation unless it identiﬁes that the algorithm is travers-

https://doi.org/10.1016/j.knosys.2018.02.001

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