鲸鱼优化算法：理论基础与改进策略综述

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"这篇文献是关于鲸鱼优化算法（WOA）的系统性综述，深入探讨了其理论基础、改进方法以及混合策略。作者Mohammad H. Nadimi-Shahraki、Hoda Zamani、Zahra Asghari Varzaneh和Seyed Ali Mirjalili在文章中分析了WOA的优缺点，并对众多WOA变体进行了评估，旨在寻找更有效的优化技术。文章发表在《计算力学档案》(Archives of Computational Methods in Engineering) 2023年，卷30，第4113-4159页，DOI为10.1007/s11831-023-09928-7。" 鲸鱼优化算法（WOA）是一种受到鲸鱼捕食行为启发的全局优化算法，由Seyed Ali Mirjalili于2016年提出。该算法基于鲸鱼群体的捕食和社交行为，如环形包围、声纳定位和泡泡网捕食等，用于解决复杂多模态优化问题。WOA的基本思想是模拟鲸鱼群在寻找最优解时的行为，包括个体间的追踪、围捕和探索。 1. **理论基础**： WOA的核心机制包括随机搜索、局部搜索和全局搜索。随机搜索阶段，鲸鱼们以随机方式分布在全球范围内寻找解决方案。局部搜索通过模拟鲸鱼追踪其他鲸鱼的行为来改善当前解决方案。全局搜索则通过模拟泡泡网捕食策略，使得一部分鲸鱼能够跳出局部最优，向全局最优移动。 2. **问题与挑战**：尽管WOA在解决一些优化问题上表现出色，但它也存在一些问题，比如早熟收敛、搜索效率低以及对参数敏感等。这些问题限制了其在更复杂问题上的应用。 3. **改进与混合**：为了解决这些问题，研究者提出了多种改进和混合策略。改进策略可能包括调整算法参数、引入新的搜索机制或改变更新规则。混合策略是将WOA与其他优化算法（如遗传算法、粒子群优化等）结合，以利用各自的优势，提高算法性能和鲁棒性。 4. **应用领域**： WOA已被广泛应用于工程设计、机器学习、能源系统优化、无线传感器网络、经济调度等多个实际问题中。 5. **未来方向**：通过对WOA及其变体的深入分析，研究人员可以识别出有效的技术，为开发更高效、更适应不同问题的优化算法提供指导。这可能涉及对现有机制的微调、引入新的动态调整策略，或者开发新的混合模型。总结来说，这篇综述文章为理解WOA的基本原理、评价其性能以及发掘潜在改进方向提供了全面的视角。它强调了对WOA进行系统性研究的重要性，这对于推动优化算法的进步和应用具有重要意义。

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A Systematic Review oftheWhale Optimization Algorithm: Theoretical Foundation, Improvements,…

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in various engineering issues, including classiﬁcation, clus-

tering, robot routing, task scheduling, networks, image pro-

cessing, and other engineering applications. Their analysis

results show that WOA has been primarily applied in solv-

ing engineering optimization problems. Mohammed etal.

[64] presented a short systematic and meta-analysis survey

on WOA regarding the algorithmic foundations, features,

restrictions, improvements, combinations, and applications.

First, they reported the WOA variants in two groups of mod-

iﬁcations and hybridizations from 2016 to 2018. In addition,

they proposed the WOA-BAT algorithm that uses the explo-

ration phase of the bat algorithm and the exploitation phase

of WOA. Although the WOA-BAT algorithm obtained the

best performance than some canonical algorithms in solving

continuous optimization problems, its superiority over the

WOA variants is not investigated.

Rana etal. [65] reviewed the studies conducted on the

applications, modiﬁcations, and hybridization of the WOA

algorithm in the years 2016 to 2020. They selected 82 papers

to review from 939 papers extracted from their search. Based

on their analysis, WOA-based techniques have been used in

ﬁve ﬁelds and 17 diﬀerent subﬁelds in engineering appli-

cations. The ﬁndings of this survey demonstrate that 61%

of papers are modiﬁed WOA using various techniques, and

27% are hybridized with other algorithms. Moreover, 12% of

WOA multi-objective variants are developed from 2016 to

2020. Although this review paper motivates the researchers

to propose more novel WOA-based algorithms, introducing

the new variant of WOA should cover the weak points of

canonical WOA and its existing variants. In 2020, Mirjalili

etal. [66] reviewed and analyzed WOA and presented brief

literature on WOA, including algorithm applications, in

various ﬁelds. This paper investigates the homogeneous and

heterogeneous hybrid variants of WOA and explains some

real-world applications of WOA. They also evaluated the

eﬃciency of WOA on several test functions and a photonic

crystal ﬁlter practical example. The ﬁndings of this study

show that the WOA algorithm beneﬁts from a good bal-

ance between two search strategies to solve this real-world

problem.

Fig. 7 WOA’s population

diversity

4122 M.Nadimi-Shahraki et al.

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In summary, most prior surveys lack a critical analysis

of the WOA algorithm, its weaknesses and behaviors, an

adapted methodology for extracting the eligible papers, and

an introduction to eﬀective techniques and algorithms to

develop more successful variants. In addition, many WOA

variants have been introduced in the last ﬁve years; therefore,

an updated systematic review of this algorithm is needed.

Hence, the scope of this systematic review is considered

from 2019. This study analyzes the WOA algorithm criti-

cally to highlight its weakness and behaviors. The reported

results of this analysis can provide informative knowledge

for further developing the WOA by knowing its strengths

and weaknesses. Then, an adapted methodology is intro-

duced to extract eligible papers of WOA variants. The eli-

gible papers are reviewed in two main categories, improved

and hybrid WOA variants. The common techniques used

in improved WOA and the eﬀective algorithms applied in

hybrid WOA are highlighted and explained, which can guide

future developments for metaheuristic algorithms.

5 The Adapted Methodology

This section introduces an adapted methodology for our

systematic review to ﬁlter the number of related documents

eﬃciently since Fig.2 alerts usto numerous developments

in WOA. Thus, as shown in Fig.8, we adapted the PRISMA

methodology [71] to select a reasonable number of the most

reputable papers for full-text reading. The introduced meth-

odology consists of three main stages as follows.

5.1 Identiﬁcation Stage

In this stage, related keywords and alternative synonyms

are deﬁned as target search problems to search and extract

documents from diﬀerent databases. The deﬁned keywords

include “WOA”, “whale algorithm”, “whale optimization”,

“whale optimiser”, “whale optimizer”, “whale optimiza-

tion algorithm”, and “whale optimisation algorithm”.

Then, the deﬁned keywords were searched in the Google

Scholar database restricted from 2019 to the end of March

2023, and 2983 documents were identiﬁed in this stage.

5.2 Evaluation Stage

This stage uses three screening steps to evaluate the identi-

ﬁed documents and select eligible papers. In the screening

steps, the Rayyan tool [67] is used for citation sharing and

allowing comparison of decisions to include or exclude.

Duplicate papers and those papers published by non-aca-

demic journals were removedinthe ﬁrst screening. There

were 39 duplicated papers extracted from theScopus and

WOS databases. The remaining 2944 papers were checked

for non-academic and disreputable journalsto remove, and

as shown in Fig.9, 1751 papers published by diﬀerent

journals were selected for the next screening.

In the second screening, the title and abstract of

candidate papers were investigated, 1096 papers were

thenexcluded respecting the study scope, and 655 papers

remained. The third screening has two steps; ﬁrst, the full

text of the candidate papers is read to select eligible papers

using the inclusion criteria. The inclusion criteria consid-

ered for this study are listed as follows.

– C

: Papers published from 2019 to the end of March

2023.

– C

: Papers written in theEnglish language.

– C

: Non-conference papers and Non-short communica-

tions.

– C

: Papers published in reputable journals.

– C

: Papers focused on WOA as the main topic.

– C

: Papers focused on developing WOA using improve-

ment or hybridizing approaches.

Although some of these criteria were checked to reduce

the number of candidate papers in the previous stage, they

were carefully rechecked in this step by reading their full

texts. This step selected 111 eligible papers and then

increased the countto 116 by studying their references in

the second step of the third screening to ﬁnd more eligible

papers based on inclusion criteria.

5.3 Reporting stage

In this stage, the116 eligible papers collected from Rayyan

as the ﬁnal set are ﬁrst classiﬁed by six main and other pub-

lishers. Then, they are reviewed for the qualitative synthesis

59%

15%

21%

Journal article (1751)

Conference paper (441)

Book & Book chapter (81) Dissertation (57)

Disreputable document (614)

Fig. 8 The percentage of diﬀerent WOA documents from 2019 to the

end of March 2023

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