改良版 cuckoo 寻找算法：无梯度优化新策略

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"Modified Cuckoo Search: A Comprehensive Overview and Analysis" 在现代优化算法的领域中，"Modified Cuckoo Search" (MCS) 是一种新兴且备受关注的无梯度优化方法，它源于近年来发展起来的Cuckoo Search (CS) 模型。该算法的创新之处在于引入了种群内的信息交流机制，即顶级蛋或最佳解决方案之间的交互。这一改动旨在增强搜索的全局探索性和收敛性，尤其是在高维优化问题中。原始的Cuckoo Search算法模仿了鸟类行为中的弃蛋策略，其中一些"不好的"解决方案（代表搜索空间中的局部最优解）会被随机选择并替换掉。然而，MCS在此基础上加入了新的动态元素，使得种群中的优秀个体能够互相学习和分享经验，这有助于避免陷入局部最优，提高整体搜索效率。为了评估MCS的效果，研究者采用了标准的优化基准测试函数，如Ackley函数、Rastrigin函数等。实验结果显示，MCS在大多数情况下表现得与原Cuckoo Search相当甚至更好，有时还能超越粒子群优化（PSO）和差分进化（DE）策略。尤其值得一提的是，即使在高维度问题中，MCS依然展现出高的收敛率，能有效地找到全局最优解。 MCS的优势在于其简单易实现，无需计算梯度信息，适用于许多实际问题，包括工程设计、机器学习参数调整、以及复杂系统优化等。此外，由于其基于生物启发的特性，MCS具有较强的抗噪性和鲁棒性，能够适应各种复杂搜索环境。总结来说，Modified Cuckoo Search是一种具有竞争力的优化算法，通过种群间的知识共享和信息交换，它不仅保持了Cuckoo Search的探索性，还提高了收敛性能。对于那些难以用传统梯度方法处理的问题，尤其是高维和非线性优化，MCS提供了有效且实用的解决方案。未来的研究可能继续深入探讨MCS的变体和改进，以进一步提升其在各种优化任务中的表现。"

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Modiﬁed cuckoo search: A new gradient free optimisation algorithm

S. Walton

⇑

, O. Hassan, K. Morgan, M.R. Brown

College of Engineering, Swansea University, Swansea SA2 8PP, Wales, UK

article info

Article history:

Received 13 January 2011

Accepted 14 June 2011

Available online 22 July 2011

abstract

A new robust optimisation algorithm, w hich can be regarded as a modiﬁcation of the

recently developed cuckoo search, is presented. The modiﬁcation involves the addition

of information exchange between the top eggs, or the best solutions. Standard optimisation

benchmarking functions are used to test the effects of these modiﬁcations and it is demon-

strated that, in most cases, the modiﬁed cuckoo search performs as well as, or better than,

the standard cuckoo search, a particle swarm optimiser, and a differential evolution strat-

egy. In particular the modiﬁed cuckoo search shows a high convergence rate to the true

global minimum even at high numbe rs of dimensions.

1. Introduction

The practicality of using gradient based optimisation

techniques has been reduced by the difﬁculty of generating

automatically objective functions and their derivatives for

highly non-linear engineering problems [1]. During the

1950s and 1960s, computer scientists investigated the pos-

sibility of applying the concepts of evolution as an optimi-

sation tool for engineers and this gave birth to a subclass of

gradient free methods called genetic algorithms (GA) [2].

Since then many other algorithms have been developed

that have been inspired by nature, for example particle

swarm optimisation (PSO) [3], differential evolution (DE)

[4] and, more recently, the cuckoo search (CS) [5]. These

are heuristic techniques which make use of a large popula-

tion of possible designs at each iteration. For each member

of the population, the objective function is evaluated and a

ﬁtness is assigned. A set of rules is then used to move the

population towards the optimum solution. Although this

results in a global search without the need to calculate

objective function gradients [5], the large number of objec-

tive function evaluations means the computational efﬁ-

ciency of these procedures is often inferior to classical

gradient-based methods [6]. The problem is exacerbated

when considering applications where a single objective

function evaluation represents a signiﬁcant computational

cost, such as ﬂuid ﬂow problems [6–8].

New optimisation algorithms are often tested by apply-

ing them to benchmark problems which have known ana-

lytical optimum ﬁtnesses. For example, Bratton and

Kennedy [3] compare several PSO algorithms by running

30 trials each for 300,000 objective function evaluations

and comparing the ﬁtness value obtained with the known

optimum ﬁtness. Yang and Deb [5] compared CS to PSO

over 100 trials for each objective function. They allowed

the algorithms to run until the spread of ﬁtnesses in the

population was smaller than 10

5

. This resulted in large

numbers of objective function evaluations, from 3015 to

110,523, depending upon the method used and the bench-

mark problem. This number of objective function evalua-

tions would not be feasible for application to practical

engineering problems with costly objective functions. The

common threads in these benchmarking tests is the appli-

cation of these techniques to problems with known min-

ima, with a deﬁned stopping criterion, and the large

number of objective function evaluations.

In a real world application of an optimisation technique,

it is very difﬁcult to deﬁne a stopping criterion. For exam-

ple, in the design of an aerofoil, the objective function might

represent the calculation of the ratio of the lift coefﬁcient to

the drag coefﬁcient. In this case, the designer would want

to maximise this quantity under certain constraints, the

maximum value is unknown and may not be unique.

doi:10.1016/j.chaos.2011.06.004

⇑

Corresponding author.

E-mail address: 512465@swansea.ac.uk (S. Walton).

Chaos, Solitons & Fractals 44 (2011) 710–718

Contents lists available at ScienceDirect

Chaos, Solitons & Fractals

Nonlinear Science, and Nonequilibrium and Complex Phenomena

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

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