Novel global harmony search algorithm for unconstrained problems

和声搜索算法, 无约束优化问题

Novel global harmony search algorithm for unconstrained problems

Novel global harmony search algorithm for unconstrained problems


Novel global harmony search algorithm for unconstrained problems

Dexuan Zou a,Ã,Liqun Gao a,Jianhua Wu a,Steven Li b

a School of Information Science and Engineering,Northeastern University,Shenyang,Liaoning110004,PR China

b Division of Business University of South Australia GPO Box2471,Adelaide,SA5001,Australia

a r t i c l e i n f o

Article history:


Received in revised form



Communicated by Y.Liu

Available online27August2010


Novel global harmony search algorithm

Position updating

Genetic mutation



Harmony search algorithm

a b s t r a c t

In this paper,we use a recently proposed algorithm—novel global harmony search(NGHS)algorithm to

solve unconstrained problems.The NGHS algorithm includes two important operations:position

updating and genetic mutation with a low probability.The former can enhance the convergence of the

NGHS,and the latter can effectively prevent the NGHS from being trapped into the local optimum.

Based on a large number of experiments,the NGHS has demonstrated stronger convergence and

stability than original harmony search(HS)algorithm and its two improved algorithms(IHS and SGHS).

&2010Elsevier B.V.All rights reserved.


Due to the computational drawbacks of existing numerical

methods,researchers have to rely on metaheuristic algorithms

based on simulations to solve some complex optimization

problems.A common feature in meta-heuristic algorithms is that

they combine rules and randomness to imitate natural phenomena.

These phenomena include the biological evolutionary process(e.g.,

the genetic algorithm(GA)[1]and the differential evolution(DE)

[2]),animal behavior(e.g.,particle swarm optimization(PSO)[3]

and ant colony algorithm(ACA)[4]),and the physical annealing

process(e.g.,simulated annealing(SA)[5]).Over the last decades,

many meta-heuristic algorithms and their improved algorithms

have been successfully applied to various engineering optimization

problems[6–12].They have outperformed conventional numerical

methods on providing better solutions for some difficult and

complicated real-world optimization problems.

Geem et al.proposed a new metaheuristic algorithm—harmony

search(HS)[13]in2001,which is inspired by the phenomenon of

musician attuning.The HS algorithm is based on natural musical

performance processes that occur when a musician searches for a

better state of harmony,such as during jazz improvisation.Jazz

improvisation seeks tofind musically pleasing harmony as

determined by an aesthetic standard,just as the optimization

process seeks tofind a global solution as determined by an

objective function.Due to its own advantage and potential,the HS

has been successfully applied to many engineering optimization

problems[14–17]during the last decade.Recently,many improved

harmony search algorithms have been proposed,such as:improved

harmony search(IHS)algorithm[18],global-best harmony search

(GHS)algorithm[19],self-adaptive global-best harmony search

(SGHS)algorithm[20],and local-best harmony search algorithm

with dynamic subpopulations(DLHS)[21].In addition,Das et al.

presented a simple mathematical analysis of the explorative search

behavior of the HS[22],and proposed a simple but very useful

modification to the classical HS in light of the mathematical


On the other hand,the novel global harmony search(NGHS)

algorithm[23]is a recently proposed algorithm,and it has been

successfully applied into constrained reliability problems.The

NGHS is an improved version of the HS,and it has shown better

performance than the HS on solving constrained reliability

problems.In this paper,we use the NGHS to solve unconstrained

problems so as to profoundly study and analyze the performance

of the NGHS.We also compare the NGHS with the other three

harmony search algorithms on solving unconstrained problems.

Experimental results indicate that the NGHS has stronger

convergence and stability than the HS and its two improved


This paper is organized as follows.In Section2,a brief

overview of three harmony search algorithms is provided,and

they are the original harmony search(HS)algorithm,the

Contents lists available at ScienceDirect

journal homepage: /locate/neucom


0925-2312/$-see front matter&2010Elsevier B.V.All rights reserved.


ÃCorresponding author.

E-mail address:zoudexuan@ (D.Zou).


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