An improved global-best harmony search algorithm

doi:10.1016/j.amc.2013.07.020

Applied Mathematics and Computation

Volume 222, 1 October 2013, Pages 94-106

https://doi.org/10.1016/j.amc.2013.07.020 Get rights and content

Abstract

This paper introduces an improved global-best harmony search (IGHS) algorithm. The proposed modifications effectively combines a novel improvisation scheme with a previously developed mechanism for updating the pitch adjustment rate (PAR) and the distance bandwidth (bw). The aim of this modification is to efficiently investigate the search space by going through the stages of exploration and exploitation. The proposed algorithm is compared against seven previous modifications to HS using rigorous statistical tests when applied to the CEC05 benchmark functions showing a superior performance on most of the tested functions.

Introduction

Harmony search (HS) [6], [16] is a relatively new optimization algorithm that has been proposed in the last decade. The main idea behind the algorithm is to simulate the behavior of a musician looking for the right harmony. Among the many benefits of HS [6] is having a few and relatively easy mathematical equations as well as considering all the members of the current population while producing a new harmony.

The main drawback of HS is the failure to fine tune the final solution towards the end of the search [7]. Many attempts have been pursued to overcome this disadvantage and improve the performance of HS. The authors in [7] introduced the improved HS by proposing new technique for adjusting the algorithm parameters during the search. Ideas borrowed from swarm intelligence have been also utilized in the global-best HS [10]. Differential evolution operators have been incorporated into HS in [4]. Finally, two adaptive versions of HS have been recently proposed in [15], [12].

In this paper, we introduce an improved version of the global-best HS by proposing a new harmony improvisation scheme that is effectively combined with a mechanism for adjusting the algorithm parameters. The main reason for this modification is to control the algorithm search strategy and allow it to gradually shift from the exploration behavior at the beginning of the search to the exploitation behavior at the end. Our algorithm is compared against all other previously introduced HS algorithms when applied to a well-known benchmark library.

Section 2 gives an introduction to HS. All previously proposed improvements for HS are covered in Section 3. Our proposed algorithm is presented in Section 4. Section 5 presents the experimental results. Finally, the paper is concluded in Section 6.

Section snippets

Harmony search

HS [6], [16] was introduced as an imitation of the musical process that searches for a harmony balance. In HS, each variable of the problem is regarded as the pitch of a different musical instrument and the complete solution is referred to as a harmony vector. If the pitch (decision variable value) makes good harmony (good objective function value), it is stored in memory.

The memory part is modeled using a memory structure referred to as the Harmony Memory (HM). Initially, HS is initialized

Previous improvements

The overview presented in [8] covered most of the previous improvements introduced into HS. These improvements were categorized into improvements in terms of parameter settings or in terms of hybridization with other meta-heuristic algorithms. According to this classification, the variants tested in this work fall in the first category.

Improved global-best harmony search

In this work, we introduce a new improved global-best harmony search (IGHS) algorithm. We believe that a lot of successful improvements were introduced in HS. However, these improvements could be mixed more efficiently to have a better performance.

The basic idea is that we need to have an explorative performance at the beginning of the search while having an exploiting one towards the end. The explorative behavior is realized by searching around randomly selected harmonies from memory with

Experimental procedure

HS, HS_Pop, DHS, GHS, IHS, AHS, SGHS and IGHS are all applied to the CEC05 benchmark functions [14] for problem sizes of $D = 10, D = 30$ and $D = 50$ . The algorithms are allowed to perform a maximum of $10^{4} \times D$ function evaluations. Function f8 was excluded from the comparisons as it has the global optimum near the bounds and it acts as the needle-in-hay-stack problem. All algorithms applied to this function practically reach the same solution.

The MATLAB code for HS was obtained through private communication

Conclusions

This paper introduced an improved global-best harmony search (IGHS) algorithm. The algorithm exhibited the desirable behavior of exploring the search space at the beginning while moving towards exploiting good solutions near the end. This was achieved by searching a wide area around random solutions (using Gaussian distribution) while searching a small area around the best solution (using uniform distribution). The searching areas were made smaller over time by exponentially decreasing bw and

References (16)

M.A. Al-Betar et al.
Novel selection schemes for harmony search
Applied Mathematics and Computation
(2012)
B. Alatas
Chaotic harmony search algorithms
Applied Mathematics and Computation
(2010)
J. Derrac et al.
A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutioary and swarm intelligence algorithms
Swarm and Evolutionary Computation
(2011)
K.S. Lee et al.
A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice
Computer Methods in Applied Mechanics Engineering
(2005)
M. Mahdavi et al.
An improved harmony search algorithm for solving optimization problems
Applied Mathematics and Computation
(2007)
M.G.H. Omran et al.
Global-best harmony search
Applied Mathematics and Computation
(2008)
Q. Pan et al.
A self-adaptive global best harmony search algorithm for continuous optimization problems
Applied Mathematics and Computation
(2010)
C. Wang et al.
Self-adaptive harmony search algorithm for optimization
Expert Systems with Applications
(2010)

There are more references available in the full text version of this article.

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Citation Excerpt :
Then, HS moves candidate solutions in the search space to find the optimal solution through application of some search operators that model the pitch selection and adjustment actions in production of right harmonies. Despite significant success of HS applications, several studies have pointed out that search mechanisms of HS exhibit excellent explorative behavior but poor exploitative ability [21,22]. This inefficiency is originated from the insufficient utilization of history information and experience gathered during search process in harmony memory (HM).
This paper presents a variant of harmony search algorithm (HS), called best–worst-mean harmony search (BWM_HS). The main difference between the proposed algorithm and the canonical HS is that it employs a modified memory consideration procedure to utilize more efficiently the accumulated knowledge and experience in harmony memory (HM). To this aim, the random harmony selection scheme of this procedure is replaced with three novel pitch selection and production rules. These rules use the information of the current best and worst harmonies as well as the mean of all harmonies to guide the search process. To further utilize the valuable information of HM, two new harmonies are generated at each iteration where the better one will compete with the current worst harmony. The mean of all harmonies is always employed to produce a new harmony. On the other hand, each pitch of the second one is obtained by the rules that consider the information of the best and worst harmonies. These rules can present either explorative or exploitative search behaviors at different stages of search. Thus, a probabilistic self-adaptive selection scheme decides to choose between them to properly balance the exploration and exploitation abilities. The general performance of BWM_HS for solving optimization problems is evaluated against CEC 2017 benchmark functions and its results are compared with HS and eight state-of-the-art variants of HS. The comparison indicates that the performance of BWM_HS is better than or equal to the compared algorithms with respect to the accuracy, robustness, and convergence speed criteria. Moreover, the performance of BWM_HS in solving clustering problems is investigated by applying it for clustering several well-known benchmark datasets. The experimental results show that, in general, the BWM_HS outperforms other well-known algorithms in the literature and in particular, it significantly improves the statistical results for one dataset.

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An improved global-best harmony search algorithm

Abstract

Introduction

Section snippets

Harmony search

Previous improvements

Improved global-best harmony search

Experimental procedure

Conclusions

Applied Mathematics and Computation

Applied Mathematics and Computation

Swarm and Evolutionary Computation

Computer Methods in Applied Mechanics Engineering

Applied Mathematics and Computation

Applied Mathematics and Computation

Applied Mathematics and Computation

Expert Systems with Applications