Cosine Harmony Search (CHS) for static optimization

Research output: Contribution to journalArticle

Abstract

Harmony Search (HS) is the behaviour imitation of a musician looking for a balanced harmony. HS has difficulty finding the best tuning parameter, especially for Pitch Adjustment Rate (PAR). PAR plays a crucial role in selecting historical solution and adjusting it using Bandwidth (BW) value. PAR in HS requires a constant value to be initialized. Furthermore, there is a delay in convergence speed due to the disproportion of global and local search capabilities. Although some HS variants have claimed to overcome this shortcoming by introducing the self-modification of PAR, these justifications have been found to be imprecise and require more extensive experiments. Local Opposition-Based Learning Self-Adaptation Global Harmony Search (LHS) implements a heuristic factor, η for self-modification of PAR. It (η) manages the probability for selecting the adaptive step, either global adaptive step or worst adaptive step. If the value of η is large, the prospects of selecting the global adaptive step is higher, thereby allowing the algorithm to exploit a better harmony value. Conversely, if η is small, the worst adaptive step is prone to selection, therefore the algorithm is closed to the best global solution. In this paper, in addressing the existing HS obstacle, we introduce a Cosine Harmony Search (CHS) which incorporates an additional strategy rule. This additional strategy employs the η inspired by LHS and contains the cosine parameter. This allows for self-modification of pitch tuning to enlarge the exploitation capabilities. We test our proposed CHS on twelve standard static benchmark functions and compare it with basic HS and five state-of-the-art HS variants. Our proposed method and these state-of-the-art algorithms are executed using 30 and 50 dimensions. The numerical results demonstrated that the CHS has outperformed other state-of-the-art algorithms in terms of accuracy and convergence speed evaluations.

Original languageEnglish
Pages (from-to)1753-1761
Number of pages9
JournalInternational Journal on Advanced Science, Engineering and Information Technology
Volume8
Issue number4-2
Publication statusPublished - 1 Jan 2018

Fingerprint

Social Adjustment
Tuning
Benchmarking
learning
Bandwidth
Learning
Experiments
testing

Keywords

  • Accuracy
  • Additional strategy rule
  • Convergence speed
  • Cosine
  • Global pitch adjustment

ASJC Scopus subject areas

  • Computer Science(all)
  • Agricultural and Biological Sciences(all)
  • Engineering(all)

Cite this

Cosine Harmony Search (CHS) for static optimization. / Bohani, Farah Aqilah; Sheikh Abdullah, Siti Norul Huda; Omar, Khairuddin.

In: International Journal on Advanced Science, Engineering and Information Technology, Vol. 8, No. 4-2, 01.01.2018, p. 1753-1761.

Research output: Contribution to journalArticle

@article{7bc855a536fd42c78fc3c4072982648e,
title = "Cosine Harmony Search (CHS) for static optimization",
abstract = "Harmony Search (HS) is the behaviour imitation of a musician looking for a balanced harmony. HS has difficulty finding the best tuning parameter, especially for Pitch Adjustment Rate (PAR). PAR plays a crucial role in selecting historical solution and adjusting it using Bandwidth (BW) value. PAR in HS requires a constant value to be initialized. Furthermore, there is a delay in convergence speed due to the disproportion of global and local search capabilities. Although some HS variants have claimed to overcome this shortcoming by introducing the self-modification of PAR, these justifications have been found to be imprecise and require more extensive experiments. Local Opposition-Based Learning Self-Adaptation Global Harmony Search (LHS) implements a heuristic factor, η for self-modification of PAR. It (η) manages the probability for selecting the adaptive step, either global adaptive step or worst adaptive step. If the value of η is large, the prospects of selecting the global adaptive step is higher, thereby allowing the algorithm to exploit a better harmony value. Conversely, if η is small, the worst adaptive step is prone to selection, therefore the algorithm is closed to the best global solution. In this paper, in addressing the existing HS obstacle, we introduce a Cosine Harmony Search (CHS) which incorporates an additional strategy rule. This additional strategy employs the η inspired by LHS and contains the cosine parameter. This allows for self-modification of pitch tuning to enlarge the exploitation capabilities. We test our proposed CHS on twelve standard static benchmark functions and compare it with basic HS and five state-of-the-art HS variants. Our proposed method and these state-of-the-art algorithms are executed using 30 and 50 dimensions. The numerical results demonstrated that the CHS has outperformed other state-of-the-art algorithms in terms of accuracy and convergence speed evaluations.",
keywords = "Accuracy, Additional strategy rule, Convergence speed, Cosine, Global pitch adjustment",
author = "Bohani, {Farah Aqilah} and {Sheikh Abdullah}, {Siti Norul Huda} and Khairuddin Omar",
year = "2018",
month = "1",
day = "1",
language = "English",
volume = "8",
pages = "1753--1761",
journal = "International Journal on Advanced Science, Engineering and Information Technology",
issn = "2088-5334",
publisher = "INSIGHT - Indonesian Society for Knowledge and Human Development",
number = "4-2",

}

TY - JOUR

T1 - Cosine Harmony Search (CHS) for static optimization

AU - Bohani, Farah Aqilah

AU - Sheikh Abdullah, Siti Norul Huda

AU - Omar, Khairuddin

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Harmony Search (HS) is the behaviour imitation of a musician looking for a balanced harmony. HS has difficulty finding the best tuning parameter, especially for Pitch Adjustment Rate (PAR). PAR plays a crucial role in selecting historical solution and adjusting it using Bandwidth (BW) value. PAR in HS requires a constant value to be initialized. Furthermore, there is a delay in convergence speed due to the disproportion of global and local search capabilities. Although some HS variants have claimed to overcome this shortcoming by introducing the self-modification of PAR, these justifications have been found to be imprecise and require more extensive experiments. Local Opposition-Based Learning Self-Adaptation Global Harmony Search (LHS) implements a heuristic factor, η for self-modification of PAR. It (η) manages the probability for selecting the adaptive step, either global adaptive step or worst adaptive step. If the value of η is large, the prospects of selecting the global adaptive step is higher, thereby allowing the algorithm to exploit a better harmony value. Conversely, if η is small, the worst adaptive step is prone to selection, therefore the algorithm is closed to the best global solution. In this paper, in addressing the existing HS obstacle, we introduce a Cosine Harmony Search (CHS) which incorporates an additional strategy rule. This additional strategy employs the η inspired by LHS and contains the cosine parameter. This allows for self-modification of pitch tuning to enlarge the exploitation capabilities. We test our proposed CHS on twelve standard static benchmark functions and compare it with basic HS and five state-of-the-art HS variants. Our proposed method and these state-of-the-art algorithms are executed using 30 and 50 dimensions. The numerical results demonstrated that the CHS has outperformed other state-of-the-art algorithms in terms of accuracy and convergence speed evaluations.

AB - Harmony Search (HS) is the behaviour imitation of a musician looking for a balanced harmony. HS has difficulty finding the best tuning parameter, especially for Pitch Adjustment Rate (PAR). PAR plays a crucial role in selecting historical solution and adjusting it using Bandwidth (BW) value. PAR in HS requires a constant value to be initialized. Furthermore, there is a delay in convergence speed due to the disproportion of global and local search capabilities. Although some HS variants have claimed to overcome this shortcoming by introducing the self-modification of PAR, these justifications have been found to be imprecise and require more extensive experiments. Local Opposition-Based Learning Self-Adaptation Global Harmony Search (LHS) implements a heuristic factor, η for self-modification of PAR. It (η) manages the probability for selecting the adaptive step, either global adaptive step or worst adaptive step. If the value of η is large, the prospects of selecting the global adaptive step is higher, thereby allowing the algorithm to exploit a better harmony value. Conversely, if η is small, the worst adaptive step is prone to selection, therefore the algorithm is closed to the best global solution. In this paper, in addressing the existing HS obstacle, we introduce a Cosine Harmony Search (CHS) which incorporates an additional strategy rule. This additional strategy employs the η inspired by LHS and contains the cosine parameter. This allows for self-modification of pitch tuning to enlarge the exploitation capabilities. We test our proposed CHS on twelve standard static benchmark functions and compare it with basic HS and five state-of-the-art HS variants. Our proposed method and these state-of-the-art algorithms are executed using 30 and 50 dimensions. The numerical results demonstrated that the CHS has outperformed other state-of-the-art algorithms in terms of accuracy and convergence speed evaluations.

KW - Accuracy

KW - Additional strategy rule

KW - Convergence speed

KW - Cosine

KW - Global pitch adjustment

UR - http://www.scopus.com/inward/record.url?scp=85055321253&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85055321253&partnerID=8YFLogxK

M3 - Article

VL - 8

SP - 1753

EP - 1761

JO - International Journal on Advanced Science, Engineering and Information Technology

JF - International Journal on Advanced Science, Engineering and Information Technology

SN - 2088-5334

IS - 4-2

ER -