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harmony search algorithm and related variants: A systematic review

SWARM AND EVOLUTIONARY COMPUTATION 2022年 74卷

作者： Qin, Feng Zain, Azlan Mohd Zhou, Kai-Qing Univ Teknol Malaysia Sch Comp Skudai Malaysia Univ Teknol Malaysia UTM Big Data Ctr Skudai Malaysia Jishou Univ Coll Informat Sci & Engn Jishou Peoples R China

harmony search (HS) algorithm is a novel metaheuristic algorithm, inspired by the phenomenon that musicians repeatedly adjust the pitch of each instrument to finally achieve a beautiful harmony state. Due to its simple concept, few adjustable parameters, easy implementation, and the ability to balance exploitation and exploration during search, HS has been widely applied to deal with various optimization problems in real life. However, HS has shortcomings such as low optimization accuracy and premature convergence. Therefore, various HS variants have been proposed. In response to this trend, this article systematically reviews HS and its variants from various aspects. First, the basic HS principle is described. Secondly, how the improvement of HS affects the performance of the algorithm is discussed. Finally, the characteristics of HS variants and their applications are analyzed. It can be seen from the literature that the improvement of HS is mainly focused on parameter improvement and mixing with other metaheuristic algorithms. Some HS even use both techniques to improve the algorithm simultaneously. HS is mainly used to solve optimization problems in engineering, which provides future research directions for improving HS.

关键词： harmony search algorithm Metaheuristic algorithm Optimization

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Hybrid harmony search algorithm Integrating Differential Evolution and Levy Flight for Engineering Optimization

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IEEE ACCESS 2025年 13卷 13534-13572页

作者： Qin, Feng Zain, Azlan Mohd Zhou, Kai-Qing Bin Yusup, Norfadzlan Prasetya, Didik Dwi Jalil, Rozita Abdul Abidin, Zaheera Zainal Bahari, Mahadi Kamin, Yusri Majid, Mazlina Abdul Univ Teknol Malaysia Fac Comp Johor Baharu 81310 Malaysia Jishou Univ Sch Commun & Elect Engn Jishou 416000 Peoples R China Univ Malaysia Sarawak Fac Comp Sci & Informat Technol Kota Samarahan 94300 Malaysia State Univ Malang Fac Engn Malang 65145 Indonesia Univ Tun Hussein Onn Malaysia Fac Comp Sci & Informat Technol Parit Raja 86400 Johor Malaysia Univ Tekn Malaysia Melaka Fac Informat & Commun Technol Durian Tunggal 76100 Malaysia Univ Teknol Malaysia Fac Management Johor Baharu 81310 Malaysia Univ Teknol Malaysia Fac Social Sci & Humanities Johor Baharu 81310 Malaysia Univ Malaysia Pahang Al Sultan Abdullah Fac Comp Gambang 26300 Pahang Malaysia

harmony search algorithm (HSA) is extensively utilized in engineering optimization. Nevertheless, it encounters problems of slow convergence and reduced accuracy, which hinder its capability to escape local optima. This paper proposes HSA-DELF, a novel hybrid algorithm that combines differential evolution (DE) and L & eacute;vy flight (LF) techniques to enhance the performance of HSA. HSA-DELF leverages multi-mutation strategies of DE and LF random walk combined with weighted individuals to improve exploration and exploitation based on population fitness standard deviation comparison, and adopts pairwise iterative updates of the population to achieve faster convergence and higher solution quality. Extensive experiments were conducted to validate performance on 23 classic benchmark functions and 12 CEC 2022 benchmark functions, followed by comprehensive testing on 7 engineering problems, demonstrating the superiority of HSA-DELF. Comparative analysis with 5 well-known algorithms (HSA, DE, CSA, GA, and PSO) and 4 HSA variants (IHS, MHSA, IHSDE, and IMGHSA) confirmed the robustness of HSA-DELF. Statistical results, including best, mean, standard deviation, and worst values, consistently highlight the superior performance of HSA-DELF in terms of convergence speed, solution quality, and robustness. The Wilcoxon signed-rank test further corroborated these significant advantages. HSA-DELF showed notable improvements in 6 out of 7 engineering problems, achieving an accuracy of 85.71%. This study establishes HSA-DELF as an effective and reliable method for solving complex engineering optimization problems.

关键词： Optimization Metaheuristics Benchmark testing Convergence Genetic algorithms Encoding Standards Space exploration search problems Robustness harmony search algorithm benchmark functions engineering optimization multi-mutation strategies pairwise iterative updates

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A comparative analysis using LEACH protocol to enhance energy efficiency in wireless sensor networks with harmony search algorithm

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DISCOVER COMPUTING 2025年第1期28卷 1-27页

作者： Sambhe, Nilesh Yenurkar, Ganesh Kanase, Vijay V. Anjana, S. Ninawe, Neeraj Babrekar, Shripad Pophali, Om Kale, Ayush Vyas, Prathmesh Yeshwantrao Chavan Coll Engn Dept Comp Technol Nagpur 441110 Maharashtra India Krishna Vishwa Vidyapeeth Deemed Be Univ Krishna Inst Med Sci Dept Surg Satara 415539 Maharashtra India Manipal Acad Higher Educ Manipal Inst Technol Manipal Dept Comp Sci & Engn Udupi 576104 Karnataka India

Wireless sensor networks (WSNs) are critical to many applications, but their use is frequently hampered by energy constraints, particularly in remote locations. WSN nodes are typically installed in remote and frequently inaccessible locations, making battery replacement challenging, thus emphasizing the importance of energy efficiency. This research presents an energy-conserving approach centred on the harmony search algorithm (HSA), optimized by considering key parameters such as the number of sensor nodes, initial energy levels, transmission range, and data rate. The network performance is tested against the LEACH algorithm by evaluating parameters including energy consumption, network lifetime, and throughput. The comparative analysis is performed using graphs depicting the energy consumption of nodes by both approaches. With the harmony Memory Size (HMS), harmony Memory Considering Rate (HMCR), and Pitch Adjustment Rate (PAR) adjusted for best outcomes, the suggested method maximizes the performance of WSNs by effectively regulating the energy consumption of sensor nodes. Unlike LEACH, which involves clustering of nodes and periodic rotation of clusters, HSA is based on energy-efficient harmony and does not rely on clustering, thereby finding the most energy-efficient communication path within the network. Simulation results indicate that the HSA algorithm is 9.52% more efficient, with its energy usage being 9.2% more economical compared to the LEACH algorithm. This demonstrates HSA's potential for enhancing WSN performance in energy-constrained environments.

关键词： Wireless sensor networks harmony search algorithm Low energy adaptive clustering hierarchy Energy constraints WSN nodes

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An improved harmony search algorithm using opposition-based learning and local search for solving the maximal covering location problem

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ENGINEERING OPTIMIZATION 2024年第8期56卷 1298-1317页

作者： Atta, Soumen Univ Nova Gorica Ctr Informat Technol & Appl Math Nova Gorica Slovenia

In this article, an improved harmony search algorithm (IHSA) that utilizes opposition-based learning is presented for solving the maximal covering location problem (MCLP). The MCLP is a well-known facility location problem where a fixed number of facilities are opened at a given potential set of facility locations such that the sum of the demands of customers covered by the open facilities is maximized. Here, the performance of the harmony search algorithm (HSA) is improved by incorporating opposition-based learning that utilizes opposite, quasi-opposite and quasi-reflected numbers. Moreover, a local search heuristic is used to improve the performance of the HSA further. The proposed IHSA is employed to solve 83 real-world MCLP instances. The performance of the IHSA is compared with a Lagrangean/surrogate relaxation-based heuristic, a customized genetic algorithm with local refinement, and an improved chemical reaction optimization-based algorithm. The proposed IHSA is found to perform well in solving the MCLP instances.

关键词： Maximal covering location problem harmony search algorithm opposition-based learning facility location problem opposite number

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A dual population collaborative harmony search algorithm with adaptive population size for the system reliability-redundancy allocation problems

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JOURNAL OF COMPUTATIONAL DESIGN AND ENGINEERING 2024年第2期11卷 285-313页

作者： Ouyang, Haibin Liang, Siqi Li, Steven Zhou, Ziyu Zhan, Zhi-Hui Guangzhou Univ Sch Mech & Elect Engn Guangzhou 510006 Peoples R China RMIT Univ Grad Sch Business & Law Melbourne 3000 Australia South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China

Aiming at the problem that the diversity of the current double population algorithm with dynamic population size reduction cannot be guaranteed in real time in iteration and is easy to fall into local optimum, this study presents a dual population collaborative harmony search algorithm with adaptive population size (DPCHS). Firstly, we propose a dual population algorithm framework for improving the algorithm global search capability. Within this framework, the guidance selection strategy and information interaction mechanism are integrated to strengthen the competition and cooperation among populations, and achieving a good balance between exploration and exploitation. A population state assessment method is designed to monitor population changes in real-time for enhancing population real-time self-regulation. Additionally, population size adjustment approach is designed to adopted to effectively streamline population resources and improve population quality. Comprehensive experiment results demonstrate that DPCHS effectively addresses system reliability-redundancy allocation problems with superior performance and robust convergence compared with other HS variants and algorithms from different categories. Graphical Abstract

关键词： harmony search algorithm population state assessment population size adaptation system reliability

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HSGS: A hybrid of harmony search algorithm and golden section for data clustering

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EXPERT SYSTEMS WITH APPLICATIONS 2023年第1期224卷

作者： Talaei, Kazem Rahati, Amin Idoumghar, Lhassane Univ Sistan & Baluchestan Dept Comp Sci Zahedan Iran Univ Haute Alsace IRIMIS UHA Mulhouse France

This paper proposes an improved variant of the harmony search (HS) algorithm called HSGS for solving clustering problems. The HSGS generates two new harmonies at each iteration. The first is produced by the harmony improvisation procedure of the canonical HS and promotes exploration ability. The second is generated by one of two new phases added to HS to enhance the exploitation capability with different ratios. Each phase employs the mathematical properties of a famous pattern found in nature, called golden section, to search around a specific harmony. In addition, these phases utilize different information of data points that need to be clustered. In each cycle of the HSGS, a self-adaptive selection mechanism selects a phase to properly adjust the exploitation ratio during the search process. A harmony with a better objective value between the two new harmonies competes with the current worst harmony to update the harmony memory. The performance of HSGS for clustering several well-known benchmark data sets, gene expression data sets, and noisy versions of gene expression data sets is compared with two modified variants of HSGS, seven HS-based clustering algorithms, k-means++, and six evolutionary clustering algorithms. In general, the results indicate that HSGS is superior to all considered algorithms in all data sets.

关键词： harmony search algorithm Golden section Clustering Gene expression K -means plus plus

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Hyperparameters optimization of convolutional neural network based on local autonomous competition harmony search algorithm

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JOURNAL OF COMPUTATIONAL DESIGN AND ENGINEERING 2023年第4期10卷 1280-1297页

作者： Liu, Dongmei Ouyang, Haibin Li, Steven Zhang, Chunliang Zhan, Zhi-Hui Guangzhou Univ Sch Mech & Elect Engn Guangzhou 510006 Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China RMIT Univ Grad Sch Business & Law Melbourne 3000 Australia

Because of the good performance of convolutional neural network (CNN), it has been extensively used in many fields, such as image, speech, text, etc. However, it is easily affected by hyperparameters. How to effectively configure hyperparameters at a reasonable time to improve the performance of CNNs has always been a complex problem. To solve this problem, this paper proposes a method to automatically optimize CNN hyperparameters based on the local autonomous competitive harmony search (LACHS) algorithm. To avoid the influence of complicated parameter adjustment of LACHS algorithm on its performance, a parameter dynamic adjustment strategy is adopted, which makes the pitch adjustment probability PAR and step factor BW dynamically adjust according to the actual situation. To strengthen the fine search of neighborhood space and reduce the possibility of falling into local optima for a long time, an autonomous decision-making search strategy based on the optimal state is designed. To help the algorithm jump out of the local fitting situation, this paper proposes a local competition mechanism to make the new sound competes with the worst harmonic progression of local selection. In addition, an evaluation function is proposed, which integrates the training times and recognition accuracy. To achieve the purpose of saving the calculation cost without affecting the search result, it makes the training time for each model depending on the learning rate and batch size. In order to prove the feasibility of LACHS algorithm in configuring CNN superparameters, the classification of the Fashion-MNIST dataset and CIFAR10 dataset is tested. The comparison is made between CNN based on empirical configuration and CNN based on classical algorithms to optimize hyperparameters automatically. The results show that the performance of CNN based on the LACHS algorithm has been improved effectively, so this algorithm has certain advantages in hyperparametric optimization. In addition, this p

关键词： harmony search algorithm convolutional neural network optimization speed hyperparameters optimization

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Test Point Layout Optimization Based on Multi-Signal Flow Graph and harmony search algorithm

Test Point Layout Optimization Based on Multi-Signal Flow Gr...

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2024 International Conference on Guidance, Navigation and Control

作者： Luo, Xin You, Zixuan Xiong, Hongrui Gao, Zhanbao AVIC Chengdu Aircraft Ind Grp Co Ltd Chengdu 6110073 Sichuan Peoples R China Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

ISBN: (纸本)9789819622665;9789819622641;9789819622634

The aim of this paper is to optimize the performance of the aircraft landing gear system's test point layout. To achieve this, we propose a method that combines the use of a Multi-Signal Flow Graph and the harmony search algorithm. First, a multi-signal flow graph model is built using the object's structure as a basis. Then a dependency matrix of tests and failure modes is generated. The harmony search algorithm is combined with the matrix to find the best test point layout according to the flexible demands of fault detection rate (FDR), fault isolation rate (FIR), and number of test points. Based on the traditional harmony search algorithm, a new control parameter, improvisation probability (IR), is introduced for the "improvisation" part to generate new harmonies. When this algorithm is used to solve binary combinatorial optimization problems, its global optimization-seeking ability and solving speed are enhanced by varying the pitch adjusting rate (PAR) according to the number of generations. To further show how successful this technology is, it is also applied to an actual airplane landing gear system.

关键词： Testability Multi-signal Flow Graph harmony search algorithm

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MTHSA-DHEI: multitasking harmony search algorithm for detecting high-order SNP epistatic interactions

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COMPLEX & INTELLIGENT SYSTEMS 2023年第1期9卷 637-658页

作者： Tuo, Shouheng Li, Chao Liu, Fan Li, Aimin He, Lang Geem, Zong Woo Shang, JunLiang Liu, Haiyan Zhu, YanLing Feng, ZengYu Chen, TianRui Xian Univ Posts & Telecommun Sch Comp Sci & Technol Xian 710121 Shaanxi Peoples R China Shaanxi Key Lab Network Data Anal & Intelligent P Xian 710121 Shaanxi Peoples R China Xian Key Lab Big Data & Intelligent Comp Xian 710121 Shaanxi Peoples R China Xian Univ Technol Sch Comp Sci & Engn Xian 710048 Shaanxi Peoples R China Gachon Univ Dept Energy IT Seongnam 13120 South Korea Qufu Normal Univ Sch Comp Sci Rizhao 276826 Peoples R China

Genome-wide association studies have succeeded in identifying genetic variants associated with complex diseases, but the findings have not been well interpreted biologically. Although it is widely accepted that epistatic interactions of high-order single nucleotide polymorphisms (SNPs) [(1) Single nucleotide polymorphisms (SNP) are mainly deoxyribonucleic acid (DNA) sequence polymorphisms caused by variants at a single nucleotide at the genome level. They are the most common type of heritable variation in humans.] are important causes of complex diseases, the combinatorial explosion of millions of SNPs and multiple tests impose a large computational burden. Moreover, it is extremely challenging to correctly distinguish high-order SNP epistatic interactions from other high-order SNP combinations due to small sample sizes. In this study, a multitasking harmony search algorithm (MTHSA-DHEI) is proposed for detecting high-order epistatic interactions [(2) In classical genetics, if genes X1 and X2 are mutated and each mutation by itself produces a unique disease status (phenotype) but the mutations together cause the same disease status as the gene X1 mutation, gene X1 is epistatic and gene X2 is hypostatic, and gene X1 has an epistatic effect (main effect) on disease status. In this work, a high-order epistatic interaction occurs when two or more SNP loci have a joint influence on disease status.], with the goal of simultaneously detecting multiple types of high-order (k(1)-order, k(2)-order, horizontal ellipsis , k(n)-order) SNP epistatic interactions. Unified coding is adopted for multiple tasks, and four complementary association evaluation functions are employed to improve the capability of discriminating the high-order SNP epistatic interactions. We compare the proposed MTHSA-DHEI method with four excellent methods for detecting high-order SNP interactions for 8 high-orderepistatic interaction models with no marginal effect (EINMEs) and 12 epistatic interaction mod

关键词： Multitasking harmony search algorithm Single nucleotide polymorphisms Epistatic interaction

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Joint economic and emission load dispatch for the Algerian grid via an improved harmony search algorithm

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INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2023年 1-16页

作者： Bouaraki, Mouloud Dekhandji, Fatma Zohra Recioui, Abdelmadjid Benmissoum, Abdellah Khellas, Oussama Univ Mhamed Bougara Inst Elect & Elect Engn Signals & Syst Res Lab LSS Blvd independance Boumerdes 35000 Algeria

Renewable energy sources (RES) have been very popular as they reduce the release of damaging toxins to the air contrary to fossil fuel combustion. The economic load dispatch (ELD) issue looks for the optimal dimensioning of the RES to lessen the fuel cost while Emission Dispatch (ED) is concerned with the best dimensioning of the RESs to decrease the quantity of the produced pollutants. A multi-purpose Joint Economic-Emission Dispatch (JEED) seeks the best RES dimensioning by compromising the fuel fee and toxin release simultaneously. In this paper, a JEED problem is solved for a ten-unit Algerian Network using a recent optimization algorithm named Improved harmony search algorithm (IHSA). The obtained results suggest that the considered JEED problem proves to be more practical than when ELD and ED are dealt with separately. Also, an enhancement in terms of economic and emission dispatch is obtained for the considered case. This work also witnesses on the superiority of the IHSA over state of art approaches.

关键词： Economic load dispatch Emission dispatch Optimization harmony search algorithm

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