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

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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Application of an Improved harmony search algorithm on Electric Vehicle Routing Problems

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ENERGIES 2024年第15期17卷 3716页

作者： Minanda, Vanny Liang, Yun-Chia Chen, Angela H. L. Gunawan, Aldy Yuan Ze Univ Dept Ind Engn & Management Taoyuan 320 Taiwan Chung Yuan Christian Univ Dept Ind & Syst Engn Taoyuan 320 Taiwan Singapore Management Univ Sch Comp & Informat Syst 80 Stamford Rd Singapore 178902 Singapore

Electric vehicles (EVs) have gained considerable popularity, driven in part by an increased concern for the impact of automobile emissions on climate change. Electric vehicles (EVs) cover more than just conventional cars and trucks. They also include electric motorcycles, such as those produced by Gogoro, which serve as the primary mode of transportation for food and package delivery services in Taiwan. Consequently, the Electric Vehicle Routing Problem (EVRP) has emerged as an important variation of the Capacitated Vehicle Routing Problem (CVRP). In addition to the CVRP's constraints, the EVRP requires vehicles to visit a charging station before the battery level is insufficient to continue service. EV battery consumption is linearly correlated to their weight. These additional constraints make the EVRP more challenging than the conventional CVRP. This study proposes an improved harmony search algorithm (HSA), with performance validated by testing 24 available benchmark instances in the EVRP. This study also proposes a novel update mechanism in the improvement stage and a strategy to improve the routes with charging stations. The results show that in small and large instances, the proposed HSA improved the number of trips to the charging stations by 24% and 4.5%, respectively. These results were also verified using the Wilcoxon signed-rank significant test.

关键词： vehicle routing problem metaheuristic electric vehicle routing problem harmony search algorithm

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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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Equilibrium optimizer-based harmony search algorithm with nonlinear dynamic domains and its application to real-world optimization problems

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ARTIFICIAL INTELLIGENCE REVIEW 2024年第7期57卷 166-166页

作者： Wang, Jinglin Ouyang, Haibin Li, Steven Ding, Weiping Gao, Liqun Guangzhou Univ Sch Mech & Elect Engn Guangzhou 510006 Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou Peoples R China RMIT Univ Grad Sch Business & Law Melbourne 3000 Australia Nantong Univ Sch Informat Sci & Technol Nantong 226019 Peoples R China

harmony search (HS) algorithm is a swarm intelligence algorithm inspired by musical improvisation. Although HS has been applied to various engineering problems, it faces challenges such as getting trapped in local optima, slow convergence speed, and low optimization accuracy when applied to complex problems. To address these issues, this paper proposes an improved version of HS called Equilibrium Optimization-based harmony search algorithm with Nonlinear Dynamic Domains (EO-HS-NDD). EO-HS-NDD integrates multiple leadership-guided strategies from the Equilibrium Optimizer (EO) algorithm, using harmony memory considering disharmony and historical harmony memory, while leveraging the hidden guidance direction information from the Equilibrium Optimizer. Additionally, the algorithm designs a nonlinear dynamic convergence domain to adaptively adjust the search space size and accelerate convergence speed. Furthermore, to balance exploration and exploitation capabilities, appropriate adaptive adjustments are made to harmony Memory Considering Rate (HMCR) and Pitch Adjustment Rate (PAR). Experimental validation on the CEC2017 test function set demonstrates that EO-HS-NDD outperforms HS and nine other HS variants in terms of robustness, convergence speed, and optimization accuracy. Comparisons with advanced versions of the Differential Evolution (DE) algorithm also indicate that EO-HS-NDD exhibits superior solving capabilities. Moreover, EO-HS-NDD is applied to solve 15 real-world optimization problems from CEC2020 and compared with advanced algorithms from the CEC2020 competition. The experimental results show that EO-HS-NDD performs well in solving real-world optimization problems.

关键词： harmony search algorithm Equilibrium optimizer Dynamic domains Optimization Meta-heuristic algorithms

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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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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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harmony search algorithm for simultaneous minimization of bi-objectives in multi-row parallel machine layout problem

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EVOLUTIONARY INTELLIGENCE 2021年第4期14卷 1495-1522页

作者： Lenin, N. Kumar, M. Siva Vel Tech Rangarajan Dr Sagunthala R&D Inst Sci & Mech Engn Chennai 600062 Tamil Nadu India

The manufacturing cost of products and productivity mainly depends on the arrangements of manufacturing facilities on the shop floor. The process of designing a good layout ensures the relative positions of different types of machines to satisfy the objectives of the manufacturers. Probably, the arrangement of machines in a single row with considering duplicate machines and forward flow of materials under a multi-product environment is providing better solutions to the manufacturers in view of satisfying the objectives. Since the usage of duplicate machines in a single row machine layout, the investment cost on machines is high along with the requirement of a lengthy space. In addition to that, the forward flow of materials is resulting from an increase in the flow distance of products. In view of eliminating these two constraints, the laying of machines in multi-row with forward and backward flow of products is being considered. The proposed work is discussed about the effective way of laying parallel machines in multiple rows to satisfy the minimization of bi-objective namely flow distance of products and area of the layout. A simple heuristic is developed to evaluate the bi-objectives for the given sequence of machines placed on the constrained multiple rows. Further, a harmony search algorithm is utilized to identify the best sequence of machines to be arranged in multi-rows to simultaneously minimize the bi-objectives. The effectiveness of the proposed algorithm is tested on the problems associated with single row machine layout and the problems dealt by Vitayasak and Pongcharoen (Expert Syst Appl 98:129-152, 2018). The results ensured that the proposed algorithm was capable of providing the best solution to the multi-row parallel machine layout problem by significantly minimizing the bi-objectives simultaneously.

关键词： Multi-row parallel machine layout problem Multi-product environment Flow distance of products Area of the layout Simple heuristic harmony search algorithm

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Enhanced harmony search algorithm with non-linear control parameters for global optimization and engineering design problems

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ENGINEERING WITH COMPUTERS 2022年第SUPPL 4期38卷 3539-3562页

作者： Gupta, Shubham Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore

harmony search algorithm (HSA), inspired by the behaviors of music improvisation process, is a widely used metaheuristic to solve global optimization problems arises in various fields. The reason of its popularity is its simplicity of algorithm structure and good performance. However, the conventional harmony search algorithm (HSA) experiences prone towards the local optima, tedious task of tuning parameters, and premature convergence. To overcome all these drawbacks of conventional HSA and further improve the precision of numerical results, a new variant of the HSA called modified harmony search algorithm (MHSA) is proposed in the present study. This MHSA utilizes the valuable information stored in the harmony memory and modifies the search strategy to make an efficient search procedure by adopting a new formulation to the pitch adjustment process, randomization process, harmony memory considering rate (HMCR), and pitch adjustment rate (PAR). The experimental validation and comparative performance study with conventional HSA, variants of HSA such as adaptive harmony search with best based search strategy (ABHS), enhanced self-adaptive global-best harmony search (ESGHS), novel self-adaptive harmony search (NSHS), parameter adaptive harmony search (PAHS), Gaussian global-best harmony search algorithm (GGHS) and other metaheuristics such as sine cosine algorithm (SCA), grey wolf optimizer (GWO), comprehensive learning particle swarm optimization (CLPSO), gbest-guided artificial bee colony (GABC), and covariance matrix adaptation evolution strategy (CMA-ES) is conducted on a set of 23 well-known benchmark problems. In addition to this benchmarking, the proposed MHSA is also used to solve three structural engineering design problem. The statistical test and convergence behaviour analysis are used to analyze the quality of search and significance of improved accuracy. The comparison illustrates the superior search efficiency of the proposed MHSA than other algorithms as

关键词： Optimization harmony search algorithm Exploration and exploitation

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Multi-objective stock market portfolio selection using multi-stage stochastic programming with a harmony search algorithm

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NEURAL COMPUTING & APPLICATIONS 2022年第24期34卷 22257-22274页

作者： Asgari, H. Behnamian, J. Bu Ali Sina Univ Fac Engn Dept Ind Engn Hamadan Hamadan Iran

The problem of stock portfolio selection is one of the most critical problems in financial markets. The portfolio selection problem is to find an optimal solution to allocate a fixed amount of capital to a set of available stocks with the objective function of having the maximum expected rate of return and, at the same time, the least possible risk. Among the shortcomings that most stock portfolio models have is not paying attention to future changes and focusing too much on past information. This study aims to provide a framework that addresses some shortcomings and provides a practical tool. In this regard, this study suggests a multi-objective and multi-stage stochastic model for portfolio selection in the financial market. The stage refers to the periods in which the stock portfolio will be reviewed. By combining the scenario generation model with multi-stage stochastic programming, the investor is expected to achieve a suitable solution based on past information and various future scenarios. To solve the proposed model, a meta-heuristic algorithm whose main idea is derived from the harmony search algorithm is proposed. Finally, numerical instances were utilized by the use of real stock information from the Iranian stocks market. The algorithm proposed in this research was compared with a genetic algorithm in terms of the quality of the generated solutions and the runtime of the algorithms, and the superiority of the proposed algorithm has been proven.

关键词： Portfolio selection Multi-stage stochastic programming Multi-objective optimization harmony search algorithm

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