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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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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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harmony search algorithm and combined index-based optimal reallocation of generators in a deregulated power system

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NEURAL COMPUTING & APPLICATIONS 2019年第6期31卷 1949-1957页

作者： Bali, Sravana Kumar Munagala, Suryakalavathi Gundavarapu, Venkata Nagesh Kumar GITAM Univ Dept EEE Visakhapatnam Andhra Pradesh India JNT Univ Dept EEE Hyderabad Telangana India Vignans Inst Informat Technol Dept EEE Visakhapatnam Andhra Pradesh India

It is compulsory for the electrical industry to make effective utilization of the available resources and provide a stable and reliable supply to the consumers. Optimal reallocation of generators and implementation of FACTS devices have been found to be very effective in this regard. In this paper, a combinatory strategy of optimal tuning of generators using harmony search algorithm in the presence of static VAR compensator has been proposed. The static VAR compensator has been placed on the basis of a combined index that comprises of V-i/V-o index and L-index. A multi-objective function comprising of voltage deviations, active power generation costs and line losses has been considered for proper tuning of the generators. The results obtained are compared with the genetic algorithm. The proposed method has been tested and implemented on an IEEE 30 bus system for normal loading and for severe system conditions due to line outage.

关键词： Optimal reallocation Static VAR compensator harmony search algorithm Voltage stability

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harmony search algorithm: application to the redundancy optimization problem

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ENGINEERING OPTIMIZATION 2010年第9期42卷 845-861页

作者： Nahas, Nabil Thien-My, Dao ETS Dept Mech Engn Montreal PQ H3C 1K3 Canada

The redundancy optimization problem is a well known NP-hard problem which involves the selection of elements and redundancy levels to maximize system performance, given different system-level constraints. This article presents an efficient algorithm based on the harmony search algorithm (HSA) to solve this optimization problem. The HSA is a new nature-inspired algorithm which mimics the improvization process of music players. Two kinds of problems are considered in testing the proposed algorithm, with the first limited to the binary series-parallel system, where the problem consists of a selection of elements and redundancy levels used to maximize the system reliability given various system-level constraints;the second problem for its part concerns the multi-state series-parallel systems with performance levels ranging from perfect operation to complete failure, and in which identical redundant elements are included in order to achieve a desirable level of availability. Numerical results for test problems from previous research are reported and compared. The results of HSA showed that this algorithm could provide very good solutions when compared to those obtained through other approaches.

关键词： redundancy allocation series-parallel systems harmony search algorithm universal generating function

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harmony search algorithm based optimum detailed design of reinforced concrete plane frames subject to ACI 318-05 provisions

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COMPUTERS & STRUCTURES 2015年 147卷 79-95页

作者： Akin, A. Saka, M. P. Thomas& Betts Meyer Steel Struct Memphis TN USA Univ Bahrain Dept Civil Engn Isa Town Bahrain

This paper presents the application of the harmony search based algorithm to the optimum detailed design of special seismic moment reinforced concrete (RC) frames under earthquake loads based on American Standard specifications. The objective function is selected as the total cost of the frame which includes the cost of concrete, formwork and reinforcing steel for individual members of the frame. The modular sizes of members, standard reinforcement bar diameters, spacing requirements of reinforcing bars, architectural requirements and other practical requirements in addition to relevant provisions are considered to obtain directly constructible designs without any further modifications. For the RC columns, predetermined section database is constructed and arranged in order of resisting capacity. The produced optimum design satisfies the strength, ductility, serviceability and other constraints related to good design and stated in the relevant specifications. The lateral seismic forces are calculated according to ASCE 7-05 and it is updated in each iteration. Number of design examples is considered to demonstrate the efficiency of the optimum design algorithm proposed. It is concluded that the developed optimum design model can be used in design offices for practical designs and this study is the first application of the harmony search method to the optimization of RC frames and also the optimization of special seismic moment RC frames to date. (C) 2014 Civil-Comp Ltd and Elsevier Ltd. All rights reserved.

关键词： Cost optimization Structural optimum design harmony search algorithm Reinforced concrete structures Heuristics

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harmony search algorithm for transmission network expansion planning

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IET GENERATION TRANSMISSION & DISTRIBUTION 2010年第6期4卷 663-673页

作者： Verma, A. Panigrahi, B. K. Bijwe, P. R. Indian Inst Technol Dept Elect Engn New Delhi 110016 India

Transmission network expansion planning (TNEP) is a very important problem in power systems. It is a mixed integer, non-linear, non-convex optimisation problem, which is very complex and computationally demanding. Various meta-heuristic optimisation techniques have been tried out for this problem. However, scope for even better algorithms still remains. In view of this, a new technique known as harmony search is presented here for TNEP with security constraints. This technique has been reported to be robust and computationally efficient compared to other meta-heuristic algorithms. Results for three sample test systems are obtained and compared with those obtained with genetic algorithm and bacteria-foraging differential evolution algorithm to verify the potential of the proposed algorithm.

关键词： transmission network expansion planning power transmission planning nonconvex optimisation problem harmony search algorithm Power transmission, distribution and supply genetic algorithm mixed integer genetic algorithms Power system planning and layout nonlinear optimisation problem differential evolution algorithm Optimisation techniques

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harmony search algorithm: a variant with Self-regulated Fretwidth

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APPLIED MATHEMATICS AND COMPUTATION 2015年 266卷 1127-1152页

作者： Amaya, Ivan Cruz, Jorge Correa, Rodrigo Univ Ind Santander Sch Elect Elect & Telecommun Engn Bucaramanga Colombia

This article presents a novel modification of the harmony search (HS) algorithm that is able to self-tune as the search progress. This adaptive behavior is independent of total iterations. Moreover, it requires less iterations and provides more precision than other variants of HS. Its effectiveness and performance was assessed, comparing our data against four well known and recent modifications of HS: IHS (Improved harmony search, 2007), ABHS (Adjustable Bandwidth harmony search, 2014), PAHS (Parameter Adaptive harmony search, 2014), and IGHS (Intelligent Global harmony search, 2014). Unlike other works, we did not analyze the data for a given number of iterations. Instead, we ran each algorithm until it achieved a given level of precision, and analyzed the number of iterations it required. Our test benchmark contained 30 standard test functions distributed like this: 11 unimodal, 8 multimodal with fixed dimensions, and 11 multimodal with variable dimensions. The latter also included a function whose optima was located at a different coordinate in each dimension. The search domain for each function was fixed according to the literature, though we also executed tests regarding the effect of varying it. We carried out a parameter sweep to find adequate values for each parameter of our proposed algorithm, analyzing 100 independent runs for 648 different combinations. Data confirm the implemented procedure outperformed the other variants for problems in 2D and in 5D. Scaling the test functions to 10D, 30D, and 50D reduced the convergence rate of the implemented procedure, but it still outperformed IHS, ABHS, and PAHS. In some cases (e.g. Schwefel function in 30D), the Self-regulated Fretwidth harmony search algorithm (SFHS) was found to be the fastest approach. It was also found that IGHS performs well for optimization problems whose optima is located at the same coordinates in all dimensions, but not as well in other scenarios. Our proposed algorithm (SFHS) is not hind

关键词： Global optimization harmony search algorithm Metaheuristic Self-regulated Fret width harmony search algorithm Standard test function

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harmony search algorithm with Adaptive Parameters to Optimize the Linear Quadratic Regulator Design

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IEEE LATIN AMERICA TRANSACTIONS 2018年第7期16卷 1862-1869页

作者： Nascimento, L. B. P. Pinto, V. P. Amora, M. A. B. Univ Fed Ceara Engn Eletr & Comp Sobral Ceara Brazil Univ Fed Ceara Curso Engn Eletr Campus Sobral Sobral Ceara Brazil Univ Fed Ceara Sobral Ceara Brazil

Linear Quadratic Regulator (LQR) is an important control technique with excellent properties associated to robust stability. This technique has been the subject of constant study until the present day, since the problems weighting matrices Q and R are still open, as well as the situations in which the dynamics is unknown. This work proposes the application of a novel harmony search (HS) algorithm to find the Q and R matrices. This algorithm ensures the automatic adjustment of parameters. By adopting the CH-47 helicopter and an inverted pendulum system, several tests involving search and simulations have been performed with two HS algorithms i.e. standard HS and Statistical Dispersion harmony search (SDHS). The latter one can be seen as the main contribution of this work, which also compares the results obtained from the algorithms.

关键词： Linear Quadratic Regulator harmony search algorithm Optimization Metaheuristic Intelligent Control

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harmony search algorithm for Patient Admission Scheduling Problem

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JOURNAL OF INTELLIGENT SYSTEMS 2020年第1期29卷 540-553页

作者： Abu Doush, Iyad Al-Betar, Mohammed Azmi Awadallah, Mohammed A. Hammouri, Abdelaziz, I Al-Khatib, Ra'ed M. AlMustafa, Siba Alkhraisat, Habes Amer Univ Kuwait Comp Sci & Informat Syst Dept Salmiya Kuwait Yarmouk Univ Comp Sci Dept Irbid Jordan Al Balqa Appl Univ Al Huson Univ Coll Dept Informat Technol Irbid Jordan Al Aqsa Univ Dept Comp Sci POB 4051 Gaza Palestine Al Balqa Appl Univ Dept Comp Informat Syst Al Salt Jordan

The patient admission scheduling (PAS) problem is an optimization problem in which we assign patients automatically to beds for a specific period of time while preserving their medical requirements and their preferences. In this paper, we present a novel solution to the PAS problem using the harmony search (HS) algorithm. We tailor the HS to solve the PAS problem by distributing patients to beds randomly in the harmony memory (HM) while respecting all hard constraints. The proposed algorithm uses five neighborhood strategies in the pitch adjustment stage. This technique helps in increasing the variations of the generated solutions by exploring more solutions in the search space. The PAS standard benchmark datasets are used in the evaluation. Initially, a sensitivity analysis of the HS algorithm is studied to show the effect of its control parameters on the HS performance. The proposed method is also compared with nine methods: non-linear great deluge (NLGD), simulated annealing with hyper-heuristic (HH-SA), improved with equal hyperheuristic (HH-IE), simulated annealing (SA), tabu search (TS), simple random simulated annealing with dynamic heuristic (DHS-SA), simple random improvement with dynamic heuristic (DHS-OI), simple random great deluge with dynamic heuristic (DHS-GD), and biogeography-based optimization (BBO). The proposed HS algorithm is able to produce comparably competitive results when compared with these methods. This proves that the proposed HS is a very efficient alternative to the PAS problem, which can be efficiently used to solve many scheduling problems of a large-scale data.

关键词： harmony search algorithm optimization patient admission problem metaheuristic patient scheduling problem

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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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