Harmony Search Research Articles

Hybrid of non-dominated sorting genetic algorithm II and invasive weed optimization for fan duct surface heat exchanger configuration optimization design

In this research, configuration optimization was conducted for FDSHX (fan duct surface heat exchanger) that is a new type of heat exchanger adopted in aero-engine heat management in recent years. Firstly, a method of Taguchi-ANFIS (Taguchi-Adaptive Neuro-Fuzzy Inference System), which can reduce training data volume utilizing orthogonal experimental matrix, was proposed to construct a rapid response mathematical model between three configuration parameters, including fin pitch, fin thickness, and oil passages number, and two design indicators, including heat transfer capacity and operating weight, based on the data prepared by an experimental validated FDSHX heat transfer capacity calculation method using heat transfer unit simulation. Secondly, a hybrid method of NSGA II-IWO (Non-dominated Sorting Genetic Algorithm II-Invasive Weed Optimization), which can simultaneously obtain the strong abilities of exploration and escaping from trap into local optima, was proposed to drive the constructed response mathematical model to enhance heat transfer through adjusting the three configuration parameters. Optimization comparison was performed between NSGA II-IWO and four classic optimization algorithms including GA (Genetic Algorithm), IWO (Invasive Weed Optimization), CA (Cultural Algorithm), and HS (Harmony Search). This research provides an integrated solution to help mechanical engineers improve the applicability and reasonableness of FDSHX design.

Bone age estimation with HS-optimized Resnet and Yolo for child growth disorder

Bone Age Assessment (BAA) plays a significant part in assessing skeletal maturity for preventing different types of skeletal disorders in the human body. Predicting BAA helps clinicians make decisions about the patient’s biological maturity. An increase or decrease in bone age (BA) causes serious issues for pediatricians who need advanced equipment for BA consistency with the chronological age. Recent techniques fail to accurately estimate the region over interest (ROI) of hand-wrist images to predict BA under low time complexity accurately. Hence, this article brings novel deep learning (DL) techniques to assess the BA to overcome child growth disorders accurately. The proposed methodology undergoes three major stages: pre-processing, ROI detection, and BA detection. In the pre-processing stage, contrast-limited fuzzy adaptive histogram equalization (CLFAHE) is done to maintain the originality of the hand image. The size of the image is also increased by using data augmentation. After pre-processing, the required hand bone region with ROI detection approaches you only live once version 3 (YOLOv3). At the final stage, the BA is predicted using the residual network-152 (ResNet152) technique. Finally, the weight updation takes place in the ResNet152 model using harmony search (HS) optimization techniques. The dataset used in this research is collected from the RSNA bone age dataset. The performance measures such as mean absolute error (MAE), root mean square error (RMSE), and root mean squared percentage error (RMSPE) are analyzed and compared with other existing measures. In an experimental scenario, the MAE of 2.59, RMSE of 2.97, and RMSPE of 0.35 for the male gender is obtained.

Evaluation of metaheuristic optimization algorithms applied to path planning

The development of autonomous ground vehicles is a topic widely discussed by the international scientific community. Path planning for these robots is an essential element to achieving a satisfactory fulfillment of missions without human intervention. This work adopts and improves the metaheuristic optimization methods harmony search and ant colony optimization, developing strategies based on the enhanced harmony search and improved ant colony optimization to achieve short, collision-free paths for robot movement. A description of the original methods and improvement procedures is presented, and their performance in path planning is compared through simulation. Theoretical results are supported by simulated experiments, which highlight the situations in which each metaheuristic algorithm is preferable and the benefits they bring to the path planning strategy.

Enhancing Ovarian Cancer Detection Using Self-Organizing Maps and Improved Recurrent Neural Networks with Extended Harmony Search Optimization

Background: Ovarian cancer (OC) is a highly fatal malignancy of the female reproductive system, characterized by its high mortality rate and the challenges associated with clinical research due to the disease's complexity and late-stage diagnosis. Advances in technology, such as the Internet of Medical Things (IoMT), offer new opportunities for improving OC detection and diagnosis. Objective: This study aimed to develop and evaluate a novel method for OC detection using IoMT data, leveraging Self-Organizing Maps (SOM) and Improved Recurrent Neural Networks (IRNN) enhanced with the Extended Harmony Search Optimization (EHSO) algorithm to improve feature selection and classification accuracy. Methods: The study utilized OC data from the IoMT and applied SOM for feature selection, which helps in managing and classifying large datasets. SOM was employed to improve data representation and address challenges in labeling and classifying data. The IRNN model, optimized using the EHSO algorithm, was developed to enhance classification performance. The model was tested using a dataset from Kaggle comprising 179 benign and 172 malignant OC images with 50 attributes. Results: The IRNN model with EHSO demonstrated superior performance compared to other methods. In the training dataset, it achieved an accuracy of 95.72% and a Root Mean Square Error (RMSE) of 4.8%. For the testing dataset, the model maintained a high accuracy of 90.4% and an RMSE of 6.8%. The IRNN with EHSO outperformed alternative methods in terms of specificity and sensitivity, while the Genetic Algorithm (GA) showed the lowest performance across all metrics. Conclusion: The proposed method using SOM and IRNN with EHSO significantly improves the detection of ovarian cancer by optimizing feature selection and classification accuracy. This approach offers a promising advancement in utilizing IoMT data for early and accurate OC diagnosis, potentially enhancing patient outcomes through more effective detection and treatment strategies.

Striking the perfect balance: Multi-objective optimization for minimizing deployment cost and maximizing coverage with Harmony Search

In the Internet of Things (IoT) era, wireless sensor networks play a critical role in communication systems. One of the most crucial problems in wireless sensor networks is the sensor deployment problem, which attempts to provide a strategy to place the sensors within the surveillance area so that two fundamental criteria of wireless sensor networks, coverage and connectivity, are guaranteed. In this paper, we look to solve the multi-objective deployment problem so that area coverage is maximized and the number of nodes used is minimized. Since Harmony Search is a simple yet suitable algorithm for our work, we propose Harmony Search algorithm along with various enhancement proposals, including heuristic initialization, random sampling of sensor types, weighted fitness evaluation, and using different components in the fitness function, to provide a solution to the problem of sensor deployment in a heterogeneous wireless sensor network where sensors have different sensing ranges. On top of that, the probabilistic sensing model is used to reflect how the sensors work realistically. We also provide the extension of our solution to 3D areas and propose a realistic 3D dataset to evaluate it. The simulation results show that the proposed algorithms solve the area coverage problem more efficiently than previous algorithms. Our best proposal demonstrates significant improvements in coverage ratio by 10.20% and cost saving by 27.65% compared to the best baseline in a large-scale evaluation.

Image Multi-threshold Segmentation Based on an Ameliorated Harmony Search Optimization Algorithm

Image segmentation is the basis and premise of image processing, though traditional multi-threshold image segmentation methods are simple and effective, they suffer the problems of low accuracy and slow convergence rate. For that reason, this paper introduces the multi-threshold image segmentation scheme by combining the harmony search (HS) optimization algorithm and the maximum between-class variance (Otsu) to solve them. Firstly, to further improve the performance of the basic HS, an ameliorated harmony search (AHS) is put forward by modifying the generation method of the new harmony improvisation and introducing a convergence coefficient. Secondly, the AHS algorithm, which takes the maximum between-class variance as its objective function, namely AHS-Otsu, is applied to image multi-level threshold segmentation. Finally, six test images are selected to verify the multilevel segmentation performance of AHS-Otsu. Peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) are two commonly used metrics for evaluating the effectiveness of image segmentation, which are both used in this article. Comprehensive experimental results indicate that the AHS-Otsu does not only has fast segmentation processing speed, but also can obtain more accurate segmentation performance than others, which prove the effectiveness and potential of the AHS-Otsu algorithm in the field of image segmentation especially for the multi-threshold.

Hybrid firefly algorithm–neural network for battery remaining useful life estimation

Abstract Accurately estimating the remaining useful life (RUL) of batteries is crucial for optimizing maintenance, preventing failures, and enhancing reliability, thereby saving costs and resources. This study introduces a hybrid approach for estimating the RUL of a battery based on the firefly algorithm–neural network (FA–NN) model, in which the FA is employed as an optimizer to fine-tune the network weights and hidden layer biases in the NN. The performance of the FA–NN is comprehensively compared against two hybrid models, namely the harmony search algorithm (HSA)–NN and cultural algorithm (CA)–NN, as well as a single model, namely the autoregressive integrated moving average (ARIMA). The comparative analysis is based mean absolute error (MAE) and root mean squared error (RMSE). Findings reveal that the FA–NN outperforms the HSA–NN, CA–NN, and ARIMA in both employed metrics, demonstrating superior predictive capabilities for estimating the RUL of a battery. Specifically, the FA–NN achieved a MAE of 2.5371 and a RMSE of 2.9488 compared with the HSA–NN with a MAE of 22.0583 and RMSE of 34.5154, the CA–NN with a MAE of 9.1189 and RMSE of 22.4646, and the ARIMA with a MAE of 494.6275 and RMSE of 584.3098. Additionally, the FA–NN exhibits significantly smaller maximum errors at 34.3737 compared with the HSA–NN at 490.3125, the CA–NN at 827.0163, and the ARIMA at 1.16e + 03, further emphasizing its robust performance in minimizing prediction inaccuracies. This study offers important insights into battery health management, showing that the proposed method is a promising solution for precise RUL predictions.

A Decomposition Approach for Sequencing Mixed-Model Two-Sided Assembly Line with Stochastic Processing Time

This study tackles the challenge of optimizing mixed-model two-sided assembly lines, where task processing times are uncertain. The objective is to reduce the expected cycle time the average time to complete one product across the assembly line. Given the complexity of assessing objectives amidst stochastic conditions, we formulate the problem as a simulation optimization problem. We introduce a strategic decomposition method that breaks down the core problem into two discrete sub-tasks: allocating tasks to respective work-stations, and determining the sequence of tasks at each station. The decomposition framework systematically partitions the solution space, though it does not ensure a global optimum, it can efficiently guide the search towards a high-quality near-optimal solution with a practical time frame. Based on this framework, we develop a novel simulation-optimization algorithm, termed the Decomposition Approach with Harmony Search (DAHS), which incorporates a harmony search heuristic to effectively navigate the partitioned solution space. Additionally, we implement two innovative strategies to improve the search and simulation procedures. Numerical experiments reveal that our DAHS algorithm outperforms benchmark algorithms in terms of solution quality and computational efficiency.

Tri-objective lot-streaming scheduling optimization for hybrid flow shops with uncertainties in machine breakdowns and job arrivals using an enhanced genetic programming hyper-heuristic

Lot-streaming scheduling has been widely recognized as a means to improve shop productivity, but there is few research on lot-streaming scheduling problems under dynamic disturbances. To fill the gap, lot-streaming scheduling optimization approach for hybrid flow shops with uncertainties in machine breakdowns and job arrivals is proposed. A mathematical model is formulated with objectives of minimizing maximum tardiness, total idle energy consumption of the machine, and maximum makespan. Since the Genetic Programming Hyper Heuristic algorithm has better results in solving dynamic scheduling problems, a Collaborative Harmony Search-based Genetic Programming Hyper Heuristic (CHS-GPHH) is presented to solve the dynamic lot-streaming hybrid flow shop scheduling problem (DLS-HFSSP) with the two dynamic events occurring simultaneously. In the improved algorithm, a neighborhood structure based on harmony search is developed for lot splitting. To verify the effectiveness of the proposed approach, the various comparative studies c are conducted on the lot-streaming dynamic hybrid flow shop scheduling. The results demonstrate the effectiveness of each improvement component of the CHS-GPHH, and verify that CHS-GPHH is an effective approach to deal with DLS-HFSSP with the in all the scenarios.

Optimizing mobility resource allocation in multiple MaaS subscription frameworks: a group method of data handling-driven self-adaptive harmony search algorithm

Optimizing mobility resource allocation in multiple MaaS subscription frameworks: a group method of data handling-driven self-adaptive harmony search algorithm

Development and Sensitivity Analysis of an Improved Harmony Search Algorithm with a Multiple Memory Structure for Large-Scale Optimization Problems in Water Distribution Networks

The continuous supply of drinking water for human life is essential to ensure the sustainability of cities, society, and the environment. At a time when water scarcity is worsening due to climate change, the construction of an optimized water supply infrastructure is necessary. In this study, an improved version of the Harmony Search Algorithm (HSA), named the Maisonette-type Harmony Search Algorithm (MTHSA), was developed. Unlike the HSA, the MTHSA has a two-floor structure, which increases the optimizing efficiency by employing multiple explorations on the first floor and additional exploitations of excellent solutions. Parallel explorations enhance the ability in terms of exploration (global search), which is the tendency to uniformly explore the entire search space. Additional exploitations among excellent solutions also enhance the ability of local searches (effective exploitation), which is the intensive exploration of solutions that seem to have high possibilities. Following the development of the improved algorithm, it was applied to water distribution networks in order to verify its efficiency, and the numerical results were analyzed. Through the considered applications, the improved algorithm is shown to be highly efficient when applied to large-scale optimization problems with large numbers of decision variables, as shown in comparison with the considered optimizers.

Performance Analysis of Metaheuristic Algorithms on Benchmark Functions

The discipline of optimization can be used to maximize or minimize several problems. The use of metaheuristic algorithms is a strategy that often works well for global optimization. They are a type of stochastic algorithm that, via trial and error, finds workable solutions to difficult optimization problems in a reasonable amount of time, but they do not provide assurance that the answers are optimal. This paper aims to offer a comparative analysis of several metaheuristics in searching for the optimal solution. The selected metaheuristics are Artificial Bee Colony, Ant Lion Optimizer, Bat, Black Hole, Cuckoo Search, Cat Swarm Optimization, Dragonfly, Differential Evolution, Firefly, Genetic, Gravitational-Based Search, Grasshopper Optimization, Grey Wolf Optimizer, Harmony Search, Krill-Herd, Moth-Flame Optimizer, Particle Swarm Optimization, Sine Cosine, Shuffled Frog-Leaping, and Whale Optimization algorithms. For this evaluation, 18 benchmark test functions, categorized as unimodal, multimodal, and fixed-dimension multimodal are used to examine various properties, such as accuracy, escape from the local optimum, and convergence. As an indicator of how effectively these metaheuristics work, metrics like minimum, maximum, average, and standard deviation of fitness are provided. There are no optimization algorithms that are adequate for all problems, as the No Free Lunch theorem suggests, but the metaheuristics that are more effective than the others will be demonstrated. This study could be helpful for young researchers to identify the most prominent metaheuristics for achieving a better global optimum. Received: 8 June 2024 / Accepted: 25 July 2024 / Published: 29 July 2024Optimization, Metaheuristic algorithm, Benchmark function, Performance metric

Optimal design of fractional-order proportional integral derivative controllers for structural vibration suppression

In designing control systems, it is known that fractional-order proportional integral derivative (FOPID) controllers often provide greater flexibility than conventional proportional integral derivative (PID) controllers. This higher level of flexibility has proven to be extremely valuable for various applications such as vibration suppression in structural engineering. In this paper, we study the optimization of FOPID controllers using twelve well-established algorithms to minimize structural responses under seismic excitations. The algorithms include crystal structure algorithm (CryStAl), stochastic paint optimizer, particle swarm optimization, krill herd, harmony search, ant colony optimization, genetic algorithm, grey wolf optimizer, Harris hawks optimization, sparrow search algorithm, hippopotamus optimization algorithm, and duck swarm algorithm. In addition to highlighting the benefits of fractional calculus in structural control, this study provides a detailed analysis of FOPID controllers as well as a brief description of the algorithms used to optimize them. To evaluate the efficiency of the proposed techniques, two building models with different numbers of stories are examined. FOPID controllers are designed based on oustaloup’s approximation and the El Centro earthquake data. Using five well-known metrics, the performances of the developed methods are evaluated against five earthquake scenarios, including the recent earthquake in Turkey. A non-parametric (Friedman) test is also employed to compare the algorithms based on their corresponding vibration reduction. The findings of this analysis show that CryStAl consistently performs better than the other algorithms for both building models, thus resulting in superior vibration suppression.

Optimal adaptive coordination of overcurrent relays in power systems protection using a new hybrid metaheuristic algorithm

AbstractAdvent of distributed generation and progression towards an intelligent grid infrastructure within the domain of contemporary electrical power systems have created dynamic load profiles. Accompanying these developments, protective relays are faced with an evolving electrical load landscape and variable fault current conditions, resulting in disparate operational timings throughout the diurnal cycle. In light of these challenges, this paper delineates the formulation and simulation of a novel adaptive protection strategy for overcurrent relays, meticulously tailored to accommodate the fluctuations in electrical load. To construct a robust framework for this adaptive mechanism, a series of hypothetical fault current scenarios are meticulously crafted to activate the relays within the briefest time interval feasible. Further innovating within this sphere, this paper introduces a new hybrid algorithm, deftly amalgamating the strengths of three preeminent metaheuristic models: Improved Harmony Search, Particle Swarm Optimization, and Differential Evolution. Simulations and analyses substantiate the efficacy of the algorithm in optimizing the coordination among overcurrent relays aiming to uphold the overarching protective imperatives of the grid. For the IEEE 6‐bus system, the mean value of the objective function during 24 h in Monte Carlo is 292.6607 and very close to 272.0758 in the simulation of eight stochastic scenarios, which contributes to the validity of the approach in practical settings. Also, in the IEEE 30‐bus system, the results of the mean relay operation time set for the hours with the lowest and highest consumption load are 17.1297 and 14.8049 s, which reveals the increase in the operation speed of the relays.

Optimum identification of aquifer parameter zone structures using the SHuffled Ant Lion Optimization approach considering general form of the Voronoi tessellation

A new simulation–optimization approach is proposed for solving the inverse parameter structure identification problems in groundwater systems. In the simulation part of the proposed approach, the numerical groundwater flow process is simulated by using MODFLOW. Parameter structures of the aquifer system are identified by partitioning the flow domain into a finite number of zones employing the general form of the Voronoi tessellation (VT). This MODFLOW and VT-based simulation model is then integrated into an optimization model where the SHuffled Ant Lion Optimization approach (SHALO) is used. This work is the first application of SHALO by considering the general form of the VT zonation approach for solving the inverse groundwater parameter structure identification problems. The applicability of the proposed simulation–optimization approach is evaluated on a hypothetical aquifer model in the literature. This evaluation is conducted by solving the same problem using Ant Lion Optimization (ALO) and its improved version, the self-adaptive ALO (saALO) for the same conditions. Furthermore, the identified results are compared with those obtained using harmony search (HS) and hybrid genetic algorithm (hybrid GA) based solution approaches in the literature. The obtained results indicated that the proposed approach provided better identification results than ALO, saALO, HS, and hybrid GA in terms of different evaluation metrics.

Optimal coordination of overcurrent relays in microgrids using meta-heuristic algorithms NSGA-II and harmony search

The emergence of distributed generation from renewable energy sources has led to the adoption microgrids as an alternative energy solution. However, implementing microgrids presents challenges, particularly in coordinating relay protection, due to factors like distributed generation sources, bidirectional power flow, variable short-circuit levels, and changes in network behavior. Although overcurrent relays (OCR) are frequently utilized in microgrid protection, a more adaptable strategy is needed as grid architectures transition from radial to non-radial. This paper proposes a new method to optimize the coordination of OCRs in microgrids by adjusting parameters like time multiplier settings (TMS), plug settings (PS), and characteristic curve selection. The study utilizes meta-heuristic techniques such as the harmony search algorithm (HSA) and the non-dominated sorting genetic algorithm-II (NSAGA-II) for optimal coordination. Simulations on a microgrid and bus test system demonstrate the effectiveness of the proposed approach in enhancing protection indicators like sensitivity, speed, selectivity, and reliability in microgrid operations. The results also indicate that the computation time of HSA is less than NSGA-II, but with an increase in DGs capacity, there is a continuous tendency to reduce the relay operation time.

Improving Earth surface temperature forecasting through the optimization of deep learning hyper-parameters using Barnacles Mating Optimizer

Time series forecasting is crucial across various sectors, aiding stakeholders in making informed decisions, planning for the short and long term, managing risks, optimizing profits, and ensuring safety. One significant application of time series forecasting is predicting Earth surface temperatures, which is vital for civil and environmental sectors such as agriculture, energy, and meteorology. This study proposes a hybrid forecasting model for Earth surface temperature using Deep Learning (DL). To improve the DL model's performance, an optimization algorithm called Barnacles Mating Optimizer (BMO) is integrated to optimize both weights and biases. The forecasting model is trained on a global temperature dataset with seven inputs and compared with DL models optimized by Particle Swarm Optimization (PSO), Harmony Search Algorithm (HSA), and Ant Colony Optimization (ACO). Additionally, a comparison is made with the Autoregressive Moving Average (ARIMA) method. Evaluation using Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the coefficient of determination (R2) demonstrates the superior performance of DL optimized by BMO, showing minimal errors.

Invasive weed optimization based compact hybridized fractal antenna design for RF energy harvesting and multifunctional wireless applications

This paper describes the optimal design and analysis of compact multiband Hybrid Fractal Antenna using Invasive Weed Optimization (HFAIWO). The configured structure involves the fusion of Minkowski, Sierpinski carpet and Giuseppe Peano in a coherent manner. The two-iterative conglomerated fractal antenna is realized physically by considering FR4 epoxy material (dielectric constant, εr = 4.4 and mass density = 1,900 kg/m3). The volumetric dimensions of the fabricated prototype are 36 x 36 x 1.6 mm3. In the designing process, the geometrical descriptors, namely, feedline width ‘WF’ and ground plane dimension ‘LG’ are optimized specifically using Invasive Weed Optimization (IWO) and Harmony Search Algorithm (HSA) strategies. The optimal solution is searched by changing the descriptor values under a set of practical constraints. The examined values of ‘WF’ and ‘LG’ using IWO and HSA are 3 and 31 mm, and 2.6 and 28.7 mm, respectively. Comparative results reveal that IWO offers superior solution quality and convergence than HSA. Afterwards, experimentation of the Projected HFAIWO is done to justify the recommended fractal hybridization approach. Measurements reveal that for VSWR ≤ 2, the fabricated structure produces nine resonance points (1.84, 3.99, 5.15, 5.55, 6.30, 6.58, 8.00, 9.29, and 12.01 GHz) with appreciable gain values. At the respective resonance points, the −10 dB impedance bandwidth is 3.9 %, 3.1 %, 2.1 %, 2.2 %, 1.4 %, 1.2 %, 6.9 %, 1.2 %, and 12.23 %. The provided radiation patterns are arbitrary bidirectional/omnidirectional. By applying the above-said approaches, the radiator size is reduced by 54 %. Importantly, the constructed structure covers two important bands i.e. 1.84 GHz (GSM 1800 band, downlink) and 5.55 GHz (WLAN (Lower) 5.150–5.725 GHz) associated with energy harvesting applications. The practical outcomes suggest that the introduced prototype is a proficient candidate for energy harvesting systems, Satellite communication for downlink, Long range tracking, Battlefield surveillance, Digital broadcast satellite service, Weather Radar, and Maritime navigation radar.

A Novel Dung Beetle Optimization Approach for Automatic CMOS Analog Circuit Design

The main objective of the automated circuit sizing technique is to deal with the challenges of design tradeoffs in analog circuit design with improved accuracy and efficacy. Analog circuit design represents a multi-objective optimization challenge, where designers must properly balance various performance factors such as input and output impedance, power dissipation, area, unity-gain bandwidth, slew rate, and open-loop DC gain. Traditional design equations provide a sizing of differential amplifier MOS transistors, further optimization can be achieved through the application of meta-heuristic search techniques. Meta-heuristic search techniques can be used as local optimizers in a smaller search area to improve the optimization of design parameters. The differential amplifier circuit with current mirror load is optimized through the application of the Dung Beetle Optimization (DBO) algorithm. By using an evolutionary algorithm called DBO, all the required parameters were achieved with the least amount of transistor area and power dissipation when compared to the results of the Seeker Optimization Algorithm (SOA), Opposition based Harmony Search Algorithm (OHS), craziness-based particle swarm optimization (CRPSO), and Cuckoo Search (CS) algorithms.

A Novel Detection Method for High-Order SNP Epistatic Interactions Based on Explicit-Encoding-Based Multitasking Harmony Search.

To elucidate the genetic basis of complex diseases, it is crucial to discover the single-nucleotide polymorphisms (SNPs) contributing to disease susceptibility. This is particularly challenging for high-order SNP epistatic interactions (HEIs), which exhibit small individual effects but potentially large joint effects. These interactions are difficult to detect due to the vast search space, encompassing billions of possible combinations, and the computational complexity of evaluating them. This study proposes a novel explicit-encoding-based multitasking harmony search algorithm (MTHS-EE-DHEI) specifically designed to address this challenge. The algorithm operates in three stages. First, a harmony search algorithm is employed, utilizing four lightweight evaluation functions, such as Bayesian network and entropy, to efficiently explore potential SNP combinations related to disease status. Second, a G-test statistical method is applied to filter out insignificant SNP combinations. Finally, two machine learning-based methods, multifactor dimensionality reduction (MDR) as well as random forest (RF), are employed to validate the classification performance of the remaining significant SNP combinations. This research aims to demonstrate the effectiveness of MTHS-EE-DHEI in identifying HEIs compared to existing methods, potentially providing valuable insights into the genetic architecture of complex diseases. The performance of MTHS-EE-DHEI was evaluated on twenty simulated disease datasets and three real-world datasets encompassing age-related macular degeneration (AMD), rheumatoid arthritis (RA), and breast cancer (BC). The results demonstrably indicate that MTHS-EE-DHEI outperforms four state-of-the-art algorithms in terms of both detection power and computational efficiency. The source code is available at https://github.com/shouhengtuo/MTHS-EE-DHEI.git .