Whale Optimization Algorithm Algorithm Research Articles

A comparative analysis of meta-heuristic optimization algorithms for feature selection on ML-based classification of heart-related diseases.

This study aims to use a machine learning (ML)-based enhanced diagnosis and survival model to predict heart disease and survival in heart failure by combining the cuckoo search (CS), flower pollination algorithm (FPA), whale optimization algorithm (WOA), and Harris hawks optimization (HHO) algorithms, which are meta-heuristic feature selection algorithms. To achieve this, experiments are conducted on the Cleveland heart disease dataset and the heart failure dataset collected from the Faisalabad Institute of Cardiology published at UCI. CS, FPA, WOA, and HHO algorithms for feature selection are applied for different population sizes and are realized based on the best fitness values. For the original dataset of heart disease, the maximum prediction F-score of 88% is obtained using K-nearest neighbour (KNN) when compared to logistic regression (LR), support vector machine (SVM), Gaussian Naive Bayes (GNB), and random forest (RF). With the proposed approach, the heart disease prediction F-score of 99.72% is obtained using KNN for population sizes 60 with FPA by selecting eight features. For the original dataset of heart failure, the maximum prediction F-score of 70% is obtained using LR and RF compared to SVM, GNB, and KNN. With the proposed approach, the heart failure prediction F-score of 97.45% is obtained using KNN for population sizes 10 with HHO by selecting five features. Experimental findings show that the applied meta-heuristic algorithms with ML algorithms significantly improve prediction performances compared to performances obtained from the original datasets. The motivation of this paper is to select the most critical and informative feature subset through meta-heuristic algorithms to improve classification accuracy.

The Performance of Electronic Current Transformer Fault Diagnosis Model: Using an Improved Whale Optimization Algorithm and RBF Neural Network

With the widely application of electronic transformers in smart grids, transformer faults have become a pressing problem. However, reliable fault diagnosis of electronic current transformers (ECT) is still an open problem due to the complexity and diversity of fault types. In order to solve this problem, this paper proposes an ECT fault diagnosis model based on radial basis function neural network (RBFNN) and optimizes the model parameters and the network size of RBFNN simultaneously via an improved whale optimization algorithm (WOA) to improve the classification accuracy and robustness of RBFNN. Since the classical WOA is easy to fall into a locally optimal performance, a hybrid multi-strategies WOA algorithm (CASAWOA) is proposed for further improvement in optimization performance. Firstly, we introduced the tent chaotic map strategy to improve the population diversity of WOA. Secondly, we introduced nonlinear convergence factor and adaptive inertia weight to enhance the exploitation ability of the WOA. Finally, on the premise of ensuring the convergence speed of the algorithm, we modified the simulated annealing mechanism in order to prevent premature convergence. The benchmark function tests show that the CASAWOA outperforms other state-of-the-art WOA algorithms in terms of convergence speed and exploration ability. Furthermore, to validate the performance of ECT fault diagnosis model based on CASAWOA-RBFNN, a comprehensive analysis of eight fault diagnosis methods is conducted based on the ECT fault samples collected from the detection circuit. The experimental results show that the CASAWOA-RBFNN achieves an accuracy of 97.77% in ECT fault diagnosis, which is 9.8% better than WOA-RBF and which shows promising engineering practicality.

Energy-Efficient Bi-Objective Optimization Based on the Moth–Flame Algorithm for Cluster Head Selection in a Wireless Sensor Network

Designing an efficient wireless sensor network (WSN) system is considered a challenging problem due to the limited energy supply per sensor node. In this paper, the performance of several bi-objective optimization algorithms in providing energy-efficient clustering solutions that can extend the lifetime of sensor nodes were investigated. Specifically, we considered the use of the Moth–Flame Optimization (MFO) algorithm and the Salp Swarm Algorithm (SSA), as well as the Whale Optimization Algorithm (WOA), in providing efficient cluster-head selection decisions. Compared to a reference scheme using the Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol, the simulation results showed that integrating the MFO, SSA or WOA algorithms into WSN clustering protocols could significantly extend the WSN lifetime, which improved the nodes’ residual energy, the number of alive nodes, the fitness function and the network throughput. The results also revealed that the MFO algorithm outperformed the other algorithms in terms of energy efficiency.

Improved Whale Optimization with Local-Search Method for燜eature燬election

Various feature selection algorithms are usually employed to improve classification models’ overall performance. Optimization algorithms typically accompany such algorithms to select the optimal set of features. Among the most currently attractive trends within optimization algorithms are hybrid metaheuristics. The present paper presents two Stages of Local Search models for feature selection based on WOA (Whale Optimization Algorithm) and Great Deluge (GD). GD Algorithm is integrated with the WOA algorithm to improve exploitation by identifying the most promising regions during the search. Another version is employed using the best solution found by the WOA algorithm and exploited by the GD algorithm. In addition, disruptive selection (DS) is employed to select the solutions from the population for local search. DS is chosen to maintain the diversity of the population via enhancing low and high-quality solutions. Fifteen (15) standard benchmark datasets provided by the University of California Irvine (UCI) repository were used in evaluating the proposed approaches’ performance. Next, a comparison was made with four population-based algorithms as wrapper feature selection methods from the literature. The proposed techniques have proved their efficiency in enhancing classification accuracy compared to other wrapper methods. Hence, the WOA can search effectively in the feature space and choose the most relevant attributes for classification tasks.

A Whale Optimization Algorithm with Distributed Collaboration and Reverse Learning Ability

Due to the development of digital transformation, intelligent algorithms are getting more and more attention. The whale optimization algorithm (WOA) is one of swarm intelligence optimization algorithms and is widely used to solve practical engineering optimization problems. However, with the increased dimensions, higher requirements are put forward for algorithm performance. The double population whale optimization algorithm with distributed collaboration and reverse learning ability (DCRWOA) is proposed to solve the slow convergence speed and unstable search accuracy of the WOA algorithm in optimization problems. In the DCRWOA algorithm, the novel double population search strategy is constructed. Meanwhile, the reverse learning strategy is adopted in the population search process to help individuals quickly jump out of the non-ideal search area. Numerical experiments are carried out using standard test functions with different dimensions (10, 50, 100, 200). The optimization case of shield construction parameters is also used to test the practical application performance of the proposed algorithm. The results show that the DCRWOA algorithm has higher optimization accuracy and stability, and the convergence speed is significantly improved. Therefore, the proposed DCRWOA algorithm provides a better method for solving practical optimization problems.

An Improved Whale Optimization Algorithm for Web Service Composition

In the current circumstance, the Web Service Composition (WSC) was introduced to address complex user needs concerning the Quality of Services (QoS). In the WSC problem, the user needs are divided into a set of tasks. The corresponding web services are retrieved from the web services discovery according to the functionality of each task, and have different non-functional constraints, such as QoS. The WSC problem is a multi-objective optimization problem and is classified as an NP-hard problem. The whale optimization algorithm (WOA) is proven to solve complex multi-objective optimization problems, and it has the advantage of easy implementation with few control parameters. In this work, we contribute to improving the WOA algorithm, where different strategies are introduced to enhance its performance and address its shortcomings, namely its slow convergence speed, which produces low solution accuracy for the WSC problem. The proposed algorithm is named Improved Whale Optimization Algorithm (IWOA) and has three different strategies to enhance the performance of the WOA. Firstly, the Sine chaos theory is proposed to initiate the WOA’s population and enhance the initialization diversity. Secondly, a Lévy flight mechanism is proposed to enhance the exploitation and exploration of WOA by maintaining the whales’ diversity. Further, a neighborhood search mechanism is introduced to address the trade-off between exploration and exploitation searching mechanisms. Different experiments are conducted with datasets on 12 different scales (small, medium, and large), and the proposed algorithm is compared with standard WOA and five state-of-the-art swarm-based algorithms on 30 different independent runs. Furthermore, four evaluation criteria are used to validate the comparison: the average fitness value, best fitness values, standard deviation, and average execution time. The results show that the IWOA enhanced the WOA algorithm’s performance, where it got the better average and best fitness values with a low variation on all datasets. However, it ranked second regarding average execution time after the WOA, and sometimes third after the WOA and OABC, which is reasonable because of the proposed strategies.

A Novel Symmetrical Peak Fitting Method Based on Improved WOA Algorithm for the Analysis of Microchip Electrophoresis Signals

The problem of overlapping peaks has been a challenge in microchip electrophoresis (ME) signal analysis. However, traditional peak fitting algorithms have difficulty analyzing overlapping peaks due to the high dependence on the starting point. In this study, we propose a symmetrical peak fitting method named the tent-mapped whale optimization algorithm and Levenberg–Marquardt (TWOALM), which combines a whale optimization algorithm (WOA) improved by one of the most commonly used chaotic maps, the tent map and the Levenberg–Marquardt (LM) algorithm. Specifically, we first derive the fitted model for the overlapping peaks, showing that it is separable nonlinear least squares, significantly reducing the number of parameters to be optimized. Second, we integrate the tent map into the WOA, which improves the convergence speed of the peak fitting algorithm. Finally, we propose an efficient peak-fitting algorithm that combines the improved WOA and LM. The advantage of the proposed algorithm is that it is significantly faster than WOA and significantly more accurate than the LM algorithm. The results of fitting the synthetic peaks and ME signals showed that the combination of the chaotic map-based WOA algorithm and the LM algorithm can significantly improve the peak fitting performance and provide an effective solution for the analysis of overlapping peaks.

HWMWOA: A Hybrid WMA–WOA Algorithm with Adaptive Cauchy Mutation for Global Optimization and Data Classification

Combinatorial metaheuristic optimization algorithms have newly become a remarkable domain for handling real-world and engineering design optimization problems. In this paper, the Whale Optimization Algorithm (WOA) and the Woodpecker Mating Algorithm (WMA) are combined as HWMWOA. WOA is an effective algorithm with the advantage of global searching ability, where the control parameters are very less. But WOA is more probable to get trapped in the local optimum points and miss diversity of population, therefore suffering from premature convergence. The fundamental goal of the HWMWOA algorithm is to overcome the drawbacks of WOA. This betterment includes three basic mechanisms. First, a modified position update equation of WMA by efficient exploration ability is embedded into HWMWOA. Second, a new self-regulation Cauchy mutation operator is allocated to the proposed hybrid method. Finally, an arithmetic spiral movement with a novel search guide pattern is used in the suggested HWMWOA algorithm. The efficiency of the suggested algorithm is appraised over 48 test functions, and the optimal outcomes are compared with 15 most popular and newest metaheuristic optimization algorithms. Moreover, the HWMWOA algorithm is applied for simultaneously optimizing the parameters of SVM (Support Vector Machine) and feature weighting to handle the data classification problem on several real-world datasets from the UCI database. The outcomes prove the superiority of the suggested hybrid algorithm compared to both WOA and WMA. In addition, the results represent that the HWMWOA algorithm outperforms other efficient techniques impressively.

Hybrid Particle Swarm and Whale Optimization Algorithm for Multi-Visit and Multi-Period Dynamic Workforce Scheduling and Routing Problems

This paper focuses on the dynamic workforce scheduling and routing problem for the maintenance work of harvesters in a sugarcane harvesting operation. Technician teams categorized as mechanical, hydraulic, and electrical teams are assumed to have different skills at different levels to perform services. The jobs are skill-constrained and have time windows. During a working day, a repair request from a sugarcane harvester may arrive, and as time passes, the harvester’s position may shift to other sugarcane fields. We formulated this problem as a multi-visit and multi-period dynamic workforce scheduling and routing problem (MMDWSRP) and our study is the first to address the workforce scheduling and routing problem (WSRP). A mixed-integer programming formulation and a hybrid particle swarm and whale optimization algorithm (HPSWOA) were firstly developed to solve the problem, with the objective of minimizing the total cost, including technician labor cost, penalty for late service, overtime, travel, and subcontracting costs. The HPSWOA was developed for route planning and maintenance work for each mechanical harvester to be provided by technician teams. The proposed algorithm (HPSWOA) was validated against Lingo computational software using numerical experiments in respect of static problems. It was also tested against the current practice, the traditional whale optimization algorithm (WOA), and traditional particle swarm optimization (PSO) in respect of dynamic problems. The computational results show that the HPSWOA yielded a solution with significantly better quality. The HPSWO was also tested against the traditional genetic algorithm (GA), bat algorithm (BA), WOA, and PSO to solve the well-known CEC 2017 benchmark functions. The computational results show that the HPSWOA achieved more superior performance in most cases compared to the GA, BA, WOA, and PSO algorithms.

WOASCALF: A new hybrid whale optimization algorithm based on sine cosine algorithm and levy flight to solve global optimization problems

In recent years, researchers have been focused on solving optimization problems in order to determine the global optimum. Increasing the dimension of a problem increases its computational cost and complexity as well. In order to solve these types of problems, metaheuristic algorithms are used. The whale optimization algorithm (WOA) is one of the most well-known algorithms based on whale hunting behavior. In this paper, the WOA algorithm is combined with the Sine Cosine Algorithm (SCA), which is based on the principle of trigonometric sine-cosine. The WOA algorithm has superior performance in the exploration phase in contrast with the exploitation phase, whereas the SCA algorithm has weaknesses in the exploitation phase. The levy flight distribution has been used in the hybrid WOA and SCA algorithm to improve these deficiencies. This study introduced a novel hybrid algorithm named WOASCALF. In this algorithm, the search agents' position updates are based on a hybridization of the WOA, SCA, and levy flight. Each of these metaheuristic algorithms has reasonable performance, however, the Levy distribution caused small and large distance leaps in each phase of the algorithm. Thus, it is possible for the appropriate search agent to move in different directions of the search space. The performance of the WOASCALF has been evaluated by the 23 well-known benchmark functions and three real-world engineering problems. The result analysis demonstrates that the exploration ability of WOASCALF has strong superiority over other compared algorithms.

Implementation of Marin Predators Algorithm for optimizing the position of multiple Optical Network Units in Fiber Wireless Access Networks

• The problem of the optimal placement of multiple ONUs in FiWi networks is solved using- Marin predators algorithm (MPA) • A cost function is defined in terms of the average distance among ONUs and users. • The optimized locations are used in a developed simulation model to analyze the performance of FiWi network in terms of throughput and average propagation delay of FiWi access network. • The results obtained through the MPA are benchmarked with respect to the Harris Hawks Optimization (HHO), Whale Optimization algorithm (WOA), Moth-Flame optimization (MFO) and Greedy algorithms. Fiber-Wireless (FiWi) access network is a hybrid network that offers huge bandwidth and ubiquity to the users and is expected to play a dominant role in the emerging next generation communication networks. In this manuscript, a novel Marine Predators algorithm (MPA) is used to optimally place multiple Optical Network Units (ONUs) in FiWi access network. The optimized locations are used in a developed simulation model to assess the performance of FiWi network in terms of throughput and average propagation delay considering peer-to-peer communication. Also, the optimizer’s performance was evaluated in terms of fitness value, exploration, exploitation, computational complexity and nature of convergence curve. The MPA's efficiency is benchmarked with respect to a heuristic, Greedy algorithm, as well as existing efficient metaheuristics – Moth-Flame Optimization (MFO), Whale Optimization algorithm (WOA) and Harris-Hawks Optimization (HHO). It was found that MPA outperforms Greedy, MFO, WOA and HHO algorithms in each of the cases.

OPTIMAL PROTECTION COORDINATION OF RELAYS IN PRESENCE OF DISTRIBUTED GENERATION USING WHALE ALGORITHM

“This paperis proposes a novel nature-inspired meta-heuristic optimization algorithm, called Whale Optimization Algorithm (WOA), which mimics the social behavior of the humpback whales. The algorithm is inspired by the bubble-net hunting strategy”which is good comparing to others. WOA is tested with 29 mathematical optimization problems and structural design problems. Optimization results prove that the WOA algorithm is very competitive compared to the state the of art meta heuristic algorithms as well as conventional methods

Synthesis of Concentric Circular Antenna Array Using Whale Optimization Algorithm

Through the ages the importance of the swarm intelligence-based algorithm has gained popularity in the field of optimization. The Whale Optimization Algorithm (WOA) is one such popular meta-heuristics nature inspired swarm intelligence-based algorithm which is well accepted for solving optimization problems, as it is simple and capable to obtain optimal results efficiently. In this paper, few benchmark functions along with radiation patterns of concentric circular antenna array are presented and their performance is optimized using WOA. Simulation results are shown by taking various benchmark functions, namely: Three hump & Six hump camel function, Ackley, Egg Crate Function, and Egg Holder Function. The capability of the WOA algorithm is also tested through pattern synthesis with respect to the thinned array as well as non-uniformly excited array for four diverse sets of CCAA geometries. When comparison is being done with respect to renowned and most popular optimization approaches like PSO, the WOA technique proves to be excellent in terms of maximum SLL suppression. Optimization results show the better capability of WOA in the field of optimization.

Short-Term Forecasting and Uncertainty Analysis of Photovoltaic Power Based on the FCM-WOA-BILSTM Model

Aiming to solve the problem that photovoltaic power generation is always accompanied by uncertainty and the short-term prediction accuracy of photovoltaic power (PV) is not high, this paper proposes a method for short-term photovoltaic power forecasting (PPF) and uncertainty analysis using the fuzzy-c-means (FCM), whale optimization algorithm (WOA), bi-directional long short-term memory (BILSTM), and no-parametric kernel density estimation (NPKDE). First, the principal component analysis (PCA) is used to reduce the dimensionality of the daily feature vector, and then the FCM is used to divide the weather into four categories: sunny, cloudy, rainy, and extreme weather. Second, the WOA algorithm is used to train the hyperparameters of BILSTM, and finally, the optimized hyperparameters were used to construct a WOA-BILSTM prediction model to train the four types of weather samples after FCM clustering. The NPKDE method was used to calculate the probability density distribution of PV prediction errors and confidence intervals for PPF. The RMSEs of the FCM-WOA-BILSTM model are 2.46%, 4.89%, and 1.14% for sunny, cloudy, and rainy weather types, respectively. The simulation results of the calculation example show that compared with the BP, LSTM, GRU, PSO-BILSTM, and FCM-PSO-BP models, the proposed FCM-WOA-BILSTM model has higher prediction accuracy under various weather types, which verifies the effectiveness of the method. Moreover, the NPKDE method can accurately describe the probability density distribution of forecast errors.

A heuristic whale optimization algorithm with niching strategy for global multi-dimensional engineering optimization

Whale optimization algorithm (WOA) has received increasing attention in engineering optimization owing to its high computation efficiency, whereas, it has exhibited the drawback of premature convergence in solving multi-dimensional engineering global optimization problems. In this research, a niching hybrid heuristic whale optimization algorithm (NHWOA) is proposed to enhance convergence speed and search coverage in solving global optimization problems. In the algorithm, the niching technique is introduced to promote the diversity of population and restrain premature convergence in search of a global best solution. A heuristic adjustment to the parameters of the hybrid WOA algorithm is made to promote the exploration potential of search agents in the evolution. A designed perturbation to all the search agents’ positions is executed to avoid their falling into a local optimum. Optimization to the CEC2014 benchmark functions as validation cases are conducted along with comparisons to both conventional intelligent optimization algorithms and other state-of-the-art modified WOAs. Results indicate the effectiveness and superiority of NHWOA in solving the problems. Five practical engineering problems for global optimization with multiply variables are introduced to validate the performance of the presented algorithm with good performance results in the global computations.

WOA (Whale Optimization Algorithm) Optimizes Elman Neural Network Model to Predict Porosity Value in Well Logging Curve

Porosity is a vital parameter in reservoir research. In the process of oil exploration, reservoir research is very important for oil and gas exploration. Because it is necessary to take cores for indoor test in order to accurately obtain the porosity value of cores, this process consumes significant manpower and material resources. Therefore, this paper introduces the method of machine learning to predict the porosity by using logging curves. This paper creatively develops a WOA (whale optimization algorithm) optimized Elman neural network model to predict porosity through logging parameters PE, DEN, M2R1, AC, GR, R25, R4 and CNL. Porosity measurement is constructed by taking cores for indoor experiments. It contains a total of 328 sample points. The data is divided into training set and test set. The logging parameters are used as the input parameters of the prediction model, and the porosity measured in the laboratory are used as the output parameter. In order to evaluate the performance of the model, RMSE, R2, MAE and VAF evaluation indexes are introduced to evaluate. This paper also introduces the non-optimized Elman neural network and BP neural network to compare with this optimization model. The research shows that the WOA algorithm optimizes the super parameters of the Elman neural network, so that the performance of the WOA–Elman model is better than the Elman neural network model and the BP neural network model.

(Retracted) Hybrid whale optimization algorithm-Levy flight approach for multilevel thresholding image segmentation

Determining the optimal threshold for multilevel image segmentation is a stimulating task. Image segmentation has many applications, such as content-based image retrieval, medical imaging, object detection, object recognition, machine vision, etc. In multilevel thresholding, multiple thresholds are used to segment complex images, and the images are segmented into multiple levels to extract meaningful information for further image analysis. Where threshold number is small, p-tile, Otsu, moment preserving, and entropy thresholding methods attain good accuracy. These classical thresholding methods are time-consuming, computation expensive, and unable to produce good segmentation accuracy with increased threshold numbers. To overcome these problems, the classical thresholding methods are utilized as objective functions with nature-inspired metaheuristic algorithms such as whale optimization algorithm (WOA), simplified swarm optimization (SSO), sine cosine algorithm (SCA), BAT algorithm, WOA-thresholding, and black widow optimization (BWO) to determine optimal multiple thresholds. Nature-inspired metaheuristic algorithms are widely used to search for an optimal solution for global optimization problems. WOA is widely used to find the optimal solution in search space. WOA suffers from entrapment into local optima due to premature convergence behavior. We introduce hybridization of WOA with Levy flight trajectory and named as hybrid whale optimization algorithm-Levy flight (HWOAL), which is utilized to find optimal multiple thresholds for multilevel image segmentation. Levy flight trajectory is utilized to increase diversity in the swarm population. The efficacy of HWOAL is tested on 23 benchmark optimization functions (F1 to F23) and compared with WOA, SSO, SCA, and BAT algorithms. Experiment arms that HWOAL is efficient and makes WOA faster, enhances the ability of exploitation and exploration phase, and can avoid getting stuck into local optima. The segmentation performance of the proposed HWOAL method has been compared with other algorithms, such as WOA, SSO, SCA, BAT, and other two recent segmentation algorithms, such as WOA-TH and BWO on several benchmark images (BSD 300). The experimental result is carried in 30 trials and analyzed based on objective fitness value, optimal multilevel threshold values, segmentation quality measures, such as mean square error, peak signal-to-noise ratio, structural similarity index, average difference, and computation time to compute optimal multilevel threshold values. The experiment conducted by the authors shows that the proposed HWOAL method is efficient, produces better fitness value, and segmentation metrics for multilevel image segmentation than other algorithms.

An Efficient and Robust Improved Whale Optimization Algorithm for Large Scale Global Optimization Problems

As an efficient meta-heuristic algorithm, the whale optimization algorithm (WOA) has been extensively applied to practical problems. However, WOA still has the drawbacks of converging slowly, and jumping out from extreme points especially for large scale optimization problems. To overcome these defects, a modified whale optimization algorithm integrated with a crisscross optimization algorithm (MWOA-CS) is proposed. In MWOA-CS, each dimension of the optimization problem updates its position by randomly performing improved WOA or crisscross optimization algorithm during the entire iterative process. The improved WOA adopts the new nonlinear convergence factor and nonlinear inertia weight to tune the ability of exploitation and exploration. To analyze the performance of MWOA-CS, a series of numerical experiments were performed on 30 test benchmark functions with dimension ranging from 300 to 1000. The experimental results revealed that the presented MWOA-CS provided better convergence speed and accuracy, and meanwhile, displayed a significantly more effective and robust performance than the original WOA and other state of the art meta-heuristic algorithms for solving large scale global optimization problems.

Modern Optimal Controllers for Hybrid Active Power Filter to Minimize Harmonic Distortion

Nowadays, AC distributed power networks are facing many challenges in guaranteeing and improving the required level of power quality indices in power networks with increasing nonlinear, time-variable and unbalanced loads. Power networks can benefit from avoiding and minimizing different AC problems, such as frequency fluctuation and Total Harmonic Distortions (THDs), by using power filters, such as Hybrid Active Power Filters (HAPFs). Therefore, attention towards responsible power quality indices, such as Total Harmonic Distortion (THD), Power Factor (P.F) and Harmonic Pollution (HP) has increased. THD and HP are important indices to show the level of power quality at the network. In this paper, modern optimization techniques have been employed to optimize HAPF parameters, and minimize HP, by using a nature-inspired optimization algorithm, namely, Whale Optimization Algorithm (WOA). The WOA algorithm is compared to the most competitive powerful metaheuristic optimization algorithms: Manta Ray Foraging Optimization (MRFO), Artificial Ecosystem-based Optimization (AEO) and Golden Ratio Optimization Method (GROM). In addition, the WOA, and the proposed modern optimization algorithms, are compared to the most competitive metaheuristic optimization algorithm for HAPF from the literature, called L-SHADE. The comparison results show that the WOA algorithm outperformed all other optimization algorithms, in terms of minimizing harmonic pollution, through optimizing parameters of HAPF; therefore, this paper aims to present the WOA as a powerful control model for HAPF.

A Cox Proportional-Hazards Model Based on an Improved Aquila Optimizer with Whale Optimization Algorithm Operators

Recently, a new optimizer, called the Aquila Optimizer (AO), was developed to solve different optimization problems. Although the AO has a significant performance in various problems, like other optimization algorithms, the AO suffers from certain limitations in its search mechanism, such as local optima stagnation and convergence speed. This is a general problem that faces almost all optimization problems, which can be solved by enhancing the search process of an optimizer using an assistant search tool, such as using hybridizing with another optimizer or applying other search techniques to boost the search capability of an optimizer. Following this concept to address this critical problem, in this paper, we present an alternative version of the AO to alleviate the shortcomings of the traditional one. The main idea of the improved AO (IAO) is to use the search strategy of the Whale Optimization Algorithm (WOA) to boost the search process of the AO. Thus, the IAO benefits from the advantages of the AO and WOA, and it avoids the limitations of the local search as well as losing solutions diversity through the search process. Moreover, we apply the developed IAO optimization algorithm as a feature selection technique using different benchmark functions. More so, it is tested with extensive experimental comparisons to the traditional AO and WOA algorithms, as well as several well-known optimizers used as feature selection techniques, like the particle swarm optimization (PSO), differential evaluation (DE), mouth flame optimizer (MFO), firefly algorithm, and genetic algorithm (GA). The outcomes confirmed that the using of the WOA operators has a significant impact on the AO performance. Thus the combined IAO obtained better results compared to other optimizers.