Standard Whale Optimization Algorithm Research Articles

A modified Manson-Halford model based on improved WOA for fatigue life prediction under multi-level loading

The Manson-Halford (M-H) nonlinear cumulative damage model is widely applied for fatigue life analysis problems under multi-level loading. In this model, the influence of loading sequence on the fatigue life can be better considerer, but the loading interaction effect is ignored. An improved whale optimization algorithm (IWOA) by integrating multiple strategies is proposed. The ability of global search and local exploitation is balanced and improved through nonlinear convergence factor, adaptive weighting factors and the Cauchy reverse learning strategies. In order to fully account for loading interaction effect, loading weighting factors are introduced to modify the M-H model, and the parameters are optimized through the global search properties of IWOA. The model is evaluated on multi-level loading fatigue experimental data from five metal materials and two aluminum alloy welded joints. The results suggest that the proposed IWOA has better optimization accuracy compared to the standard whale optimization algorithm (WOA). The proposed modified M-H model has better prediction performance compared to the four traditional cumulative damage models, which can be effectively applied to multi-level loading fatigue life analysis problems under actual working conditions. The proposed model is useful for the study of fatigue life evaluation methods.

A Hybrid Particle Whale Optimization Algorithm with application to workflow scheduling in cloud–fog environment

Workflow scheduling aims to optimize task allocation and execution in cloud–fog​ computing environments. Finding an optimal algorithm for workflow scheduling poses a significant challenge due to the complexity and variability of tasks and resources involved. Although meta-heuristic algorithms have been proposed to address these challenges, they often suffer from being trapped in local optima, failing to achieve the global optimal solution. Our work used a hybrid approach “Particle Whale Optimization Algorithm” (PWOA) to overcome the above-mentioned problem by combining Particle Swarm Optimization (PSO) and Whale Optimization Algorithm (WOA).PSO’s limitation in high-dimensional search spaces, characterized by slow convergence toward the global optimum, and the population-based WOA algorithm’s limited exploration of search spaces are overcome by the proposed algorithm PWOA. The proposed algorithm PWOA overcomes the limitations of PSO and WOA.The objective of the PWOA algorithm is to minimize the Total Execution Time (TET) and Total Execution Cost (TEC) associated with dependent tasks in a cloud–fog computing environment. To evaluate the performance of the PWOA algorithm, extensive simulations are conducted using test cases (30, 50, 100 and 1000) from five different scientific workflows: Cybershake, Epigenomics, Inspiral, Montage and Sipht. These workflows encompassed varying numbers of assigned tasks. The simulation results demonstrated that the proposed PWOA algorithm outperformed the standard PSO and WOA algorithms to improve TET and TEC across all the diverse workflows. This study also provides a comparative view of the effectiveness of the PWOA algorithm in enhancing workflow scheduling performance.

Modeling an Optimal Environmentally Friendly Energy-Saving Flexible Workshop

From the perspective of energy efficiency and environmental sustainability, the scheduling problem in a flexible workshop with the utilization of automated guided vehicles (AGVs) was investigated for material transportation. Addressing the dual-constrained integrated scheduling challenge involving machining machines and AGVs, a scheduling optimization model was established with makespan, workshop energy consumption, and processing quality as the optimization objectives. To effectively solve this model, an enhanced whale optimization algorithm (IWOA) was proposed. Specifically, nonlinear convergence factors, adaptive inertia weights, and improved helix positions were introduced into the standard whale optimization algorithm to update the model. Furthermore, a loss function was constructed based on fuzzy membership theory to obtain the optimal compromise solution of the multi-objective model. The research results indicate that: (1) The IWOA obtained the optimal solutions on benchmark instances MK01, MK02, MK04, MK07, and MK08; (2) The IWOA outperformed the WOA(1), WOA(2), WOA-LEDE, and NSGA-II algorithms in the two instances provided in this paper, demonstrating strong robustness of the model; (3) Although the multi-objective model constructed in this paper could not surpass the single-objective optimal solution in individual objectives, it achieved compensation in other objectives, effectively balancing the trade-offs among the makespan, workshop energy consumption, and processing quality of the three objectives. This research offers an effective practical approach to address green flexible workshop scheduling with AGV transportation.

Battery SOH estimation and RUL prediction framework based on variable forgetting factor online sequential extreme learning machine and particle filter

Battery life prediction is of great practical significance to ensure the safety and reliability of equipment. This paper proposes a new framework to realize battery state of health (SOH) estimation and remaining useful life (RUL) prediction. The variable forgetting factor online sequential extreme learning machine (VFOS-ELM) is used to estimate battery SOH, and particle filter (PF) algorithm used to predict battery RUL. To improve the estimation accuracy, a new nonlinear decline method, adaptive weight and Gaussian variation are used to improve the standard whale optimization algorithm (WOA) algorithm. And the improved IWOA algorithm is used for parameter optimization of the VFOS-ELM and PF algorithm. The extremely randomized trees (ERT) algorithm is used to obtain the features with high correlation with the available capacity to reduce the complexity of the model and improve the estimation accuracy. Compared with other methods, the proposed IWOA-VFOS-ELM algorithm has higher estimation performance and noise anti-interference ability. The MAE of APR-3 and APR-4 for SOH estimation are both within 0.12 %, RMSE are within 0.15 %, and IA are both higher than 99.9 %. Compared with PF algorithm, the RUL prediction accuracy obtained by IWOA-PF algorithm is improved by 7.143 %, 6.445 % and 15.094, respectively. In summary, the IWOA-PF algorithm proposed in this paper can be used to predict the battery RUL, and the prediction performance is better than the PF algorithm.

Variable-length deep convolutional neural networks by Internet Protocol Addresses Whale Optimization Algorithm for random and complex image classification

While Deep Convolutional Neural Network (DCNN) is one of the most reliable deep learning methods for image classification, choosing the optimal DCNN architecture for a particular application can be quite challenging. This study aims to examine the usage of the Whale Optimization Algorithm (WOA) to discover the optimal structure for DCNNs automatically. Three advancements based on standard WOA are proposed to accomplish the objective. First, a novel Internet Protocol Address (IPA)-based coding approach is suggested, which makes it easier to encode DCNN layers utilizing whale vectors. The construction of variable-length DCNNs is then suggested using an Enfeebled layer to include certain whale vector dimensions. The learning procedure concludes by subdividing large datasets into smaller portions which are then arbitrarily assessed. In order to evaluate the proposed model’s effectiveness, it is compared to the performance of twenty-three different classifiers, including the state-of-the-art algorithm, on nine standard image classification benchmark datasets. The experimental results indicate that the suggested technique outperforms other benchmarks in 81 of 95 assessments. This variable-length approach is the first of its kind, utilizing WOA to evolve the topologies of DCNNs automatically.

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 Multi-Period Vehicle Routing Problem for Emergency Perishable Materials under Uncertain Demand Based on an Improved Whale Optimization Algorithm

The distribution of emergency perishable materials after a disaster, such as an earthquake, is an essential part of emergency resource dispatching. However, the traditional single-period distribution model can hardly solve this problem because of incomplete demand information for emergency perishable materials in affected sites. Therefore, for such problems we firstly construct a multi-period vehicle path distribution optimization model with the dual objectives of minimizing the cost penalty of distribution delay and the total corruption during delivery, and minimizing the total amount of demand that is not met, by applying the interval boundary and most likely value weighting method to make uncertain demand clear. Then, we formulate the differential evolutionary whale optimization algorithm (DE-WOA) combing the differential evolutionary algorithm with the whale algorithm to solve the constructed model, which is an up-and-coming algorithm for solving this type of problem. Finally, to validate the feasibility and practicality of the proposed model and the novel algorithm, a comparison between the proposed model and the standard whale optimization algorithm is performed on a numerical instance. The result indicates the proposed model converges faster and the overall optimization effect is improved by 23%, which further verifies that the improved whale optimization algorithm has better performance.

Reactive Power Optimization Using New Enhanced Whale Optimization Algorithm

The standard Whale Optimization Algorithm (WOA) involves exploitation and exploration operations which require to be balanced for improved performance. This paper suggests a new enhanced WOA to improve the convergence speed and enhance the global optimum by balancing exploitation and exploration processes. New stages have been suggested at the hunting stages of the WOA to increase the exploitation capability. The performance of the modified algorithm has been analyzed on few commonly used test functions and Reactive Power Optimization (RPO) problem. The numerical studies have shown that the proposed WOA variant has outperformed other compared optimization algorithms in terms of global optimum and convergence speed.

Energy-Aware Bag-of-Tasks Scheduling in the Cloud Computing System Using Hybrid Oppositional Differential Evolution-Enabled Whale Optimization Algorithm

Bag-of-Tasks (BoT) scheduling over cloud computing resources called Cloud Bag-of-Tasks Scheduling (CBS) problem, which is a well-known NP-hard optimization problem. Whale Optimization Algorithm (WOA) is an effective method for CBS problems, which still requires further improvement in exploration ability, solution diversity, convergence speed, and ensuring adequate exploration–exploitation tradeoff to produce superior scheduling solutions. In order to remove WOA limitations, a hybrid oppositional differential evolution-enabled WOA (called h-DEWOA) approach is introduced to tackle CBS problems to minimize workload makespan and energy consumption. The proposed h-DEWOA incorporates chaotic maps, opposition-based learning (OBL), differential evolution (DE), and a fitness-based balancing mechanism into the standard WOA method, resulting in enhanced exploration, faster convergence, and adequate exploration–exploitation tradeoff throughout the algorithm execution. Besides this, an efficient allocation heuristic is added to the h-DEWOA method to improve resource assignment. CEA-Curie and HPC2N real cloud workloads are used for performance evaluation of scheduling algorithms using the CloudSim simulator. Two series of experiments have been conducted for performance comparison: one with WOA-based heuristics and another with non-WOA-based metaheuristics. Experimental results of the first series of experiments reveal that the h-DEWOA approach results in makespan improvement in the range of 5.79–13.38% (for CEA-Curie workloads), 5.03–13.80% (for HPC2N workloads), and energy consumption in the range of 3.21–14.70% (for CEA-Curie workloads) and 10.84–19.30% (for HPC2N workloads) over well-known WOA-based metaheuristics. Similarly, h-DEWOA also resulted in significant performance in comparison with recent state-of-the-art non-WOA-based metaheuristics in the second series of experiments. Statistical tests and box plots also revealed the robustness of the proposed h-DEWOA algorithm.

A novel nonlinear time-varying sigmoid transfer function in binary whale optimization algorithm for descriptors selection in drug classification.

In computational chemistry, the high-dimensional molecular descriptors contribute to the curse of dimensionality issue. Binary whale optimization algorithm (BWOA) is a recently proposed metaheuristic optimization algorithm that has been efficiently applied in feature selection. The main contribution of this paper is a new version of the nonlinear time-varying Sigmoid transfer function to improve the exploitation and exploration activities in the standard whale optimization algorithm (WOA). A new BWOA algorithm, namely BWOA-3, is introduced to solve the descriptors selection problem, which becomes the second contribution. To validate BWOA-3 performance, a high-dimensional drug dataset is employed. The proficiency of the proposed BWOA-3 and the comparative optimization algorithms are measured based on convergence speed, the length of the selected feature subset, and classification performance (accuracy, specificity, sensitivity, and f-measure). In addition, statistical significance tests are also conducted using the Friedman test and Wilcoxon signed-rank test. The comparative optimization algorithms include two BWOA variants, binary bat algorithm (BBA), binary gray wolf algorithm (BGWOA), and binary manta-ray foraging algorithm (BMRFO). As the final contribution, from all experiments, this study has successfully revealed the superiority of BWOA-3 in solving the descriptors selection problem and improving the Amphetamine-type Stimulants (ATS) drug classification performance.

Experimental study on multi-robot 3D source localization in indoor environments with weak airflow

The purpose of this paper is to provide a new method for solving the problem of the 3D source localization in indoor environments with weak airflow by the experimental study on the multi-robot method. For this purpose, we developed a 3D MRO (mobile robot olfaction) system consisting of three mobile robots. The gas sensor carried with each robot has a moving range of 0.5 m to 1.5 m on the Z-axis. A total of 60 experiments were conducted to validate and compare the standard whale optimization algorithm (SWOA) and the standard particle swarm optimization (SPSO) methods in a 7.65 m×4.1 m experimental area with two source heights (0.75 m and 1.05 m). For two source heights, the success rate and localization step of the SPSO method are 56.7% (17/30) and 31.4 steps, respectively. In addition, the success rate and localization step of the SWOA method are 80% (24/30) and 32.9 steps, respectively. These results show that the SWOA method has strong application potential in indoor environments with weak airflow.

An image denoising method based on BP neural network optimized by improved whale optimization algorithm

As an important part of smart city construction, traffic image denoising has been studied widely. Image denoising technique can enhance the performance of segmentation and recognition model and improve the accuracy of segmentation and recognition results. However, due to the different types of noise and the degree of noise pollution, the traditional image denoising methods generally have some problems, such as blurred edges and details, loss of image information. This paper presents an image denoising method based on BP neural network optimized by improved whale optimization algorithm. Firstly, the nonlinear convergence factor and adaptive weight coefficient are introduced into the algorithm to improve the optimization ability and convergence characteristics of the standard whale optimization algorithm. Then, the improved whale optimization algorithm is used to optimize the initial weight and threshold value of BP neural network to overcome the dependence in the construction process, and shorten the training time of the neural network. Finally, the optimized BP neural network is applied to benchmark image denoising and traffic image denoising. The experimental results show that compared with the traditional denoising methods such as Median filtering, Neighborhood average filtering and Wiener filtering, the proposed method has better performance in peak signal-to-noise ratio.

Improved grey wolf algorithm for optimization problems

The grey wolf optimization (GWO) is a nature inspired and meta-heuristic algorithm, it has successfully solved many optimization problems and give better solution as compare to other algorithms. However, due to its poor exploration capability, it has imbalance relation between exploration and exploitation. Therefore, in this research work, the poor exploration part of GWO was improved through hybrid with whale optimization algorithm (WOA) exploration. The proposed grey wolf whale optimization algorithm (GWWOA) was evaluated on five unimodal and five multimodal benchmark functions. The results shows that GWWOA offered better exploration ability and able to solve the optimization problem and give better solution in search space. Additionally, GWWOA results were well balanced and gave the most optimal in search space as compare to the standard GWO and WOA algorithms.

Improved Whale Optimization Algorithm for Solving Constrained Optimization Problems

In view of the shortcomings of the whale optimization algorithm (WOA), such as slow convergence speed, low accuracy, and easy to fall into local optimum, an improved whale optimization algorithm (IWOA) is proposed. First, the standard WOA is improved from the three aspects of initial population, convergence factor, and mutation operation. At the same time, Gaussian mutation is introduced. Then the nonfixed penalty function method is used to transform the constrained problem into an unconstrained problem. Finally, 13 benchmark problems were used to test the feasibility and effectiveness of the proposed method. Numerical results show that the proposed IWOA has obvious advantages such as stronger global search ability, better stability, faster convergence speed, and higher convergence accuracy; it can be used to effectively solve complex constrained optimization problems.

Load balancing in cloud environs: Optimal task scheduling via hybrid algorithm

In cloud computing, a lot of challenges like the server failures, loss of confidentiality, improper workloads, etc. are still bounding the efficiency of cloud systems in real-world scenarios. For this reason, many research works are being performed to overcome the shortcoming of existing systems. Among them, load balancing seems to be the most critical issue that worsen the performance of the cloud sector, and hence there necessitates the optimal load balancing with optimal task scheduling. With the intention of accomplishing optimal load balancing by effectual task deployment, this paper plans to develop an advanced load balancing model with the assistance acquired from the metaheuristic algorithms. Usually, handling of tasks in cloud system is an NP-hard problem and moreover, nonpreemptive independent tasks are crucial in cloud computing. This paper goes with the introduction of a new optimal load balancing model by considering three major objectives: minimum makespan, priority, and load balancing, respectively. Moreover, a new single-objective function is also defined that incorporates all the three objectives mentioned above. Furthermore, the deployment of tasks must be optimal and for this a new hybrid optimization algorithm referred as Firefly Movement insisted WOA (FM-WOA) is introduced. This FM-WOA is the conceptual amalgamation of standard Whale Optimization Algorithm (WOA) and Firefly (FF) algorithm. Finally, the performances of the proposed FM-WOA model is compared over the conventional models with the intention of proving its efficiency in terms of makespan, task completion (priority), and degree of imbalance as well.

A novel Whale Optimization Algorithm integrated with Nelder–Mead simplex for multi-objective optimization problems

Recently, several meta-heuristics and evolutionary algorithms have been proposed for tackling optimization problems. Such methods tend to suffer from degraded performance when solving multi-objective optimization problems due to addressing the conflicting goals of finding accurate estimation of Pareto optimal solutions and increasing their distribution across all objectives. In this paper, the Whale Optimization Algorithm (WOA) is improved and extended to solve such multi-objective optimization problems with the purpose of alleviating these drawbacks. The improvements include: (1) modifying the distance control factor of the standard WOA to contain values generated dynamically instead of a fixed one, (2) the trade-off between moving toward the opposite of the best solution and its original values based on a certain probability to prevent stuck into local minima, and (3) accelerating the convergence and coverage using Nelder–Mead method and the Pareto Archived Evolution Strategy (PAES). The proposed algorithm is tested on three benchmark multi-objective test functions (DTLZ, CEC 2009, and GLT), including 25 test functions, to verify its effectiveness by comparing with nine robust multi-objective algorithms. The experiments demonstrate the superiority of the proposed algorithm compared to some of the existing multi-objective algorithms in the literature.

A Modified Whale Optimization Algorithm with Single-Dimensional Swimming for Global Optimization Problems

As a novel meta-heuristic algorithm, the Whale Optimization Algorithm (WOA) has well performance in solving optimization problems. However, WOA usually tends to trap in local optimal and it suffers slow convergence speed for large-scale and high-dimension optimization problems. A modified whale optimization algorithm with single-dimensional swimming (abbreviated as SWWOA) is proposed in order to overcome the shortcoming. First, tent map is applied to generate the initialize population for maximize search ability. Second, quasi-opposition learning is adopted after every iteration for further improving the search ability. Third, a novel nonlinearly control parameter factor that is based on logarithm function is presented in order to balance exploration and exploitation. Additionally, the last, single-dimensional swimming is proposed in order to replace the prey behaviour in standard WOA for tuning. The simulation experiments were conducted on 20 well-known benchmark functions. The results show that the proposed SWWOA has better performance in solution precision and higher convergence speed than the comparison methods.

Multi-Strategy Ensemble Whale Optimization Algorithm and Its Application to Analog Circuits Intelligent Fault Diagnosis

The whale optimization algorithm (WOA) is a new swarm intelligence (SI) optimization algorithm, which has the superiorities of fewer parameters and stronger searching ability. However, previous studies have indicated that there are shortages in maintaining diversity and avoiding local optimal solutions. This paper proposes a multi-strategy ensemble whale optimization algorithm (MSWOA) to alleviate these deficiencies. First, the chaotic initialization strategy is performed to enhance the quality of the initial population. Then, an improved random searching mechanism is designed to reduce blindness in the exploration phase and speed up the convergence. In addition, the original spiral updating position is modified by the Levy flight strategy, which leads to a better tradeoff between local and global search. Finally, an enhanced position revising mechanism is utilized to improve the exploration further. To testify the superiorities of the proposed MSWOA algorithm, a series of comparative experiments are carried out. On the one hand, the numerical optimization experimental results, which are conducted under nineteen widely used benchmark functions, indicate that the performance of MSWOA stands out compared with the standard WOA and six other well-designed SI algorithms. On the other hand, MSWOA is utilized to tune the parameters of the support vector machine (SVM), which is applied to the fault diagnosis of analog circuits. Experimental results confirm that the proposed method has higher diagnosis accuracy than other competitors. Therefore, the MSWOA is successfully applied as a novel and efficient optimization algorithm.

Refraction-learning-based whale optimization algorithm for high-dimensional problems and parameter estimation of PV model

Whale optimization algorithm (WOA) is a relatively new meta-heuristic optimization algorithm which mimics the hunting behavior of humpback whales. This paper presents a modified version of WOA, called RLWOA, for solving high-dimensional optimization problems. The proposed RLWOA adopts a modified conversion parameter update rule that relies on Logistic model to balance between diversity and convergence during the search process, and a new refraction-learning strategy based on the principle of refraction of light is proposed to help the population jump out of a local optimum. The experiments on a set of benchmark test functions with various features, i.e., 12 widely used benchmark functions with 100, 1000, and 10000 dimensions, two practical engineering design problems, and parameter estimation problem of photovoltaic model. The comparisons demonstrate that the proposed RLWOA shows better or at least competitive performance against the standard WOA, WOA variants and other state-of-the-art meta-heuristic algorithms for solving high-dimensional numerical optimization, practical engineering design optimization, and photovoltaic model parameter estimation problems.

A Novel Feature Selection Method Using Whale Optimization Algorithm and Genetic Operators for Intrusion Detection System in Wireless Mesh Network

Machine learning–based intrusion detection system (IDS) is an important requirement for securing data traffic in wireless mesh networks. The noisy and redundant features of network data tend to degrade the performance of the attack detection classifiers. Therefore , the selection of informative features plays a vital role in the enhancement to the IDS. In this paper, we propose a wrapper-based approach using the modified whale optimization algorithm (WOA). One drawback of WOA is that premature convergence results in a local optimal solution. To overcome this limitation, we proposed a method in which the genetic algorithm operators were combined with the WOA. The crossover operator was used to further improve the search space of whales, and the mutation operator helped to avoid being stuck in the local optimum. The proposed method selects the informative features in the network data, which helps to accurately detect intrusions. Using a support vector machine (SVM), we identified the types of intrusions based on the selected features. The performance of the improved method was analyzed by using the CICIDS2017 and ADFA-LD standard datasets. Our proposed method had better attack detection rate than the standard WOA and other evolutionary algorithms; it also had good accuracy and was suitable for IDS in the wireless mesh networks. The performance of the IDS was increased by selecting the informative features with the improved whale optimization algorithm. The attack detection ratio was higher than that of the standard WOA.