Traditional Optimization Algorithms Research Articles

Optimization of low-loss, high birefringence parameters of a hollow-core anti-resonant fiber with back-propagation neural network assisted hyperplane segmentation algorithm

In engineering, optimizing parameters often involves computationally expensive tasks, especially when dealing with multi-dimensional variables and multiple performance metrics. This falls under the category of multi-objective black-box optimization. To address this, we propose two optimization algorithms for low and medium-dimensional spaces, incorporating relaxation conditions for hyperplane segmentation. For the specific parameter optimization of HC-ARF, we employed a two-stage approach. It combines a BP neural network as a surrogate model with a hyperplane separation optimization algorithm. This method efficiently optimizes both confinement loss (CL) and birefringence, using a weighted sum approach to identify their Pareto sets. We validate the effectiveness and stability of the surrogate model by comparing it with traditional optimization algorithms. Exhaustive experiments confirm the superiority of this algorithm and the results show that our optimized structure achieves impressive performance metrics, including a loss of 0.8 dB/m, a birefringence of 2.2×10−4, and a critical bending radius of 0.5 cm under optimal parameters.

Intelligent Prediction and Application Research on Soft Rock Tunnel Deformation Based on the ICPO-LSTM Model

In tunnel construction, the prediction of the surrounding rock deformation is related to the construction safety and stability of the tunnel structure. In order to achieve an accurate prediction of the surrounding rock deformation in soft rock tunnel construction, a Long Short-Term Memory (LSTM) neural network is used to construct a prediction model of the vault settlement and the horizontal convergence of the upper conductor in soft rock tunnels. The crested porcupine optimisation (CPO) algorithm is used to realise the hyper-parameter optimisation of the LSTM model and to construct the framework of the calculation process of the CPO-LSTM model. Taking the soft rock section of the Baoshishan Tunnel as an example, the large deformation of the surrounding rock is measured and analysed in situ, and the monitoring data of arch settlement and superconducting level convergence are obtained, which are substituted into the CPO-LSTM model for calculation, and compared and analysed with traditional machine learning and optimisation algorithms. The results show that the CPO-LSTM model has an R2 of 0.9982, a MAPE of 0.8595% and an RMSE of 0.1922, which are the best among all the models. In order to further improve the optimisation capability of the CPO, some improvements were made to the CPO and an Improved Crested Porcupine Optimiser (ICPO) was proposed. The ICPO-LSTM prediction model was established, and the ZK6 + 834 section was selected as a research object for comparison and analysis with the CPO-LSTM model. The results of the error analysis show that the prediction accuracy of the improved ICPO-LSTM model has been further improved, and the prediction accuracy of the model meets the requirements of guiding construction.

A Data and Model-Driven Clutter Suppression Method for Airborne Bistatic Radar Based on Deep Unfolding

Space–time adaptive processing (STAP) based on sparse recovery achieves excellent clutter suppression and target detection performance, even with a limited number of available training samples. However, most of these methods face performance degradation due to grid mismatch, which impedes their application in bistatic clutter suppression. Some gridless methods, such as atomic norm minimization (ANM), can effectively address grid mismatch issues, yet they are sensitive to parameter settings and array errors. In this article, the authors propose a data and model-driven algorithm that unfolds the iterative process of atomic norm minimization into a deep network. This approach establishes a concrete and systematic link between iterative algorithms, extensively utilized in signal processing, and deep neural networks. This methodology not only addresses the challenges associated with parameter settings in traditional optimization algorithms, but also mitigates the lack of interpretability issues commonly found in deep neural networks. Moreover, due to more rational parameter settings, the proposed algorithm achieves effective clutter suppression with fewer iterations, thereby reducing computational time. Finally, extensive simulation experiments demonstrate the effectiveness of the proposed algorithm in clutter suppression for airborne bistatic radar.

A Data and Model-Driven Clutter Suppression Method for Airborne Bistatic Radar Based on Deep Unfolding

Space–time adaptive processing (STAP) based on sparse recovery achieves excellent clutter suppression and target detection performance, even with a limited number of available training samples. However, most of these methods face performance degradation due to grid mismatch, which impedes their application in bistatic clutter suppression. Some gridless methods, such as atomic norm minimization (ANM), can effectively address grid mismatch issues, yet they are sensitive to parameter settings and array errors. In this article, the authors propose a data and model-driven algorithm that unfolds the iterative process of atomic norm minimization into a deep network. This approach establishes a concrete and systematic link between iterative algorithms, extensively utilized in signal processing, and deep neural networks. This methodology not only addresses the challenges associated with parameter settings in traditional optimization algorithms, but also mitigates the lack of interpretability issues commonly found in deep neural networks. Moreover, due to more rational parameter settings, the proposed algorithm achieves effective clutter suppression with fewer iterations, thereby reducing computational time. Finally, extensive simulation experiments demonstrate the effectiveness of the proposed algorithm in clutter suppression for airborne bistatic radar.

Path optimization of underwater vehicles in multi-obstacle environment based on energy constraint strategy

Purpose To solve the problem that the underwater vehicles is difficult to turn and exit in a small range in the face of complex marine environment such as concave and ring under the limitation of its limitation of its shape and maximum steering angle, this paper aims to propose an improved ant colony algorithm based on trap filling strategy and energy consumption constraint strategy. Design/methodology/approach Firstly, on the basis of searching the global path, the disturbed terrain was pre-filled in the complex marine environments. Based on the energy constraint strategy, the ant colony algorithm was improved to make the search path of the underwater vehicle meet the requirements of the lowest energy consumption and the shortest path in the complex obstacle environment. Findings The simulation results showed that the modified grid environment diagram effectively reduced the redundancy search and improved the optimization efficiency. Aiming at the problem of “the shortest distance is not the lowest energy consumption” in the traditional path optimization algorithm, the energy consumption level was reduced by 26.41% after increasing the energy consumption constraint, although the path length and the number of inflection points were slightly higher than the shortest path constraint, which was more conducive to the navigation of underwater vehicles. Originality/value The method proposed in this paper is not only suitable for trajectory planning of underwater robots but also suitable for trajectory planning of land robots.

Enhancing Reptile search algorithm with shifted distribution estimation strategy for coverage optimization in wireless sensor networks

The rapid development of the Internet of Things (IoT) has extensively promoted the development of Wireless Sensor Networks (WSNs), an essential technology for series displaying perception and data collected from the physical world. In densely distributed areas, sensor nodes are unevenly distributed, which leads to the network coverage build-up and the consequent efficiency and effectiveness of WSNs. To address this issue, this paper proposes a new method for WSN coverage optimization based on the Reptile Search Algorithm (RSA). In the past, the Reptile Search algorithm has been used to solve optimization problems, which means it can improve different processes. However, the RSA needs to track the trajectory of optimal individuals in each iteration, which will ignore non-optimal individuals' bioeconomic characteristics. Therefore, the paper introduces a distribution estimation strategy into the RSA framework, which can fully mine all the positional information hidden in the entire population. We selected several functions as optimization test benchmark functions to evaluate the feasibility of the proposed method. This paper compares the proposed improved RSA with the standard RSA and some traditional optimization algorithms. The result has been calculated through a series of experiments on network coverage optimization, and the change of parameters also determines the effect of the RSA in the optimization of network coverage. The simulated results of the three similar network coverage optimization experiments show that the improved RSA can be used efficiently within different scenarios.

A review of coordinated multi-robot exploration

Abstract A multiple robots system provides advantages over a single robot when it comes to exploring an unfamiliar area. Due to its applications in localization and mapping, search and rescue, etc. This technology has attracted a lot of study interest. The main challenge is properly distributing target points among several robots so that they can each investigate a separate section of the environment simultaneously and ensure the shortest possible total exploration time. However, more work still needs to be done to incorporate research issues in a real setting, such as how to eliminate duplicate exploration areas by giving robots multiple target locations or how to avoid unanticipated barriers in new situations. The allocation algorithms, motion planning techniques, and exploration strategies used in multi-robot collaboration (CME) are reviewed in this paper. Additionally, it provides an explanation of the methods research teams employ to optimize traditional whale optimization algorithm (WOA), how they enhance exploration performance and speed, and a comparative analysis of these methods. We also discussed a cooperative exploration method based on dynamic Voronoi partitioning. However, we also need some obstacle avoidance algorithms to help understand the gaps and issues that will need to be solved in the upcoming years, namely how to handle unexpected impediments in unfamiliar surroundings. Lastly, a summary of potential future lines of inquiry and uses is given.

An unrolled neural network for accelerated dynamic MRI based on second-order half-quadratic splitting model

The reconstruction of dynamic magnetic resonance images from incomplete k-space data has sparked significant research interest due to its potential to reduce scan time. However, traditional iterative optimization algorithms fail to faithfully reconstruct images at higher acceleration factors and incur long reconstruction time. Furthermore, end-to-end deep learning-based reconstruction algorithms suffer from large model parameters and lack robustness in the reconstruction results. Recently, unrolled deep learning models, have shown immense potential in algorithm stability and applicability flexibility. In this paper, we propose an unrolled deep learning network based on a second-order Half-Quadratic Splitting(HQS) algorithm, where the forward propagation process of this framework strictly follows the computational flow of the HQS algorithm. In particular, we propose a degradation-aware module by associating random sampling patterns with intermediate variables to guide the iterative process. We introduce the Information Fusion Transformer(IFT) to extract both local and non-local prior information from image sequences, thereby removing aliasing artifacts resulting from random undersampling. Finally, we impose low-rank constraints within the HQS algorithm to further enhance the reconstruction results. The experiments demonstrate that each component module of our proposed model contributes to the improvement of the reconstruction task. Our proposed method achieves comparably satisfying performance to the state-of-the-art methods and it exhibits excellent generalization capabilities across different sampling masks. At the low acceleration factor, there is a 0.7% enhancement in the PSNR. Furthermore, when the acceleration factor reached 8 and 12, the PSNR achieves an improvement of 3.4% and 5.8% respectively.

FISTA acceleration inspired network design for underwater image enhancement

Underwater image enhancement, especially in color restoration and detail reconstruction, remains a significant challenge. Current models focus on improving accuracy and learning efficiency through neural network design, often neglecting traditional optimization algorithms’ benefits. We propose FAIN-UIE, a novel approach for color and fine-texture recovery in underwater imagery. It leverages insights from the Fast Iterative Shrink-Threshold Algorithm (FISTA) to approximate image degradation, enhancing network fitting speed. FAIN-UIE integrates the residual degradation module (RDM) and momentum calculation module (MC) for gradient descent and momentum simulation, addressing feature fusion losses with the Feature Merge Block (FMB). By integrating multi-scale information and inter-stage pathways, our method effectively maps multi-stage image features, advancing color and fine-texture restoration. Experimental results validate its robust performance, positioning FAIN-UIE as a competitive solution for practical underwater imaging applications.

A new industrially magnetic capsule MedRobot integrated with smart motion controller

Capsule medical robots with unique application advantages have broad prospects for gastrointestinal detection, targeted drug delivery, medical assistance, and other fields. However, due to the complexity of the gastrointestinal environment and the limitations of the space magnetic field, robust motion control of capsule robots is still a challenge. Using a permanent magnet (NdFeB) as a space magnetic source, a capsule robot manipulation instrument with an integrated motion intelligent control approach is proposed in this work. First of all, a steering fixture controlling a permanent magnet is designed, and a manipulation instrument capable of five degrees of motion freedom is built with low cost and high accuracy. Furthermore, an integrated motion control approach, consisting of a primary motion subsystem and an auxiliary motion subsystem, is presented, where the motion route of the capsule robot is planned. A parallel optimization strategy is adopted to improve the traditional Gray Wolf Optimization Algorithm, the improved version of which is utilized to tune the parameters of controllers. Finally, some experiments of the designed capsule robot are carried out in different planes and slopes, as well as simulated stomach and real pig stomach, respectively. The results show that the motion characteristics are continuous and stable, and the average position error is 4.2 mm, which meets the application requirements.

Research on a Multi-Strategy Improved Sand Cat Swarm Optimization Algorithm for Three-Dimensional UAV Trajectory Path Planning

In response to the issues of premature convergence, lack of population diversity, and poor convergence accuracy in the traditional Sand Cat Swarm Optimization (SCSO) algorithm, a Multi-Strategy Improved SCSO (MISCSO) algorithm is proposed. Firstly, multiple population strategies are used to avoid premature convergence and falling into local optima traps. Secondly, a distribution estimation learning strategy is introduced to represent the relationships between individuals, using probability models to improve algorithm performance. Next, the diversity of candidate solutions in the elite pool is utilized to expand the search space and enhance the algorithm’s ability to avoid local solutions. Lastly, a Cauchy disturbance strategy is adopted to accelerate the convergence speed of the algorithm, thereby improving the search efficiency and convergence accuracy. The experimental results of CEC2017 tests show that the improved algorithm balances convergence speed and global search capabilities effectively. Finally, the algorithm is applied to actual drone path planning and compared with six other intelligent algorithms, demonstrating the practicality and effectiveness of the improved algorithm.

Multi-scene application of intelligent inspection robot based on computer vision in power plant

As industries develop, the automation and intelligence level of power plants is constantly improving, and the application of patrol robots is also increasingly widespread. This research combines computer vision technology and particle swarm optimization algorithm to build an obstacle recognition model and obstacle avoidance model of an intelligent patrol robot in a power plant respectively. Firstly, the traditional convolutional recurrent neural network is optimized, and the obstacle recognition model of an intelligent patrol robot is built by combining the connection timing classification algorithm. Then, the artificial potential field method optimizes the traditional particle swarm optimization algorithm, and an obstacle avoidance model of an intelligent patrol robot is built. The performance of the two models was tested, and it was found that the highest precision, recall, and F1 values of the identification model were 0.978, 0.974, and 0.975. The highest precision, recall, and F1 values of the obstacle avoidance model were 0.97, 0.96, and 0.96 respectively. The two optimization models designed in this research have better performance. In conclusion, the two models in this study are superior to the traditional methods in recognition effect and obstacle avoidance efficiency, providing an effective technical scheme for intelligent patrol inspection of power plants.

Assessing Residential Building Energy Efficiency Using Evolutionary Dendritic Neural Regression

Assessing building energy consumption is of paramount significance in sustainability and energy efficiency (EE) studies. The development of an accurate EE prediction model is pivotal for optimizing energy resources and facilitating effective building planning. Traditional physical modeling approaches are encumbered by high complexity and protracted modeling cycles. In this paper, we introduce a novel evolutionary dendritic neural regression (EDNR) model tailored to forecasting residential building EE. Acknowledging the vast landscape and complexity of the EDNR weight space, coupled with the inherent susceptibility of traditional optimization algorithms to local optima, we propose a complex network-guided strategy-based differential evolution algorithm for training the EDNR model. This strategy adeptly strikes a balance between exploration and exploitation during the search process, significantly enhancing the predictive and generalization capacities of EDNR. To our knowledge, this study represents the inaugural application of dendritic neural regression in real-world prediction scenarios. Extensive experimental findings demonstrate the efficacy of EDNR in accurately predicting building EE with commendable performance. Furthermore, the results of two nonparametric statistical tests affirm the validity and stability of EDNR. Consequently, our proposed methodology exhibits high potential and competitiveness in machine learning applications within the energy domain.

Long Short-Term Memory Parameter Optimization Based on Improved Sparrow Search Algorithm for Molten Iron Quality Prediction

Blast furnace (BF) ironmaking is a key process in iron and steel production. Because BF ironmaking is a dynamic time series process, it is more appropriate to use a recurrent neural network for modeling. The long short-term memory (LSTM) network is commonly used to model time series data. However, its model performance and generalization ability heavily depend on the parameter configuration. Therefore, it is necessary to study parameter optimization for the LSTM model. The sparrow search algorithm (SSA) holds advantages over traditional optimization algorithms in several aspects, such as no need for prior knowledge, fewer parameters, fast convergence, and high scalability. However, the algorithm still faces some challenges, such as the tendency to become trapped in the local optimum and the imbalance between global search ability and local search ability. Therefore, on the basis of SSA, this study examined the Levy flight strategy, sine search strategy, and step size factor adjustment strategy to improve it. This algorithm, improved by three strategies, is called the improved sparrow search algorithm (ISSA). Then, the ISSA-LSTM model was established. Furthermore, considering the limitations of SSA in dealing with multi-objective problems, the fast non-dominated sorting genetic algorithm (NSGAII) was introduced, and the ISSA-NSGAII model was established. Finally, experimental validation was performed using real blast furnace operation data, which demonstrated the proposed algorithm’s superiority in parameter optimization for the LSTM model and prediction for real industrial data.

Multi-Objective Topology Optimization of Conjugate Heat Transfer Using Level Sets and Anisotropic Mesh Adaptation

This study proposes a new computational framework for the multi-objective topology optimization of conjugate heat transfer systems using a continuous adjoint approach. It relies on a monolithic solver for the coupled steady-state Navier–Stokes and heat equations, which combines finite elements stabilized by the variational multi-scale method, level set representations of the fluid–solid interfaces and immersed modeling of heterogeneous materials (fluid–solid) to ensure that the proper amount of heat is exchanged to the ambient fluid by solid objects in arbitrary geometry. At each optimization iteration, anisotropic mesh adaptation is applied in near-wall regions automatically captured by the level set. This considerably cuts the computational effort associated with calling the finite element solver, in comparison to traditional topology optimization algorithms operating on isotropic grids with a comparable refinement level. Given that we operate within the constraint of a specified number of nodes in the mesh, this allows not only to improve the accuracy of interface representation and motion but also to retain the high fidelity of the numerical solutions at the grid points just adjacent to the interface. Finally, the remeshing and resolution steps both run within a highly parallel environment, which makes it possible for the proposed algorithm to tackle large-scale problems in three dimensions with several tens of millions of state degrees of freedom. The developed solver is validated first by minimizing dissipation in a flow splitter device, for which the method delivers relevant optimal designs over a wide range of volume constraints and flow rate distributions over the multiple outlet orifices but yields better accuracy compared to reference data from literature obtained using uniform meshes (in the sense that the layouts are more smooth, and the solutions are better resolved). The scheme is then applied to a two-dimensional heat transfer problem, using bi-objective cost functionals combining flow resistance and thermal recoverable power. A comprehensive parametric study reveals a complex arrangement of optimal solutions on the Pareto front, with multiple branches of symmetric and asymmetric designs, some of them previously unreported. Finally, the algorithmic developments are substantiated with several three-dimensional numerical examples tackled under fixed weights for heat transfer and flow resistance, for which we show that the optimal layouts computed at low Reynolds number, that are intrinsically relevant to a broad range of microfluidic application, can also serve as smooth solutions to high-Reynolds-number engineering problems of practical interest.

A Multi-Objective Optimization Problem Solving Method Based on Improved Golden Jackal Optimization Algorithm and Its Application

The traditional golden jackal optimization algorithm (GJO) has slow convergence speed, insufficient accuracy, and weakened optimization ability in the process of finding the optimal solution. At the same time, it is easy to fall into local extremes and other limitations. In this paper, a novel golden jackal optimization algorithm (SCMGJO) combining sine–cosine and Cauchy mutation is proposed. On one hand, tent mapping reverse learning is introduced in population initialization, and sine and cosine strategies are introduced in the update of prey positions, which enhances the global exploration ability of the algorithm. On the other hand, the introduction of Cauchy mutation for perturbation and update of the optimal solution effectively improves the algorithm’s ability to obtain the optimal solution. Through the optimization experiment of 23 benchmark test functions, the results show that the SCMGJO algorithm performs well in convergence speed and accuracy. In addition, the stretching/compression spring design problem, three-bar truss design problem, and unmanned aerial vehicle path planning problem are introduced for verification. The experimental results prove that the SCMGJO algorithm has superior performance compared with other intelligent optimization algorithms and verify its application ability in engineering applications.

Subnetwork prediction approach for aircraft schedule recovery

The combinatorial optimization techniques for the aircraft schedule recovery problem are too expensive to compute. However, we require a reasonable solution within 1–2 min for real-time application. The computational time of traditional optimization algorithms will drastically reduce if we can accurately predict the subnetwork affected by the disruption. In this study, we advocate the use of machine learning (ML) as a promising tool to predict the subnetwork. The optimal recovery schedules for a large number of disruptions are used for offline training, and subsequently, the trained ML model is employed to reduce the search space for new disruption cases substantially. To achieve this, we employ a unique feature space specifically designed to capture the essential characteristics of the problem. A notable contribution is constructing a novel feature space based on revised aircraft schedules designed to capture the essential characteristics of the problem. The recursive feature elimination technique is employed for optimal feature selection. Five machine learning classifiers: Logistic Regression, Random Forest, Extreme gradient boosting, Light gradient boosting, and Categorical Boosting are compared. The performance is evaluated on real data obtained from an airline company. Our study demonstrates that, with the subnetwork of aircraft predicted by the classifier, the computational time of the column generation approach is remarkably reduced without deteriorating the solution quality in all the disruption instances tested, with more than 98% of the instances being solved within 60 s. The results highlight the remarkable advantage of integrating ML in the pre-optimization phase.

Improved ant colony optimization algorithms for multi-objective investment decision model based on intelligent fuzzy clustering algorithm

With the continuous changes and development of financial markets, it has brought many difficulties to investment decision-making. For the multi-objective investment decision-making problem, the improved Ant colony optimization algorithms was used to improve the effectiveness and efficiency of the multi-objective investment decision-making. Therefore, based on intelligent Fuzzy clustering algorithm and Ant colony optimization algorithms, this paper studied a new multi-objective investment decision model, and proved the advantages of this method through comparative analysis of experiments. The experimental results showed that the improved Ant colony optimization algorithms has significantly reduced the system’s construction costs, operating costs and financial costs, all of which were controlled below 41%. Compared with the traditional Ant colony optimization algorithms, this method had lower values in policy risk, technical risk and market risk, and can effectively control risks. Meanwhile, the environmental, economic, and social benefits of this method were all above 58%, and the average absolute return rate and success rate in this experiment were 21.5450% and 69.4083%, respectively. Therefore, from the above point of view, the multi-objective investment decision model based on intelligent Fuzzy clustering algorithm and the improved Ant colony optimization algorithms can effectively help decision-makers to find the best investment decision-making scheme, and can improve the accuracy and stability of decision-making. This research can provide reference significance for other matters in the field of investment decision-making.

Quantum particle swarm optimization algorithm based on diversity migration strategy

Particle swarm optimization algorithm has been successfully applied to solve practical optimization problems due to its simplicity and efficiency. However, the traditional particle swarm optimization algorithm has inferior search performance in complicated high-dimensional optimization issues and is prone to falling into local optima. To address these problems, a new migration mechanism is introduced and a quantum particle swarm optimization method based on diversity migration is proposed. The strategy can capture different ranges of particles in the population, and the selection of migrating individuals depends not only on their fitness values but is also influenced by the positions within the population. The individual with the minimal average Hamming distance in the population can indicate the direction of iterative population optimization. After comparing the fitness values and the average Hamming distance between particles, the particles deviating from the central range of the population are replaced. The performance of the proposed algorithm is investigated under seven different sets of benchmark function optimization problems in the CEC2020 single-objective boundary-constrained optimization competition, and is compared with those of several other representative optimization algorithms. The quantum particle swarm optimization algorithm based on diversity migration strategy outperforms other typical optimization algorithms. Moreover, the proposed algorithm is convergent and stable.

Individual Updating Strategies-based Elephant Herding Optimization Algorithm for Effective Load Balancing in Cloud Environments

In this manuscript, an Individual Updating Strategies-based Elephant Herding Optimization Algorithm are proposed to facilitate the effective load balancing (LB) process in cloud computing. Primary goal of proposed Individual Updating Strategies-based Elephant Herding Optimization Algorithm focus on issuing the workloads pertaining to network links by the purpose of preventing over-utilization and under-utilization of the resources. Here, NIUS-EHOA-LB-CE is proposed to exploit the merits of traditional Elephant Herd Optimization algorithm to achieve superior results in all dimensions of cloud computing. In this NIUS-EHOA-LB-CE achieves the allocation of Virtual Machines for the incoming tasks of cloud, when the number of currently processing tasks of a specific VM is less than the cumulative number of tasks. Also, it attains potential load balancing process differences with the help of each individual virtual machine’s processing time and the mean processing time (MPT) incurred by complete virtual machine. Efficacy of the proposed technique activates the Cloudsim platform. Experimental results of the proposed method shows lower Mean Response time 11.6%, 18.4%, 20.34%and 28.1%, lower Mean Execution Time 78.2%, 65.4%, 40.32% and 52.6% compared with existing methods, like Improved Artificial Bee Colony utilizing Monarchy Butterfly Optimization approach for Load Balancing in Cloud Environments (IABC-MBOA-LB-CE), An improved Hybrid Fuzzy-Ant Colony Algorithm Applied to Load Balancing in Cloud Computing Environment (FACOA-LB-CE), Hybrid firefly and Improved Multi-Objective Particle Swarm Optimization for energy efficient LB in Cloud environments (FF-IMOPSO-LB-CE) and A hybrid gray wolf optimization and Particle Swarm Optimization algorithm for load balancing in cloud computing environment (GWO-PSO-LB-CE).