Local Optimal Solution Research Articles

Path Planning for Conformal Antenna Surface Detection Based on Improved Genetic Algorithm

The conformal antenna is a precision device installed on the wing of an aircraft, and its components are distributed on a curved surface. Quality detection is required after assembly. In solving the path planning problem for conformal antenna surface detection, the traditional genetic algorithm faces problems such as slow convergence and easily falling into a local optimal solution. To solve this problem, an improved genetic algorithm combining the historical optimal population (CHOP-IGA) is proposed. First, the algorithm uses the probability-based four-nearest-neighbor method to construct an initial population. Subsequently, the probabilities of the crossover and mutation operators are dynamically adjusted. Next, the algorithm applies the crossover and mutation operators to the population and performs mutation operations on each individual of the historical optimal population. Then, the fitness value is calculated and the next generation of individuals is selected from the parent, offspring, and historical optimal populations according to the elite selection strategy. Finally, the current best fitness is checked to determine whether updating the historical optimal population is necessary. When the termination condition is satisfied, the algorithm outputs the optimal result. Experiments showed that the algorithm satisfactorily solved the path planning problem for conformal antenna surface detection, with a 48.44% improvement in detection efficiency.

A Multi-Strategy Crazy Sparrow Search Algorithm for the Global Optimization Problem

A multi-strategy crazy sparrow search algorithm (LTMSSA) for logic-tent hybrid chaotic maps is given in the research to address the issues of poor population diversity, slow convergence, and easily falling into the local optimum of the sparrow search algorithm (SSA). Firstly, the LTMSSA employs an elite chaotic backward learning strategy and an improved discoverer-follower ratio factor to improve the population’s quality and diversity. Secondly, the LTMSSA updates the positions of discoverers and followers by the crazy operator and the Lévy flight strategy to expand the selection range of target following individuals. Finally, during the algorithm’s optimization search, the LTMSSA introduces the tent hybrid and Corsi variable perturbation strategies to improve the population’s ability to jump out of the local optimum. Different types and dimensions of test functions are used as performance benchmark functions to test the performance of the LTMSSA with SSA variants and other algorithms. The simulation results show that the LTMSSA can jump out of the optimal local solution, converge faster, and have higher accuracy. Its overall performance is better than the other seven algorithms, and the LTMSSA can find smaller optimal values than other algorithms in the welded beam and reducer designs. The results confirm that the LTMSSA is an effective aid for computationally complex practical tasks, provides high-quality solutions, and outperforms other algorithms.

Genetic based density peak possibilistic fuzzy c-means algorithms to cluster analysis- a case study on customer segmentation

Finding the target consumers for a business depends heavily on its market segmentation approach. Applying clustering analysis to consumer segmentation is one of the most common methods. However, most clustering algorithms can easily fall into the local optimum solution. Besides, it can be challenging to handle noise and outliers and determine the optimal parameters. The initial cluster centers can also affect the clustering result. Thus, this study proposes a clustering algorithm that first employs density peak clustering to obtain the initial cluster centers. Then, the proposed method integrates genetic algorithm (GA) with possibilistic fuzzy c-means (PFCM) algorithm, where GA is used to optimize the cluster centers and the parameters of the PFCM algorithm to overcome the problems above. Using eleven benchmark datasets, the computational results demonstrate that the proposed algorithm can provide better and more robust results in terms of accuracy, adjusted rand index (ARI), and normalized mutual information (NMI) compared to previous clustering algorithms. Additionally, the proposed algorithm is used to segment customers of a retail company in a dataset containing recency, frequency, and monetary (RFM) variables. The clustering result for customer segmentation is also very promising.

Multi-Parameter Auto-Tuning Algorithm for Mass Spectrometer Based on Improved Particle Swarm Optimization.

Quadrupole mass spectrometers (QMS) are widely used for clinical diagnosis and chemical analysis. To obtain the best experimental results, mass spectrometers must be calibrated to an ideal setting before use. However, tuning the current QMS is challenging. Traditional tuning techniques possess low automation levels and rely primarily on skilled engineers. Therefore, in this study, we propose an innovative auto-tuning algorithm for QMS based on the improved particle swarm optimization (PSO) algorithm to automatically find the optimal solution of QMS parameters and make the QMS reach the optimal state. The improved PSO algorithm is combined with simulated annealing, multiple inertia weights, dynamic boundaries, and other methods to prevent the traditional PSO algorithm from the issue of a local optimal solution and premature convergence. According to the characteristics of the mass spectrum peaks, a termination function is proposed to simplify the termination conditions of the PSO algorithm and further improve the automation level of the mass spectrometer. The results of auto-calibration testing of resolution and mass axis show that both resolution and mass axis calibration could effectively meet the requirements of mass spectrometry experiments. By the experiment of auto-optimization testing of lens and ion source parameters, these parameters were all in the vicinity of the optimal solution, which achieved the expected performance. Through numerous experiments, the reproducibility of the algorithm was established as meeting the auto-tuning function of the QMS. The proposed method can automatically tune the mass spectrometer from its non-optimal condition to the optimal one, which can effectively reduce the tuning difficulty of QMS.

Prediction of milling force based on identified milling force coefficients and tool runout parameters in time-frequency domain

Milling force is the key variable related to machining performance. Mechanistic models are commonly used to predict milling forces. However, the identification process of milling force coefficients and tool runout parameters in this model is prone to local optimal solutions. This paper develops a time–frequency domain identification method, and then the prediction of milling force is implemented on this basis. First, a milling force model considering the influence of tool runout is established, where the milling force coefficients and tool runout parameters are identified based on the time–frequency domain identification method. The simulation and experimental data are used to compare the time–frequency domain identification method with the time-domain and frequency-domain identification methods, respectively. Then, the variation of milling force coefficients and tool runout parameters with milling conditions is studied, based on which the linear interpolation method of coefficients and parameters is used to predict the milling force. Finally, the effectiveness of the milling force prediction is verified by experiments.

An improved fuzzy c-means-raindrop optimizer for brain magnetic resonance image segmentation

<p>The performance of healthcare systems, particularly regarding disease diagnosis and treatment planning, depends on the segmentation of medical images. Fuzzy c-means (FCM) is one of the most widely used clustering techniques for image segmentation due to its simplicity and effectiveness. FCM, on the other hand, has the disadvantages of being noise-sensitive, quickly settling on local optimal solutions, and being sensitive to initial values. This paper suggests a fuzzy c-means clustering improved with a nature-inspired raindrop optimizer for lesion extraction in brain magnetic resonance (MR) images to get around this constraint. In the preprocessing stage, the possible noises in a digital image, such as speckles, gaussian, etc., are eliminated by a hybrid filter—A combination of Gaussian, mean, and median filters. This paper presents a comparative analysis of FCM clustering and FCM-raindrop optimization (FCM-RO) approach. The algorithm performance is evaluated for images subjected to various possible noises that may affect an image during transmission and storage. The proposed FCM-RO approach is comparable to other methods now in use. The suggested system detects lesions with a partition coefficient of 0.9505 and a partition entropy of 0.0890. Brain MR images are analyzed using MATLAB software to find and extract malignancies. Image data retrieved from the public data source Kaggle are used to assess the system’s performance.</p>

An enhanced turbulent flow of water-based optimization for optimal power flow of power system integrated wind turbine and solar photovoltaic generators

This paper uses enhanced turbulent flow in water-based optimization (TFWO), specifically ETFWO, to achieve optimal power flow (OPF) in electrical networks that use both solar photovoltaic (PV) units and wind turbines (WTs). ETFWO is an enhanced TFWO that alters the TFWO structure through the promotion of communication and collaboration. Individuals in the population now interact with each other more often, which makes it possible to search more accurately in the search area while ignoring local optimal solutions. Probabilistic models and real-time data on wind speed and solar irradiance are used to predict the power output of WT and PV producers. The OPF and solution methods are evaluated using the IEEE 30-bus network. By comparing ETFWO to analogical other optimization techniques applied to the same groups of constraints, control variables, and system data, we can gauge the algorithm’s robustness and efficiency in solving OPF. It is shown in this paper that the proposed ETFWO algorithm can provide suitable solutions to OPF problems in electrical networks with integrated PV units and WTs in terms of energy generation costs, improved voltage profiles, emissions, and losses, compared to the traditional TFWO and other proposed algorithms in recent studies.

Improving the stability of phase retrieval algorithm in speckle autocorrelation imaging by Huber penalty sparsity constraint

One of the most widely used methods for reconstructing images through a scattering medium is the Hybrid Input Output (HIO) phase retrieval algorithm. However, the stability and noise robustness of the HIO method are poor, as they are affected by initial values and noise during the imaging process. This paper presents an optimized HIO phase retrieval algorithm that utilizes the Huber penalty as a sparsity constraint to effectively enhance the quality and stability of the reconstruction algorithm. The introduced constraint is designed to guide the iteration process away from local optimal solutions, ensuring superior recovery images even with random initial values. Additionally, an adaptive step size parameter is incorporated to control the iterations and convergence steps, resulting in stronger robustness against noise effects. Moreover, the error criterion for image restoration is defined as the sum of the Fourier transform amplitude of the gradient. Experimental results demonstrate that the proposed phase retrieval algorithm achieves superior quality in the recovered images, while significantly improving noise immunity and stability for randomly selected initial values.

A nonlinear African vulture optimization algorithm combining Henon chaotic mapping theory and reverse learning competition strategy

As a new intelligent optimization algorithm, the African vultures optimization algorithm (AVOA) has been widely used in various fields today. However, when solving complex multimodal problems, the AVOA still has some shortcomings, such as low searching accuracy, deficiency on the search capability and tendency to fall into local optimum. In order to alleviate the main shortcomings of the AVOA, a nonlinear African vulture optimization algorithm combining Henon chaotic mapping theory and reverse learning competition strategy (HWEAVOA) is proposed. Firstly, the Henon chaotic mapping theory and elite population strategy are proposed to improve the randomness and diversity of the vulture's initial population; Furthermore, the nonlinear adaptive incremental inertial weight factor is introduced in the location update phase to rationally balance the exploration and exploitation abilities, and avoid individual falling into a local optimum; The reverse learning competition strategy is designed to expand the discovery fields for the optimal solution and strengthen the ability to jump out of the local optimal solution. HWEAVOA and other advanced comparison algorithms are used to solve classical and CEC2022 test functions. Compared with other algorithms, the convergence curves of the HWEAVOA drop faster and the line bodies are smoother. These experimental results show the proposed HWEAVOA is ranked first in all test functions, which is superior to the comparison algorithms in convergence speed, optimization ability, and solution stability. Meanwhile, HWEAVOA has reached the general level in the algorithm complexity, and its overall performance is competitive in the swarm intelligence algorithms.

Max-Min Fairness Precoding for Physical Layer Security With Partial Channel Knowledge

We propose secure max-min fairness (MMF) precoding for a downlink multi-antenna system with multiple users and eavesdroppers. Since the problem is non-convex and non-smooth and partial channel knowledge is assumed, it is highly challenging to solve. To resolve the difficulties, we first reformulate the problem with conditional average rates, allowing to exploit the partial channel knowledge. Then, we derive the original problem as an approximate smoothing problem using a LogSumExp approach. We identify the first-order optimality condition and cast it to a generalized eigenvalue problem. Solving the problem via a power iteration offers the best local optimal solution. Simulations validate the proposed secure-MMF precoding method.

State of charge estimation of lithium-ion batteries using improved BP neural network and filtering techniques

The state of charge (SOC) is a critical parameter in the battery management system (BMS), and its accurate estimation is essential for ensuring the safety and reliability of batteries. This paper presents a lithium-ion battery SOC estimation method that combines an improved neural network with a filtering algorithm. Firstly, the backpropagation (BP) algorithm is chosen as the architecture of the neural network in the hybrid method due to its strong nonlinear approximation ability, and the particle swarm optimization (PSO) algorithm is used to optimize it to avoid falling into local optimal solutions. By combining the search ability of PSO with the learning ability of the BP neural network, the accuracy of the neural network model is improved. The proposed method integrates the PSO-BP model with the extended Kalman filter based on minimum error entropy (MEE-EKF). PSO-BP is utilized as the measurement equation for MEE-EKF, while the ampere-hour integration method is employed as the state equation to achieve closed-loop SOC estimation. Finally, experimental validation is conducted under four typical operating conditions and one random condition across a wide temperature range. The results demonstrate that the proposed method achieves high accuracy across all conditions compared with the results of other algorithms, with a maximum absolute error of not exceeding 3.13%, a mean absolute error of less than 0.54%, and a root mean square error of no more than 0.66%.

Extracting weak electromagnetic signals based on RMPSO-SPBSR in virtual anechoic chamber

To enhance the signal extraction performance at weak noise intensity in virtual anechoic chamber, this study investigates the correlation between the generation conditions of a stochastic resonance (SR) system and its output performance. To achieve optimal resonance effects, an adaptive system called symmetric piecewise bistable SR (SPBSR) is proposed. This system improves its structure by modifying the potential function to facilitate the occurrence of SR. Meanwhile, it combines a regional multi-role strategy and particle swarm optimization algorithm to determine the optimal structural parameters. The adaptive optimization process utilizes update rules that balance global and local optimal solutions, thereby mitigating the tendency to quickly converge to a local optimum. Experimental results demonstrate that the proposed system exhibits excellent performance within a noise intensity range of 0–10 dB, with a correlation coefficient of over 0.75, which can effectively suppress noise interference. In practical signal processing, the system excels at accurately extracting signal characteristics, resulting in improved similarity and smoothness of the detected signal. Both simulation and experimental results validate this algorithm’s strong practical relevance.

Optimization of Water Distribution Network Design Using Rafflesia Optimization Algorithm Based on Opposition-based Learning

<p>About 70% of the total cost of the water distribution system is used in the design of water distribution network (WDN), and selecting the most suitable pipe diameter for the WDN is the main way to reduce construction costs. The Rafflesia optimization algorithm (ROA) is a novel meta-heuristic algorithm, which was proposed recently. It has the characteristics of escaping local optimal solutions and stable performance. To further increase the solution quality and convergence speed of the algorithm, the opposition-based learning strategy is adopted in this paper to initialize the ROA algorithm population (namely the OBLROA algorithm). In this paper, the two-loop pipe network is taken as an actual test case, and the OBLROA algorithm is used to design the minimum cost pipe diameter combination. The experimental results show that the OBLROA algorithm can find the lowest cost pipe diameter combination of the two-loop pipe network under the constraints of pressure and velocity. Compared with some previous research work, the OBLROA algorithm needs the least number of evaluations to find the optimal solution, showing strong competitiveness.</p> <p> </p>

Design and Implementation of High QoS 3D-NoC using Modified Double Particle Swarm Optimization on FPGA

One technique to overcome the exponential growth bottleneck is to increase the number of cores on a processor, although having too many cores might cause issues including chip overheating and communication blockage. The problem of the communication bottleneck on the chip is presently effectively resolved by networks-on-chip (NoC). A 3D stack of chips is now possible, thanks to recent developments in IC manufacturing techniques, enabling to reduce of chip area while increasing chip throughput and reducing power consumption. The automated process associated with mapping applications to form three-dimensional NoC architectures is a significant new path in 3D NoC research. This work proposes a 3D NoC partitioning approach that can identify the 3D NoC region that has to be mapped. A double particle swarm optimization (DPSO) inspired algorithmic technique, which may combine the characteristics having neighbourhood search and genetic architectures, also addresses the challenge of a particle swarm algorithm descending into local optimal solutions. Experimental evidence supports the claim that this hybrid optimization algorithm based on Double Particle Swarm Optimisation outperforms the conventional heuristic technique in terms of output rate and loss in energy. The findings demonstrate that in a network of the same size, the newly introduced router delivers the lowest loss on the longest path. Three factors, namely energy, latency or delay, and throughput, are compared between the suggested 3D mesh ONoC and its 2D version. When comparing power consumption between 3D ONoC and its electronic and 2D equivalents, which both have 512 IP cores, it may save roughly 79.9% of the energy used by the electronic counterpart and 24.3% of the energy used by the latter. The network efficiency of the 3D mesh ONoC is simulated by DPSO in a variety of configurations. The outcomes also demonstrate an increase in performance over the 2D ONoC. As a flexible communication solution, Network-On-Chips (NoCs) have been frequently employed in the development of multiprocessor system-on-chips (MPSoCs). By outsourcing their communication activities, NoCs permit on-chip Intellectual Property (IP) cores to communicate with one another and function at a better level. The important components in assigning application duties, distributing the work to the IPs, and coordinating communication among them are mapping and scheduling methods. This study aims to present an entirely advanced form of research in the area of 3D NoC mapping and scheduling applications, grouping the results according to various parameters and offering several suggestions for further research.

Enhanced Harris hawks optimization-based fuzzy k-nearest neighbor algorithm for diagnosis of Alzheimer's disease

In order to stop deterioration and give patients with Alzheimer's disease (AD) early therapy, it is crucial to correctly diagnose AD and its early stage, mild cognitive impairment (MCI). A framework for diagnosing AD is presented in this paper, which includes magnetic resonance imaging (MRI) image preprocessing, feature extraction, and the Fuzzy k-nearest neighbor algorithm (FKNN) model. In particular, the framework's novelty lies in the use of an improved Harris Hawks Optimization (HHO) algorithm named SSFSHHO, which integrates the Sobol sequence and Stochastic Fractal Search (SFS) mechanisms for optimizing the parameters of FKNN. The HHO method improves the quality of the initial population overall by incorporating the Sobol sequence, and the SFS mechanism increases the algorithm's capacity to get out of the local optimum solution. Comparisons with other classical meta-heuristic algorithms, state-of-the-art HHO variants in low and high dimensions, and enhanced meta-heuristic algorithms on 30 typical IEEE CEC2014 benchmark test problems show that the overall performance of SSFSHHO is significantly better than other comparative algorithms. Moreover, the created framework based on the SSFSHHO-FKNN model is employed to classify AD and MCI using MRI scans from the ADNI dataset, achieving high classification performance for 6 representative cases. Experimental findings indicate that the proposed algorithm performs better than a number of high-performance optimization algorithms and classical machine learning algorithms, thus offering a promising approach for AD classification. Additionally, the proposed strategy can successfully identify relevant features and enhance classification performance for AD diagnosis.

A novel hybrid particle swarm optimization with marine predators

Particle swarm optimization algorithms are often applied to solve optimization problems. However, the traditional particle swarm optimization algorithm has a single search method and is less capable of exploration and exploitation when solving high-dimensional and complex problems. In this paper, a hybrid particle swarm optimization algorithm for marine predators (HMPPSO) is proposed by combining the multi-stage search strategy of marine predators algorithm (MPA). We divide the search process of HMPPSO into three stages: the first stage uses Brownian motion for exploration; the middle stage divides the population into two parts, the first half remains responsible for exploration through Brownian motion. Besides, in the second half of the population, a random wandering strategy is proposed to randomly select five particles so that it can control the update of particles to prevent falling into the local optimal solution; the learning strategy is improved in the later stage. The control parameters are used to adjust the strategy, while making the single case learning method and the example averaging method alternate. This strategy accelerates the convergence of the algorithm while enhancing the diversity of the algorithm in the later stage and improving the development ability of the algorithm. In addition, the population diversity is enhanced using chaotic initialization and opposition-based learning strategies. The algorithm in this paper is applied to different types of CEC2017 benchmark test functions and four multi-dimensional non-linear structural design optimization problems. Compared with other recent algorithms, the results show that the performance of HMPPSO is significantly better than other algorithms.

Hierarchical shape optimization for large deployable membrane reflector with spatial skirt cable

In the shape optimization analysis of electrostatically controlled deployable membrane reflector (ECDMR), the poor balance of the membrane with spatial skirt cable is the main reason for the degradation of the reflector surface precision. At the same time, while in the optimization of the pre-stress of large deployable reflectors, the membrane structure has strong geometric nonlinearity, and the lack of necessary gradient information leads to low efficiency of the calculation. Therefore, according to the structural characteristics of the cable-membrane reflector, the two optimization objectives of the highest surface precision and the most uniform stress distribution is considered, and a hierarchical shape optimization method is proposed based on membrane theory and unbalance force analysis, which realizes the solution of the multi-objective optimization problem when the three optimization objectives have different priorities. The interior effective membrane reflective surface is analyzed using membrane theory, and the external membrane with spatial skirt cable is analyzed using nonlinear finite element method. The gradient information required for optimization is also obtained by unbalance force analysis, which ensures better optimization efficiency and can solve large-scale optimization problems. Therefore, the node positions and element equilibrium stresses of the structure can be optimized simultaneously, which further expands the search space of the equilibrium state and reduces the possibility of falling into local optimal solutions. Finally, a numerical example of a 30 m aperture ECDMR is calculated and analyzed, and the results show that the proposed method can obtain a high surface precision with a fast solution speed.

Environmental, economic and exergy analysis of separation of ternary azeotrope by variable pressure extractive distillation based on multi-objective optimization

In this work, the ternary azeotrope of tert-butyl alcohol/ethyl acetate/water is separated by extractive distillation (ED) to recover the available constituents and protect the environment. Based on the conductor like shielding model and relative volatility method, ethylene glycol was selected as the extractant in the separation process. In addition, in view of the characteristic that the relative volatility between components changes with pressure, the multi-objective optimization method based on nondominated sorting genetic algorithm II optimizes the pressure and the amount of solvent cooperatively to avoid falling into the optimal local solution. Based on the optimal process parameters, the proposed heat-integrated process can reduce the gas emissions by 29.30%. The heat-integrated ED, further coupled with the pervaporation process, can reduce gas emission by 42.36% and has the highest exergy efficiency of 47.56%. In addition, based on the heat-integrated process, the proposed two heat pump assisted heat-integrated ED processes show good economic and environmental performance. The double heat pump assisted heat-integrated ED can reduce the total annual cost by 28.78% and the gas emissions by 55.83% compared with the basis process, which has a good application prospect. This work provides a feasible approach for the separation of ternary azeotropes.

A hybrid search mode-based differential evolution algorithm for auto design of the interval type-2 fuzzy logic system

This article proposed a hybrid search mode-based differential evolution (HSM-DE) algorithm to overcome the complex design of an interval type-2 fuzzy logic system (IT2FLS). First, transform complex design processes of the IT2FLS into optimization problems for our proposed evolutionary algorithm by decoding the whole system into design parameters regarded as search objectives. Then, the DE algorithm with a rapid convergence characteristic is adopted as a global search method for exploration according to a memetic algorithm (MA) structure. Considering the conventional DE algorithm is lack of escaping ability for the local optimal solution, a local search method combined with a simulated binary crossover (SBX) and polynomial mutation (PM) is utilized to enhance the exploitation behavior of our proposed method. In addition, simple constraints on the design parameters of the membership function are added to balance the searching freedom of the HSM-DE algorithm and the readability of the optimal IT2FLS. Finally, a simulation of a mobile two-wheel vehicle (MTWV) under a goal search task is performed to verify the effectiveness of the optimal IT2FLS auto designed by HSM-DE. All results demonstrate that the HSM-DE realizes auto design for the IT2FLS with high-performance control and outperforms the comparative methods. Moreover, four comparison methods are performed to validate the high-performance of the proposed HSM-DE on the search ability of the optimal solution.

A novel chaotic transient search optimization algorithm for global optimization, real-world engineering problems and feature selection.

Metaheuristic optimization algorithms manage the search process to explore search domains efficiently and are used efficiently in large-scale, complex problems. Transient Search Algorithm (TSO) is a recently proposed physics-based metaheuristic method inspired by the transient behavior of switched electrical circuits containing storage elements such as inductance and capacitance. TSO is still a new metaheuristic method; it tends to get stuck with local optimal solutions and offers solutions with low precision and a sluggish convergence rate. In order to improve the performance of metaheuristic methods, different approaches can be integrated and methods can be hybridized to achieve faster convergence with high accuracy by balancing the exploitation and exploration stages. Chaotic maps are effectively used to improve the performance of metaheuristic methods by escaping the local optimum and increasing the convergence rate. In this study, chaotic maps are included in the TSO search process to improve performance and accelerate global convergence. In order to prevent the slow convergence rate and the classical TSO algorithm from getting stuck in local solutions, 10 different chaotic maps that generate chaotic values instead of random values in TSO processes are proposed for the first time. Thus, ergodicity and non-repeatability are improved, and convergence speed and accuracy are increased. The performance of Chaotic Transient Search Algorithm (CTSO) in global optimization was investigated using the IEEE Congress on Evolutionary Computation (CEC)'17 benchmarking functions. Its performance in real-world engineering problems was investigated for speed reducer, tension compression spring, welded beam design, pressure vessel, and three-bar truss design problems. In addition, the performance of CTSO as a feature selection method was evaluated on 10 different University of California, Irvine (UCI) standard datasets. The results of the simulation showed that Gaussian and Sinusoidal maps in most of the comparison functions, Sinusoidal map in most of the real-world engineering problems, and finally the generally proposed CTSOs in feature selection outperform standard TSO and other competitive metaheuristic methods. Real application results demonstrate that the suggested approach is more effective than standard TSO.