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LCAHA : A hybrid artificial hummingbird algorithm with multi-strategy for engineering applications
Abstract
The recently introduced Artificial Hummingbird Algorithm (AHA) exhibits competitive performance in developing optimization concerns. However, AHA has an imbalance between exploration and utilization abilities, often prematurely converging with low precision. Therefore, in this paper, a multi-strategy boosted hybrid artificial hummingbird algorithm called LCAHA combined with sinusoidal chaotic map strategy, Lévy flight, cross, and update foraging strategy is proposed. Firstly, LCAHA is initialized by the sinusoidal chaotic map strategy to obtain a population with better ergodicity. Secondly, introducing the Lévy flight can boost the diversity of the population, control premature convergence and boost the stability of the population. Then, two new strategies, cross foraging and update foraging, are introduced. The introduction of new foraging strategies further enhances the exploration and developmental capabilities. These three strategies work together to improve the overall performance of the AHA. Finally, the performance of the LCAHA is examined on 23 classical test suites, the CEC2017, CEC2019, and CEC2020 test suites, and six engineering optimization cases. The numerical experimental results show that LCAHA provides very promising numerical results in solving challenging optimization problems. The algorithm is applied to two spacecraft trajectory optimization cases. The experimental results demonstrate the applicability and potential of the LCAHA in solving practical applications.
... Feature selection is a common method for recognizing emotions and reducing dimensionality [7][8][9]. Metaheuristic algorithms have universal and diverse heuristic strategies [10,11], and they are powerful tools for handling complex optimization problems such as feature selection [12][13][14]. A genetic algorithm (GA) mimics the process of natural selection, in which promising individuals are selected for producing the next generation [15,16]. ...
... (1) In CREMA-D, the second derivative of PCM, and the variances in logMelFreqBand [6] and logMelFreqBand_FDE [2] 10,11,12,14], PCM, jitterLocal, and jitterDDP are gender-difference features. (4) In IEMOCAP-S1, the first derivative of logMelFreqBand_FDE[0], and the variances in logMelFreqBand [4,5] are features with distinct gender-related variations. ...
Speech emotion recognition based on gender holds great importance for achieving more accurate, personalized, and empathetic interactions in technology, healthcare, psychology, and social sciences. In this paper, we present a novel gender–emotion model. First, gender and emotion features were extracted from voice signals to lay the foundation for our recognition model. Second, a genetic algorithm (GA) processed high-dimensional features, and the Fisher score was used for evaluation. Third, features were ranked by their importance, and the GA was improved through novel crossover and mutation methods based on feature importance, to improve the recognition accuracy. Finally, the proposed algorithm was compared with state-of-the-art algorithms on four common English datasets using support vector machines (SVM), and it demonstrated superior performance in accuracy, precision, recall, F1-score, the number of selected features, and running time. The proposed algorithm faced challenges in distinguishing between neutral, sad, and fearful emotions, due to subtle vocal differences, overlapping pitch and tone variability, and similar prosodic features. Notably, the primary features for gender-based differentiation mainly involved mel frequency cepstral coefficients (MFCC) and log MFCC.
... The AHA often struggles with a balance between exploration and exploitation abilities, leading to premature convergence and low precision. Model of [64] proposed a multi-strategy enhanced version of AHA, termed the LCAHA (Levy Chaotic AHA), which incorporates a sinusoidal chaotic map strategy, LF, and novel cross and update foraging strategies. Initially, the LCAHA employs the sinusoidal chaotic map strategy during initialization, enhancing the population's ergodicity. ...
In the last few decades, metaheuristic algorithms that use the laws of nature have been used dramatically in numerous and complex optimization problems. The artificial hummingbird algorithm (AHA) is one of the metaheuristic algorithms that was invented in 2022 based on the foraging and migration behavior of the hummingbird for modeling and solving optimization problems. The algorithm initially starts with an initial random population of solutions. It then uses iterative processes and hummingbird position updates to balance exploration and exploitation toward the most optimal solutions. This paper has a detailed and extensive review of the AHA algorithm considering the aspects of hybrid, improved, binary, multi-objective, and optimization problems. In addition, a wide range of applications of AHA in various fields such as feature selection, image processing, scheduling, Internet of Things, classification, clustering, financial and economic issues, forecasting, wireless sensor networks, and many engineering challenges are explored. The statistical and numerical results showed that the AHA algorithm with deep learning methods, Levy flight, and opposition-based learning had the best performance. Also, the AHA algorithm is most widely used in solving multimodal optimization problems and continuous functions.
... However, this approach needs to conduct numerous iterations for selecting these samples, which is unable to obtain ideal results for the problem of high-dimensional space. In this paper, we adopt the artificial hummingbird algorithm to find the optimal radius of compact support region and ensure these effective samples, the reason is that this algorithm can efficiently achieve global parameters for solving high-dimensional nonlinear problems [26,27]. To select the effective samples, the optimal function of minimizing the difference between the true values and predicted values is derived, and the optimal function for analytical is treated as an example to illustrate the form of expression, i.e., ...
To effectively estimate the reliability level of low-cycle fatigue (LCF) life of mechanical structures, a novel
method of collaborative modeling-based improved moving Kriging (IMKCM) approach is proposed by fusing
improved moving Kriging method and collaborative modeling strategy. In this method, the improved moving
Kriging model is developed by the Kriging model, moving least squares method and artificial hummingbird al-
gorithm, in which the Kriging model is selected as the basis function, the artificial hummingbird algorithm is
used to define the optimal radius of compact support region and determine the effective modeling samples, and
the moving least squares method is adopted to resolve the unknown coefficients; the collaborative modeling
strategy is developed from the decomposition and coordination method, in which the mathematical models of
the decomposed sub-objectives are synchronously built by the cell array theory, and the mathematical model
between the objective and the sub-objectives is established by the improved moving Kriging model. Furthermore,
a numerical example (i.e., nested nonlinear function) and an engineering example (i.e., turbine blisk LCF life
reliability estimation) are employed to verify the effectiveness of the IMKCM approach. The results show that the
proposed IMKCM method holds excellent abilities in modeling features and simulation performance.
... The Levy flight originates from the integration of Levy's symmetric stable distribution, serving as a method to generate special random step lengths. Addressing the issue of random searches, many scholars have incorporated this strategy to enhance algorithms, thereby achieving superior optimization results [33,34]. In this paper, the Levy flight strategy is introduced in the second phase of NGO to prevent the population from falling into local optima. ...
Tool wear condition significantly influences equipment downtime and machining precision, necessitating the exploration of a more accurate tool wear state identification technique. In this paper, the wavelet packet thresholding denoising method is used to process the acquired multi-source signals and extract several signal features. The set of features most relevant to the tool wear state is screened out by the support vector machine recursive feature elimination (SVM-RFE). Utilizing these selected features, we propose a tool wear state identification model, which utilizes an improved northern goshawk optimization (INGO) algorithm to optimize the support vector machine (SVM), hereby referred to as INGO-SVM. The simulation tests reveal that INGO demonstrates superior convergence efficacy and stability. Furthermore, a milling wear experiment confirms that this approach outperforms five other methods in terms of recognition accuracy, achieving a remarkable accuracy rate of 97.9%.
Pathfinder algorithm (PFA) is a swarm intelligent optimization algorithm inspired by the collective activity behavior of swarm animals, imitating the leader in the population to guide followers in finding the best food source. This algorithm has the characteristics of a simple structure and high performance. However, PFA faces challenges such as insufficient population diversity and susceptibility to local optima due to its inability to effectively balance the exploration and exploitation capabilities. This paper proposes an Ameliorated Pathfinder Algorithm called APFA to solve complex engineering optimization problems. Firstly, a guidance mechanism based on multiple elite individuals is presented to enhance the global search capability of the algorithm. Secondly, to improve the exploration efficiency of the algorithm, the Logistic chaos mapping is introduced to help the algorithm find more high-quality potential solutions while avoiding the worst solutions. Thirdly, a comprehensive following strategy is designed to avoid the algorithm falling into local optima and further improve the convergence speed. These three strategies achieve an effective balance between exploration and exploitation overall, thus improving the optimization performance of the algorithm. In performance evaluation, APFA is validated by the CEC2022 benchmark test set and five engineering optimization problems, and compared with the state-of-the-art metaheuristic algorithms. The numerical experimental results demonstrated the superiority of APFA.
The sand cat is a creature suitable for living in the desert. Sand cat swarm optimization (SCSO) is a biomimetic swarm intelligence algorithm, which inspired by the lifestyle of the sand cat. Although the SCSO has achieved good optimization results, it still has drawbacks, such as being prone to falling into local optima, low search efficiency, and limited optimization accuracy due to limitations in some innate biological conditions. To address the corresponding shortcomings, this paper proposes three improved strategies: a novel opposition-based learning strategy, a novel exploration mechanism, and a biological elimination update mechanism. Based on the original SCSO, a multi-strategy improved sand cat swarm optimization (MSCSO) is proposed. To verify the effectiveness of the proposed algorithm, the MSCSO algorithm is applied to two types of problems: global optimization and feature selection. The global optimization includes twenty non-fixed dimensional functions (Dim = 30, 100, and 500) and ten fixed dimensional functions, while feature selection comprises 24 datasets. By analyzing and comparing the mathematical and statistical results from multiple perspectives with several state-of-the-art (SOTA) algorithms, the results show that the proposed MSCSO algorithm has good optimization ability and can adapt to a wide range of optimization problems.
With the more and more amelioration of our quality of life, our needs for clothing have altered from having clothes to wearing good-looking, among which the wrinkle resistance of clothing fabric owns a giant effect on the beauty of clothing. Nowadays, artificial subjective evaluation is mainly used to evaluate the wrinkle grade of garment fabrics in the textile industry. This evaluation method owns the shortcoming of poor accuracy, being time-consuming and poor objectivity. For solving this problem, it is very important to put forward an objective evaluation model of fabric wrinkle grade. In this paper, we proposed a fabric wrinkle objective evaluation model with the optimized random vector functional link. The model applies DarkNet19 deep neural network to abstract the high-order visual features of the wrinkled surface image of the fabric, uses the improved artificial hummingbird optimization algorithm to ameliorate the import bias and weight of the random vector function link’s hidden layer, and uses $$ {{\rm{L}}_{2,1}}$$L2,1 norm regularization computes output weights for random vector function links. The relative tests reveal that the objective evaluation model of fabric wrinkles put forward in this paper has excellent performance.
This work presents a novel nature-inspired metaheuristic called Nutcracker Optimization Algorithm (NOA) inspired by Clark’s nutcrackers. The nutcrackers exhibit two distinct behaviors that occur at separate periods. The first behavior, which occurs during the summer and fall seasons, represents the nutcracker’s search for seeds and subsequent storage in an appropriate cache. During the winter and spring seasons, another behavior based on the spatial memory strategy is regarded to search for the hidden caches marked at different angles using various objects or markers as reference points. If the nutcrackers cannot find the stored seeds, they will randomly explore the search space to find their food. NOA is herein proposed to mimic these various behaviors to present a new, robust metaheuristic algorithm with different local and global search operators, allowing it to solve various optimization problems with better outcomes. NOA is evaluated on test suites of CEC-2005, CEC-2014, CEC-2017, and CEC-2020 and five real-world engineering design problems. NOA is compared with three classes of existing optimization algorithms: (1) SMA, GBO, EO, RUN, AVOA, RFO, and GTO as recently-published algorithms, (2) SSA, WOA, and GWO as highly-cited algorithms, and (3) AL-SHADE, L-SHADE, LSHADE-cnEpSin, and LSHADE-SPACMA as highly-performing optimizers and winners of CEC competition. NOA was ranked first among all methods and demonstrated superior results when compared to LSHADE-cnEpSin and LSHADE-SPACMA as the best-performing optimizers and the winners of CEC-2017, and AL-SHADE and L-SHADE as the winners of CEC-2014.
Jellyfish search (JS) algorithm impersonates the foraging behavior of jellyfish in the ocean. It is a new developed meta-heuristic algorithm that solves complex and real world optimization problems. The global explore capability and robustness of JS are strong, but JS still has great development space in solving complex optimization problems with high dimensions and multiple local optima. Therefore, an enhanced jellyfish search (EJS) algorithm is developed in this study, and three improvements are made: (i) By adding sine and cosine learning factors, the jellyfish can learn from both random individual and best individual during Type B motion in swarm to enhance the optimization capability and convergence speed; (ii) Adding local escape operator can skip local optimal trap and boost the exploitation ability of JS; (iii) Opposition-based learning operator and quasi-opposition learning operator can increase and strengthen the population distribution more diversified, and better individuals are selected from present and new opposition-solution to participates in the next iteration, which can boost the solution’s quality, meanwhile convergence speed is fasted and its precision is increased. In addition, the performance contrast of the developed EJS and some previous outstanding and advanced methods are evaluated on CEC2017, CEC2019 test suite and six real engineering example of case. It is demonstrated that EJS algorithm escaped the trap of local optimum, enhanced the solution’s quality and the calculation speed. What’s more, the practical engineering applications of EJS algorithm also verify its superiority and effectiveness in solving both constrained and unconstrained optimization problems, and it stretched one’s mind for solving such optimization problems.
This paper offers an efficient tool to define the unknown parameters of electrical transformers. The proposed methodology is developed based on artificial hummingbird optimizer (AHO) to generate the best values of the transformer’s unknown parameters. At initial stage, the parameters’ extraction of the transformer electrical equivalent is adapted as an optimization function along with the associated operating inequality constraints. In which, the sum of absolute errors (SAEs) among many variables from nameplate data of transformers is decided to be minimized. Two test cases of 4 kVA and 15 kVA transformers ratings are demonstrated to indicate the ability of the AHO compared to other recent challenging optimizers. The proposed AHO achieves the lowest SAE’s value than other competing algorithms. At advanced stage of this effort, the capture of percentage of loading to achieve maximum efficiency is ascertained. At later stage, the performance of transformers utilizing the extracted parameters cropped by the AHO to investigate the principal behavior at energization of these transformer units is made. At the end, it can be confirmed that the AHO produces best values of transformer parameters which help much in achieving accurate simulations for steady-state and inrush behaviors.
Many engineering and scientific problems in the real-world boil down to optimization problems, which are difficult to solve by using traditional methods. Meta-heuristics are appealing algorithms for solving optimization problems while keeping computational costs reasonable. The marine predators algorithm (MPA) is a modern optimization meta-heuristic, inspired by widespread Lévy and Brownian foraging strategies in ocean predators as well as optimal encounter rate strategies in biological interactions between predator and prey. However, MPA is not without its shortcomings. In this paper, a quasi-opposition based learning and Q-learning based marine predators algorithm (QQLMPA) is proposed. This offers multiple improvements over standard MPA. Primely, Q-learning allows MPA to fully use the information generated by previous iterations. And also, quasi-opposition based learning serves to increase population diversity, reducing the risk of convergence to inferior local optima. Numerical experiments demonstrate better performance by QQLMPA on 32 benchmark optimization functions and three engineering problems: designs of pressure vessel, hydro-static thrust bearing, and speed reducer.
The sine cosine algorithm (SCA) is a well-known meta-heuristic optimization algorithm. SCA has received much attention in various optimization fields due to its simple structure and excellent optimization capabilities. However, the dimension of objective function also increases with the increasing complexity of optimization tasks. This makes the original SCA appear to have insufficient optimization capability and likely to fall into premature convergence. A multi-mechanism acting variant of SCA, called ARSCA, is proposed to address the above deficiencies. ARSCA is an enhanced SCA algorithm based on the adaptive quadratic interpolation mechanism (AQIM) and Rounding mechanism (RM). RM enables a more balanced state between exploration and exploitation of the ARSCA. AQIM enhances local exploitation capabilities. To verify the performance of ARSCA, we compared ARSCA with some advanced traditional optimization algorithms and variants of algorithms for 30 consecutive benchmark functions of IEEE CEC2014. In addition, ARSCA was applied to 6 constrained engineering optimization problems. These six algorithms include the tension-compression spring design problem, the welded beam design problem, the pressure vessel design problem, the I-beam design problem, the speed reducer design problem, and the three-bar design problem. Experimental results show that ARSCA outperforms its competitors in both the solution quality and the ability to jump out of the local optimum. The relevant codes for the paper are publicly available at https://github.com/YangXiao9799/paper_ARSCA.
Recycling tasks are the most effective method for reducing waste generation, protecting the environment, and boosting the overall national economy. The productivity and effectiveness of the recycling process are strongly dependent on the cleanliness and precision of processed primary sources. However, recycling operations are often labor intensive, and computer vision and deep learning (DL) techniques aid in automatically detecting and classifying trash types during recycling chores. Due to the dimensional challenge posed by pre-trained CNN networks, the scientific community has developed numerous techniques inspired by biology, swarm intelligence theory, physics, and mathematical rules. This research applies a new meta-heuristic algorithm called the artificial hummingbird algorithm (AHA) to solving the waste classification problem based on feature selection. However, the performance of the AHA is barely satisfactory; it may be stuck in optimal local regions or have a slow convergence. To overcome these limitations, this paper develops two improved versions of the AHA called the AHA-ROBL and the AHA-OBL. These two versions enhance the exploitation stage by using random opposition-based learning (ROBL) and opposition-based learning (OBL) to prevent local optima and accelerate the convergence. The main purpose of this paper is to apply the AHA-ROBL and AHA-OBL to select the relevant deep features provided by two pre-trained models of CNN (VGG19 & ResNet20) to recognize a waste classification. The TrashNet dataset is used to verify the performance of the two proposed approaches (the AHA-ROBL and AHA-OBL). The effectiveness of the suggested methods (the AHA-ROBL and AHA-OBL) is compared with that of 12 modern and competitive optimizers, namely the artificial hummingbird algorithm (AHA), Harris hawks optimizer (HHO), Salp swarm algorithm (SSA), aquila optimizer (AO), Henry gas solubility optimizer (HGSO), particle swarm optimizer (PSO), grey wolf optimizer (GWO), Archimedes optimization algorithm (AOA), manta ray foraging optimizer (MRFO), sine cosine algorithm (SCA), marine predators algorithm (MPA), and rescue optimization algorithm (SAR). A fair evaluation of the proposed algorithms’ performance is achieved using the same dataset. The performance analysis of the two proposed algorithms is applied in terms of different measures. The experimental results confirm the two proposed algorithms’ superiority over other comparative algorithms. The AHA-ROBL and AHA-OBL produce the optimal number of selected features with the highest degree of precision.
This study proposes an artificial hummingbird algorithm (AHA) for energy management (EM) for optimal operation of a microgrid (MG), including conventional sources and renewable energy sources (RES), with an incentive-based demand response (DR). Due to the stochastic nature of solar and wind output power and the uncertainty of prices and load, a probabilistic EM with hybrid AHA and point estimation method (PEM) is proposed to model this uncertainty by utilizing the normal and Weibull distribution functions. The PEM method is considered a good tool for handling stochastic EM problems. It achieves good results using the same procedures used with the deterministic problems while maintaining low computational efforts. The proposed AHA technique is employed to solve a deterministic incentive DR program, with the goal of reducing the overall cost, which includes the cost of conventional generator fuel and the cost of power transaction with the main grid while taking into account the load demand. Two different case studies are tested. The simulation results of the proposed AHA is compared with the results of well-known metaheuristic algorithms to demonstrate its efficacy. According to AHA's results, a total reduction of energy consumption by 104 KWh for the first case study and 2677 MWh for the second case study is achieved while achieving the lowest overall operating cost. The results demonstrate that the AHA is adequate for tackling the EM problem. Then, to examine the effect of uncertainty on the MG state, a probabilistic EM problem is solved using AHA-PEM.
Renewable distributed generators (RDGs) have been widely used in distribution networks for technological, economic, and environmental reasons. The main concern with renewable-based distributed generators, particularly photovoltaic and wind systems, is their intermittent nature, which causes output power to fluctuate, increasing power system uncertainty. As a result, it's critical to think about the resource's uncertainty when deciding where it should go in the grid. The main innovation of this paper is proposing an efficient and the most recent technique for optimal sizing and placement of the RDGs in radial distribution systems considering the uncertainties of the loading and RDGs output powers. Monte-Carlo simulation approach and backward reduction algorithm are used to generate 12 scenarios to model the uncertainties of loading and RDG output power. The artificial hummingbird algorithm (AHA), which is considered the most recent and efficient technique, is used to determine the RDG ratings and placements for a multi-objective function that includes minimizing expected total cost, the expected total emissions, and the expected total voltage deviation, as well as improving expected total voltage stability with considering the uncertainties of loading and RDGs output powers. The proposed technique is tested using an IEEE 33-bus network and an actual distribution system in Portugal (94-bus network). Simulations show that the suggested method effectively solves the problem of optimal DG allocation. In addition of that the expected costs, the emissions, the voltage deviation, are reduced considerably and the voltage stability is also enhanced with inclusion of RDGs in the tested systems.
In this article, an artificial algorithm called hummingbirds optimization method, named AHA algorithm, is settled to extract accurately the parameters of PV modules under outdoor operational conditions. AHA is the main contribution in this work, regarding its efficiency and good performance in terms of standard deviation (StD), root mean square error (RMSE), sum of squared error (SSE), maximum number of iterations (MaxIt), particularly, for extracting parameter from modules operating in real conditions, and under different temperature and irradiance levels. The AHA is applied on a Polycrystalline-solar panel module type 320W-72P at real operating conditions and on a PV array of three polycrystalline PV modules connected in series. PV cells of the same modules are assumed operating under the same conditions where they share the same electric current and voltage values. In this last pattern, eight different scenarios are chosen. In the first five scenarios, the temperatures are (46.97, 44.23, 42.87, 40.59 and 30.60°C), and the irradiance varies, such as (910, 800.57, 614.13, 415.1 and 200.87W/m2), respectively. In the other three testing scenarios, the solar irradiance is equal (803 W/ m2), and the temperature differs, such as
$\text{T}= 47.93\,\,^{\circ }\text{C}$
, 53.38 °C and 36.62°C. Lower values of root mean square errors (RMSE) are achieved (
$9.8602\times {10}^{-4}$
and
$2.572533\times {10}^{-2}$
for RTC France PV cell and the 320W-72P module respectively) with 6000 iterations. Moreover, all the eight scenarios are lower than
$7.245916\times {10}^{-2}$
for the last case study. Moreover, results show that we could recommend the AHA algorithm as an advanced and efficient method for dealing with real time parameter optimization of photovoltaic modules. In fact, a high closeness between the simulated and the experimental curves is achieved, which indicates the perfectness of this optimization method. Finally, the proposed AHA algorithm can be engaged as tools for the best designing of PV systems.
Appropriate installation of renewable energy-based distributed generation units (RDGs) is
one of the most important challenges and current topics of interest in the optimal functioning of modern
power networks. Due to the intermittent nature of renewable energy sources, optimal allocation and sizing
of RDGs, particularly photovoltaic (PV) and wind turbine (WT), remains a critical task. Based on a new
metaheuristic known as the Artificial hummingbird algorithm (AHA), this paper provides a novel approach
for addressing the problem of RDG planning optimization. Considering various operational constraints, the
optimization problem is developed with multiple objectives including power loss reduction, voltage stability
margin (VSM) enhancement, voltage deviation minimization, and yearly economic savings. Furthermore,
using relevant probability distribution functions, the ambiguities related with the stochastic nature of
PV and WT output powers are evaluated. The proposed algorithm was compared to two of the recent
metaheuristics applied in this domain known as improved harris hawks and particle swarm optimization
algorithm (HHO-PSO) and hybrid of phasor particle swarm and gravitational search algorithm (PPSOGSA).
The IEEE 33-bus and 69-bus systems are assessed as the test systems in this study. According to the findings,
AHA delivers superior solutions and enhances the techno-economic benefits of distribution systems in all
the scenarios evaluated.
This paper presents a machine learning model to predict the effect of Al2O3 nanoparticles content on the wear rates in Cu-Al2O3 nanocomposite prepared using in situ chemical technique. The model developed is a modification of the random vector functional link (RVFL) algorithm using artificial hummingbird algorithm (AHA). The objective of using AHA is used to find the optimal configuration of RVFL to enhance the prediction of Al2O3 nanoparticles. The preparation of the composite was done using aluminum nitrate that was added to a solution containing scattered copper nitrate. After that, the powders of CuO and Al2O3 were obtained, and the leftover liquid was removed using a thermal treatment at 850 °C for 1 h. The powders were consolidated using compaction and sintering processes. The microhardness of the nanocomposite with 12.5% Al2O3 content is 2.03-fold times larger than the pure copper, while the wear rate of the same composite is reduced, reaching 55% lower than pure copper. These improved properties are attributed to the presence of Al2O3 nanoparticles and their homogenized distributions inside the matrix. The developed RVFl-AHA model was able to predict the wear rates of all the prepared composites at different wear load and speed, with very good accuracy, reaching nearly 100% and 99.5% using training and testing, respectively, in terms of coefficient of determination R2.
Optimization is an important and fundamental challenge to solve optimization problems in different scientific disciplines. In this paper, a new stochastic nature-inspired optimization algorithm called Pelican Optimization Algorithm (POA) is introduced. The main idea in designing the proposed POA is simulation of the natural behavior of pelicans during hunting. In POA, search agents are pelicans that search for food sources. The mathematical model of the POA is presented for use in solving optimization issues. The performance of POA is evaluated on twenty-three objective functions of different unimodal and multimodal types. The optimization results of unimodal functions show the high exploitation ability of POA to approach the optimal solution while the optimization results of multimodal functions indicate the high ability of POA exploration to find the main optimal area of the search space. Moreover, four engineering design issues are employed for estimating the efficacy of the POA in optimizing real-world applications. The findings of POA are compared with eight well-known metaheuristic algorithms to assess its competence in optimization. The simulation results and their analysis show that POA has a better and more competitive performance via striking a proportional balance between exploration and exploitation compared to eight competitor algorithms in providing optimal solutions for optimization problems.
The greater the demand for energy, the more important it is to improve and develop
permanent energy sources, because of their advantages over non-renewable energy sources. With the development of artificial intelligence algorithms and the presence of so many data, the evolution of simulation models has increased. In this research, an improvement to one recent optimization algorithm called the artificial hummingbird algorithm (AHA) is proposed. An adaptive opposition approach is suggested to select whether or not to use an opposition-based learning (OBL) method. This improvement is developed based on adding an adaptive updating mechanism to enable the original algorithm to obtain more accurate results with more complex problems, and is called the
adaptive opposition artificial hummingbird algorithm (AOAHA). The proposed AOAHA was tested on 23 benchmark functions and compared with the original algorithm and other recent optimization algorithms such as supply–demand-based optimization (SDO), wild horse optimizer (WHO), and tunicate swarm algorithm (TSA). The proposed algorithm was applied to obtain accurate models for solar cell systems, which are the basis of solar power plants, in order to increase their efficiency, thus increasing the efficiency of the whole system. The experiments were carried out on two important
models—the static and dynamic models—so that the proposed model would be more representative of real systems. Two applications for static models have been proposed: In the first application, the AOAHA satisfies the best root-mean-square values (0.0009825181). In the second application, the performance of the AOAHA is satisfied in all variable irradiance for the system. The results were evaluated in more than one way, taking into account the comparison with other modern and powerful optimization techniques. Improvement showed its potential through its satisfactory results
in the tests that were applied to it.
Feature selection is an important data processing method to reduce dimension of the raw datasets while preserving the information as much as possible. In this paper, an enhanced version of Black Widow Optimization Algorithm called SDABWO is proposed to solve the feature selection problem. The Black Widow Optimization Algorithm (BWO) is a new population-based meta-heuristic algorithm inspired by the evolution process of spider population. Three main improvements were included into the BWO to overcome the shortcoming of low accuracy, slow convergence speed and being easy to fall into local optima. Firstly, a novel strategy for selecting spouses by calculating the weight of female spiders and the distance between spiders is proposed. By applying the strategy to the original algorithm, it has faster convergence speed and higher accuracy. The second improvement includes the use of mutation operator of differential evolution at mutation phase of BWO which helps the algorithm escape from the local optima. And then, three key parameters are set to adjust adaptively with the increase of iteration times. To confirm and validate the performance of the improved BWO, other 10 algorithms are used to compared with the SDABWO on 25 benchmark functions. The results show that the proposed algorithm enhances the exploitation ability, improves the convergence speed and is more stable when solving optimization problems. Furthermore, the proposed SDABWO algorithm is employed for feature selection. Twelve standard datasets from UCI repository prove that SDABWO-based method has stronger search ability in the search space of feature selection than the other five popular feature selection methods. These results confirm the capability of the proposed method simultaneously improve the classification accuracy while reducing the dimensions of the original datasets. Therefore, SDABWO-based method was found to be one of the most promising for feature selection problem over other approaches that are currently used in the literature.
Nowadays, the design of optimization algorithms is very popular to solve problems in various scientific fields. The optimization algorithms usually inspired by the natural behaviour of an agent, which can be humans, animals, plants, or a physical or chemical agent. Most of the algorithms proposed in the last decade inspired by animal behaviour. In this article, we present a new optimizer algorithm called the wild horse optimizer (WHO), which is inspired by the social life behaviour of wild horses. Horses usually live in groups that include a stallion and several mares and foals. Horses exhibit many behaviours, such as grazing, chasing, dominating, leading, and mating. A fascinating behaviour that distinguishes horses from other animals is the decency of horses. Horse decency behaviour is such that the foals of the horse leave the group before reaching puberty and join other groups. This departure is to prevent the father from mating with the daughter or siblings. The main inspiration for the proposed algorithm is the decency behaviour of the horse. The proposed algorithm was tested on several sets of test functions such as CEC2017 and CEC2019 and compared with popular and new optimization methods. The results showed that the proposed algorithm presented very competitive results compared to other algorithms. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/90787-wild-horse-optimizer.
The major purpose of this study is to provide a proper approach for model identification of the Proton Exchange Membrane Fuel Cells (PEMFCs) to use in different applications. The method introduces a modified version of the Extreme Learning Machine (ELM) model for identification purposes. The modification is based on proposing and designing a new improved metaheuristic, called the developed Arithmetic Optimization Algorithm (dAOA). The algorithm is then verified by various algorithms to demonstrate its effectiveness and is then employed for optimizing the ELM configuration with the aim of minimizing the sum of the square error between the output voltage of the real PEMFC data and the output voltage achieved by the network. Simulation results of the proposed system are validated based on four scenarios that their results are as follows: for 3/5bar with 353.15 K, the maximum training error for dAOA and AOA are 6.01 and 9.899, respectively. For 1/1bar with 343.15 K, the maximum training error for dAOA and AOA are 0.0045 and 0.012, respectively. For 2.5/3bar with 343.15 K, the maximum training error for dAOA and AOA are 0.0132 and 0.0177, respectively, and for 1.5/1.5 bar with 343.15 K, the maximum training error for dAOA and AOA are 0.01and 0.01584, respectively. This shows the better results of the proposed dAOA to provide accurate parameters of the PEMFC stack system.
A recent set of overused population-based methods have been published in recent years. Despite their popularity, most of them have uncertain, immature performance, partially done verifications, similar overused metaphors, similar immature exploration and exploitation components and operations, and an insecure tradeoff between exploration and exploitation trends in most of the new real-world cases. Therefore, all users need to extensively modify and adjust their operations based on main evolutionary methods to reach faster convergence, more stable balance, and high-quality results. To move the optimization community one step ahead toward more focus on performance rather than change of metaphor, a general-purpose population-based optimization technique called Hunger Games Search (HGS) is proposed in this research with a simple structure, special stability features and very competitive performance to realize the solutions of both constrained and unconstrained problems more effectively. The proposed HGS is designed according to the hunger-driven activities and behavioural choice of animals. This dynamic, fitness-wise search method follows a simple concept of “Hunger” as the most crucial homeostatic motivation and reason for behaviours, decisions, and actions in the life of all animals to make the process of optimization more understandable and consistent for new users and decision-makers. The Hunger Games Search incorporates the concept of hunger into the feature process; in other words, an adaptive weight based on the concept of hunger is designed and employed to simulate the effect of hunger on each search step. It follows the computationally logical rules (games) utilized by almost all animals and these rival activities and games are often adaptive evolutionary by securing higher chances of survival and food acquisition. This method's main feature is its dynamic nature, simple structure, and high performance in terms of convergence and acceptable quality of solutions, proving to be more efficient than the current optimization methods. The effectiveness of HGS was verified by comparing HGS with a comprehensive set of popular and advanced algorithms on 23 well-known optimization functions and the IEEE CEC 2014 benchmark test suite. Also, the HGS was applied to several engineering problems to demonstrate its applicability. The results validate the effectiveness of the proposed optimizer compared to popular essential optimizers, several advanced variants of the existing methods, and several CEC winners and powerful differential evolution (DE)-based methods abbreviated as LSHADE, SPS_L_SHADE_EIG, LSHADE_cnEpSi, SHADE, SADE, MPEDE, and JDE methods in handling many single-objective problems. We designed this open-source population-based method to be a standard tool for optimization in different areas of artificial intelligence and machine learning with several new exploratory and exploitative features, high performance, and high optimization capacity. The method is very flexible and scalable to be extended to fit more form of optimization cases in both structural aspects and application sides. This paper's source codes, supplementary files, Latex and office source files, sources of plots, a brief version and pseudocode, and an open-source software toolkit for solving optimization problems with Hunger Games Search and online web service for any question, feedback, suggestion, and idea on HGS algorithm will be available to the public at https://aliasgharheidari.com/HGS.html.
The honey badger algorithm (HBA) is a meta-heuristic optimization algorithm that simulates the foraging behavior of honey badgers. Since the algorithm is prone to premature convergence when solving complex optimization problems. To improve the overall optimization performance of the basic HBA, this paper develops a modified HBA named SaCHBA_PDN based on the Bernoulli shift map, piecewise optimal decreasing neighborhood, and horizontal crossing with strategy adaptation and applies it to solve the unmanned aerial vehicle (UAV) path planning problem. Firstly, the Bernoulli shift map is invoked to the HBA algorithm to change its initialization process, thus increasing the diversity of the population and speeding up the convergence speed. Secondly, a new piecewise optimal decreasing neighborhood strategy (PODNS) is proposed to address the shortcomings of unbalanced convergence of the traditional optimal neighborhood strategy. The proposed PODNS increases the optimization efficiency of HBA and enhances the local search ability to avoid falling into the local optimum. Finally, a novel horizontal crossing with strategy adaptation is introduced to balance exploration and exploitation and enhance the global optimization ability. These strategies collaborate to enhance HBA in accelerating overall performance. The superiority of SaCHBA_PDN is comprehensively verified by comparing it with the original HBA and numerous celebrated and newly developed algorithms on the well-known 23 classical benchmark functions and IEEE CEC2017 test suite, respectively. Experimental results show that SaCHBA_PDN has a better performance than other optimization algorithms. Furthermore, SaCHBA_PDN is used to solve a UAV path planning problem based on the threat source model and applied to circular and irregular obstacle scenarios as well as two-dimensional grid maps. Simulation results show that SaCHBA_PDN can obtain more feasible and efficient paths in different obstacle environments.
Starling murmuration optimizer is a newly well-developed swarm intelligence algorithm inspired by the behavior of starlings during stunning murmuration and has performed competitively with other well-known methods. However, starling murmuration optimizer faces the issues of poor search capability, iterative stagnation, and low convergence accuracy when dealing with complex engineering optimization and high-dimensional problems. To ameliorate these deficiencies, an efficient hybrid starling murmuration optimizer that combines dynamic opposition, Taylor-based optimal neighborhood strategy, and crossover operator is developed in this paper. Firstly, introducing the Taylor-based optimal neighborhood strategy ensures a more careful and reasonable reliance on optimal individuals, thus reducing the possibility of falling into local optima. Meanwhile, dynamic opposition successfully balances the exploration and development phases by incorporating the ideas of quasi- and reflective opposition. In addition, the exploration-development capability is further enhanced by introducing the crossover operator. To ensure the adaptivity of the crossover factor, 12 different inertia weights are explored for crossover factors, and the sigmoidal decreasing inertia weights achieve optimality. Finally, the excellent performance of the proposed algorithm is verified by comparing it with the improved algorithm and the state-of-the-art search algorithms on 26 benchmark functions and the CEC2020 test suite, respectively. In addition, the proposed algorithm is used to optimize ten practical engineering optimization problems. Experimental results demonstrate that the proposed algorithm has strong competitiveness in this algorithm regarding computational power and convergence accuracy. Finally, the proposed algorithm is applied to two truss topology optimization designs. The experimental results demonstrate the applicability and potential of the proposed algorithm in practical applications. The proposed algorithm is a competitive optimization algorithm for solving optimization problems.
Recent advancements in renewable energy provide a clean, alternative source to fossil fuels. Smart grids (SGs) work by collecting data about customer requests, comparing them to current supply data, computing electricity costs, and so on. Because the processes are time-dependent, a dynamic estimate of SG stability is a critical system need. Analyzing fluctuations and disturbances in a dynamic manner is critical for the SGs to work properly. Recent advancements in data science, machine learning (ML), and deep learning (DL) models have facilitated the creation of useful stability prediction models for the SGs environment. In this regard, this study provides an Artificial Hummingbird (AHB) algorithm-based feature selection model for the SG environment with optimal DL enabled stability prediction (AHBFS-ODLSP). The AHBFS-ODLSP model is primarily concerned with the design of an AHB-based feature selection technique. Furthermore, a prediction system based on Multiheaded-Self Attention Long Short-Term Memory (MHSA-LSTM) is being created right now to predict the stability level. Then, using the symbiotic organism search (SOS) optimization technique, the MHSA-LSTM model hyperparameters were adjusted. The AHBFS and SOS algorithm designs have a big impact on how well the MHSA-LSTM model predicts stability. AHBFS-ODLSP model modifications are demonstrated through a number of simulations, and the outcomes are assessed in a variety of ways. The AHBFS-ODLSP method has achieved its maximum performance with a F score of 99.02 percent. The AHBFS-ODLSP model outperformed other prediction models, according to a thorough comparative analysis.
Cardiac arrhythmias indicate cardiovascular disease which is the leading cause of mortality worldwide, and can be detected by an electrocardiogram (ECG). Automated deep learning methods have been developed to overcome the disadvantages of manual interpretation by medical experts. The performance of the networks strongly depends on hyperparameter optimization (HPO), and this NP-hard problem is suitable for metaheuristic (MH) methods. In this study, a novel method is proposed for the HPO of a convolutional neural network (CNN) arrhythmia classifier using an MH algorithm. The approach utilizes our variant of an MH method, named the memory-enhanced artificial hummingbird algorithm, which has an additional memory unit that stores the evaluations of the solutions and reduces the computation time significantly. The study also proposes a novel fitness function that considers both the accuracy rate and the total number of parameters of each candidate network. Experiments were conducted on raw ECG samples from the MIT-BIH arrhythmia database. The proposed method was compared with five other MH methods and achieved equal or outperforming results, with classification accuracy reaching 98.87%. The proposed method yielded promising results in finding a high-performing solution with relatively lower complexity.
Real-world optimization problems require some advanced metaheuristic algorithms, which functionally sustain a variety of solutions and technically explore the tracking space to find the global optimal solution or optimizer. One such algorithm is the newly developed COOT algorithm that is used to solve complex optimization problems. However, like other swarm intelligence algorithms, the COOT algorithm also faces the issues of low diversity, slow iteration speed, and stagnation in local optimization. In order to ameliorate these deficiencies, an improved population-initialized COOT algorithm named COBHCOOT is developed by integrating chaos map, opposition-based learning strategy and hunting strategy, which are used to accelerate the global convergence speed and boost the exploration efficiency and solution quality of the algorithm. To validate the dominance of the proposed COBHCOOT, it is compared with the original COOT algorithm and the well-known natural heuristic optimization algorithm on the recognized CEC2017 and CEC2019 benchmark suites, respectively. For the 29 CEC2017 problems, COBHCOOT performed the best in 15 (51.72%, 30-Dim), 14 (48.28%, 50-Dim) and 11 (37.93%, 100-Dim) respectively, and for the 10 CEC2019 benchmark functions, COBHCOOT performed the best in 7 of them. Furthermore, the practicability and potential of COBHCOOT are also highlighted by solving two engineering optimization problems and four truss structure optimization problems. Eventually, to examine the validity and performance of COBHCOOT for medical feature selection, eight medical datasets are used as benchmarks to compare with other superior methods in terms of average accuracy and number of features. Particularly, COBHCOOT is applied to the feature selection of cervical cancer behavior risk dataset. The findings testified that COBHCOOT achieves better accuracy with a minimal number of features compared with the comparison methods.
Chameleon swarm algorithm (CSA) is a newly proposed swarm intelligence algorithm inspired by the chameleon’s foraging strategies of tracking, searching and attacking targets, and has shown well competitive performance with other state-of-the-art algorithms. Interestingly, CSA mathematically models and implements the steps of chameleon’s unique food-seeking behavior. Nevertheless, the original CSA suffers from the challenges of insufficient exploitation ability, ease of falling into local optima, and low convergence accuracy in complex large-scale applications. Aiming at these challenges, an efficient enhanced chameleon swarm algorithm termed MCSA, combined with fractional-order calculus, sinusoidal adjustment of parameters and crossover-based comprehensive learning (CCL) strategy, is developed in this paper. Firstly, a good fractional-order calculus strategy is added to update the chameleon’s attack velocity, which heightens the local search ability of CSA and accelerates the convergence speed of the algorithm; meanwhile, the sinusoidal adjustment of parameters is adopted to provide a better balance between exploration and exploitation of CSA. Secondly, the CCL strategy is used for the mutation to increase the diversity of the population and avoid becoming trapped in local optima. Three strategies enhance the overall performance and efficiency of the native CSA. Finally, the superiority of the presented MCSA is verified in detail by comparing it with native CSA and several state-of-the-art algorithms on the well-known 23 benchmark test functions, CEC2017 and CEC2019 test suites, respectively. Furthermore, the practicability of MCSA is also highlighted by six real-world engineering designs and two truss topology optimization problems. Simulation results demonstrate that MCSA has strong competitive capabilities and promising prospects. MCSA is potentially an excellent meta-heuristic algorithm for solving engineering optimization problems.
The Mountain Gazelle Optimizer (MGO), a novel meta-heuristic algorithm inspired by the social life and hierarchy of wild mountain gazelles, is suggested in this paper. In this algorithm, gazelles' hierarchical and social life is formulated mathematically and used to develop an optimization algorithm. The MGO algorithm is evaluated and tested using Fifty-two standard benchmark functions and seven different engineering problems. It is compared with nine other powerful meta-heuristic algorithms to validate the result. The significant differences between the comparative algorithms are demonstrated using Wilcoxon's rank-sum and Friedman's tests. Numerous experiments have shown that the MGO performs better than the comparable algorithms on utmost benchmark functions. In addition, according to the tests performed, the MGO maintains its search capabilities and shows good performance even when increasing the dimensions of optimization problems. The source codes of the MGO algorithm are publicly available at
https://www.mathworks.com/matlabcentral/fileexchange/1186 80-mountain-gazelle-optimizer.
Wireless Sensor Networks (WSN) are widely used in recent years due to the advancements in wireless and sensor technologies. Many of these applications require to know the location information of nodes. This information is useful to understand the collected data and to act on them. Existing localization algorithms make use of a few reference nodes for estimating the locations of sensor nodes. But, the positioning and utilization of reference nodes increase the cost and complexity of the network. To reduce the dependency on reference nodes, in this paper, we have developed a novel optimization based localization method using only two reference nodes for the localization of the entire network. This is achieved by reference nodes identifying a few more nodes as reference nodes by the analysis of the connectivity information. The sensor nodes then use the reference nodes to identify their locations in a distributive manner using Artificial Hummingbird Algorithm (AHA). We have observed that the localization performance of the reported algorithm at a lower reference node ratio is comparable with other algorithms at higher reference node ratios.
In view of the shortcomings such as slow search speed, low optimization precision and premature convergence of artificial hummingbird algorithm, an enhanced artificial hummingbird algorithm based on golden sine factor named DGSAHA is proposed. Firstly, chaos mapping is used to generate the initial candidate solution to increase the diversity of the population, which lays the foundation for the global search. Then, perturb the individuals by means of the differential variation between individuals on the group, thereby enhancing the diversity of the population, preserving the excellent individuals, eliminating the inferior individuals, and guiding the search process to approach the global optimal solution, avoiding the phenomenon of premature convergence. Finally, the golden sine factor were introduced in the guided foraging stage is conducive to the full exploration of the global optimal solution, reducing the search space for individuals to approach the optimal solution. And, it facilitates the balance between “exploration” and “exploitation” of algorithm. Thereby, the accuracy and speed of the DGSAHA can be improved to a certain extent. 25 classic functions, the CEC2014 and CEC2019 benchmark functions were tested, and several representative meta-heuristic algorithms and its improved algorithm are compared for evaluate the validity of DGSAHA. Meanwhile, the dimensional scalability of the variable-dimensional test function is discussed. The results of non-parametric statistical analysis and performance index show that DGSAHA in this paper has better comprehensive optimization performance, significantly improves the search speed and convergence precision, and has strong ability to get rid of the local optimal solution. Finally, the performance of DGSAHA and the practicability of truss structure are answered by three engineering examples of plane and space truss topology optimization problem. This optimization problem considers not only the static constraints such as stress, displacement and buckling, but also the dynamic constraints of frequency and motion stability. In order to avoid singularity and unnecessary analysis, the stiffness, mass and load matrices are reconstructed in finite element analysis. A lighter truss structure than the existing solution is obtained. The validity, extensibility and practicability of the algorithm are further illustrated.
The true modeling of solar photovoltaic units can boost their performance. However, on account of the lack of accurate solar cell parameters, cell modeling is erroneous. This is because the required parameters for modeling a trustworthy solar photovoltaic cell are not given in the manufacturer's data sheets. As a consequence, it is significant to accurately estimate the essential parameters of solar photovoltaic triple-diode models. Diverse optimization techniques have addressed this problem; nevertheless, due to premature convergence and local minima, most of the techniques obtain suboptimal results. Accordingly, artificial hummingbird technique (AHBT) is attempted for estimating SPV uncertain parameters in this current effort. Furthermore, the AHBT approach improves quality of solution by preserving a history of past locations that may be compared to the present ones. To demonstrate the competency of the AHBT, its performance is compared to other well-known frameworks and newly developed techniques (e.g. African vulture's optimization technique, Tuna swarm technique, and teaching learning studying-based technique) that are applied for the first time in this article. Some actual results of the minimum values of the errors in measured and estimated currents by employed ABHT method are 1.6945 mA for STM6-40/36 module, 0.5144 mA for mSi cell, and 0.4447 mA for KC200GT module. The solar photovoltaic modules are tested with varying temperature and irradiance sunshine levels. In addition to this, the calculated parameters are compared to experimental findings, including statistical analysis to validate the presentation of the AHBT. At last stage of this current effort, the principal performance of triple-diode models is investigated under varied operating temperatures and varied sun irradiances as well. Based on the findings, it can be concluded that the AHBT are effective at estimating solar photovoltaic models. The performance of a solar photovoltaic generating unit might be improved by precise modeling. ARTICLE HISTORY
Particle swarm optimization (PSO) is a population-based optimization method and has been successfully applied to solve many real-world problems. This method belongs to the stochastic optimization method and is mainly driven by two random streams utilized in the stochastic search mechanism, namely, individual (cognition) and social randomness effects. To our best knowledge, no research work has been conducted about the manipulation of the random stream assignment for stochastic search mechanism in the PSO algorithm. In this work, the influences of controlling randomness in the searching scheme of PSO is studied by introducing different pseudo random number (PRN) assignment strategies. The order-1 and order-2 stability analyses for particle dynamics under different PRN assignment strategies are also conducted to understand the influences. Stability analysis is carried out using the stochastic process theory. Our results show that the correlation caused by PRN has no effect on the unbiasedness of the expectation of particle position, but it would reduce or increase the variance of particle dynamics. Second, the convergent conditions of the PSO system under different PRN assignment strategies and the corresponding parameter selection ranges are provided. Finally, an empirical analysis via experimental simulations evaluated by six common swarm diversity measures, eight benchmark test functions, and two parameter tuples is presented.
Improving the performance of the electric distribution network is essential to meet the needs of the customer and guarantee the service continuity. Installing generators with small sizes known as distributed generators (DGs) can contribute to enhance the network operation by mitigating the network loss and improving the voltage profile. Integrating these generators in inappropriate places can cause serious consequences to the network operation. Therefore, this paper proposes a novel metaheuristic approach of artificial hummingbird algorithm (AHA) to identify the best locations and sizes of biomass-based DGs in radial distribution network. The proposed approach has enriched exploration and exploitation phases that enhancing its search capability and avoiding stuck in local optima. The network active power loss and the voltage deviation are selected as the targets to be minimized. Moreover, a new version of AHA is programmed to solve multi-objective problem with the purpose of mitigating both targets. The analysis is conducted on three radial distribution networks of IEEE 33-bus, IEEE 69-bus, and IEEE 119-bus. Three scenarios are implemented in each network, the first one is minimizing the active power loss, the second one is mitigating the voltage deviation, and the last one is multi-objective problem. Also, biomass-based DGs with unity, fixed, and optimal power factors are analyzed. Excessive comparison to fractal search algorithm, particle swarm optimizer, genetic algorithm, the whale optimization algorithm, sperm swarm optimization, tunicate swarm algorithm, pathfinder algorithm, seagull optimization algorithm, and sine cosine algorithm, multi-objective water cycle algorithm, multi-objective grey wolf optimizer, and multi-objective sparrow search algorithm is conducted. Moreover, statistical tests of Wilcoxon, Friedman, ANOVA, and Kruskal Wallis are performed to assess the performance of the proposed approach. The gotten results confirmed the preference and competence of the proposed approach in integrating the biomass-based DGs in radial distribution networks.
Nature-inspired algorithms known as metaheuristics have been significantly adopted by large-scale organizations and the engineering research domain due their several advantages over the classical optimization techniques. In the present article, a novel hybrid metaheuristic algorithm (HAHA-SA) based on the artificial hummingbird algorithm (AHA) and simulated annealing problem is proposed to improve the performance of the AHA. To check the performance of the HAHA-SA, it was applied to solve three constrained engineering design problems. For comparative analysis, the results of all considered cases are compared to the well-known optimizers. The statistical results demonstrate the dominance of the HAHA-SA in solving complex multi-constrained design optimization problems efficiently. Overall study shows the robustness of the adopted algorithm and develops future opportunities to optimize critical engineering problems using the HAHA-SA.
Artificial hummingbird algorithm (AHA) is a recently developed bio-based metaheuristic and it shows superior performance in handling single-objective optimization problems. Despite the merit, this algorithm can only solve problems with one objective. To solve complex multi-objective optimization problems, including engineering design problems, a multi-objective AHA (MOAHA) is developed in this study. In MOAHA, an external archive is employed to save Pareto optimal solutions, and a dynamic elimination-based crowding distance (DECD) method is developed to maintain this archive to effectively preserve the population diversity. In addition, a non-dominated sorting strategy is merged with MOAHA to construct a solution update mechanism, which effectively refines Pareto optimal solutions for improving the convergence of the algorithm. The superior results over 7 competitors on 28 benchmark functions in terms of convergence, diversity and solution distribution are demonstrated with a suite of comprehensive tests. The MOAHA algorithm is also applied to 5 real-world engineering design problems with multiple objectives, demonstrating its superiority in handling challenging real-world multi-objective problems with unknown true Pareto optimal solutions and fronts.
Arithmetic optimization algorithm (AOA) is a newly well-developed meta-heuristic algorithm that is inspired by the distribution behavior of main arithmetic operators in mathematics. Although the original AOA has shown well competitive performance with popular meta-heuristic algorithms, it still faces the issues of insufficient exploitation ability, ease of falling into local optima and low convergence accuracy in large-scale applications. In order to ameliorate these deficiencies, an enhanced hybrid AOA named CSOAOA, integrated with point set strategy, optimal neighborhood learning strategy and crisscross strategy, is developed in this paper. First, a good point set initialization strategy is added to obtain a higher-quality initial population, which improves the convergence speed of the algorithm. Then, the optimal neighborhood learning strategy is adopted to guide the individual’s search behavior and avoid the algorithm falling into the current local optimum, which boosts the search efficiency and calculation accuracy. Finally, by combining AOA with the crisscross optimization algorithm, the exploration and utilization ability of the crisscross algorithm are integrated into the CSOAOA. These strategies collaborate to enhance AOA in accelerating overall performance. The superiority of the proposed CSOAOA is comprehensively verified by comparing with the original AOA, six improved AOA and numerous celebrated and newly developed algorithms on the well-known 23 classical benchmark functions, IEEE Congress on Evolutionary Computation (CEC) 2019 test suite and IEEE CEC 2020 benchmark functions, respectively. Meanwhile, the practicability of CSOAOA is also highlighted by solving eight real-world engineering design problems. Furthermore, the statistical testing of CSOAOA has been conducted to validate its significance. Experimental results and statistical comparisons manifest the superior performance of CSOAOA over the comparison algorithms in terms of precision, convergence rate and solution quality. Therefore, CSOAOA is potentially a powerful and competitive meta-heuristic algorithm for solving complex engineering optimization problems.
This paper presents a novel meta-heuristic algorithm so-called White Shark Optimizer (WSO) to solve optimization problems over a continuous search space. The core ideas and underpinnings of WSO are inspired by the behaviors of great white sharks, including their exceptional senses of hearing and smell while navigating and foraging. These aspects of behavior are mathematically modeled to accommodate a sufficiently adequate balance between exploration and exploitation of WSO and to assist search agents to explore and exploit each potential area of the search space in order to achieve optimization. The search agents of WSO randomly update their position in connection with best-so-far solutions, to eventually arrive at the optimal outcome. The performance of WSO was comprehensively benchmarked on a set of 29 test functions from the CEC-2017 test suite for several dimensions. WSO was further applied to solve the benchmark problems of the CEC-2011 evolutionary algorithm competition to prove its reliability and applicability to real-world problems. A thorough analysis of computational and convergence results was presented to shed light on the efficacy and stability levels of WSO. The performance score of WSO in terms of several statistical methods was compared with 9 well-established meta-heuristics based on the solutions generated. Friedman’s and Holm’s tests of the results showed that WSO revealed reasonable solutions, in terms of global optimality, avoidance of local minima and solution quality, compared to other existing meta-heuristics.
This paper presents a novel bio-inspired algorithm inspired by starlings' behaviors during their stunning murmuration named starling murmuration optimizer (SMO) to solve complex and engineering optimization problems as the most appropriate application of metaheuristic algorithms. The SMO introduces a dynamic multi-flock construction and three new search strategies, separating, diving, and whirling. The separating search strategy aims to enhance the population diversity and local optima avoidance using a new separating operator based on the quantum harmonic oscillator. The diving search strategy aims to explore the search space sufficiently by a new quantum random dive operator, whereas the whirling search strategy exploits the vicinity of promising regions using a new operator called cohesion force. The SMO strikes a balance between exploration and exploitation by selecting either a diving strategy or a whirling strategy based on the flocks' quality. The SMO was tested using various benchmark functions with dimensions 30, 50, 100. The experimental results prove that the SMO is more competitive than other state-of-the-art algorithms regarding solution quality and convergence rate. Then, the SMO is applied to solve several mechanical engineering problems in which results demonstrate that it can provide more accurate solutions. A statistical analysis shows that SMO is superior to the other contenders.
In recent years, several metaheuristic algorithms have been introduced in engineering and scientific fields to address real-life optimization problems. In this study, a novel nature-inspired metaheuristics algorithm named as Snake Optimizer (SO) is proposed to tackle a various set of optimization tasks which imitates the special mating behavior of snakes. Each snake (male/female) fights to have the best partner if the existed quantity of food is enough and the temperature is low. This study mathematically mimics and models such foraging and reproduction behaviors and patterns to present a simple and efficient optimization algorithm. To verify the validity and superiority of the proposed method, SO is tested on 29 unconstrained Congress on Evolutionary Computation (CEC) 2017 benchmark functions and four constrained real-world engineering problems. SO is compared with other 9 well-known and newly developed algorithms such as Linear population size reduction- Success-History Adaptation for Differential Evolution (L-SHADE), Ensemble Sinusoidal incorporated with L-SHADE (LSHADE-EpSin), Covariance matrix adaptation evolution strategy (CMAES), Coyote Optimization Algorithm (COA), Moth-flame Optimization, Harris Hawks Optimizer, Thermal Exchange optimization, Grasshopper Optimization Algorithm, and Whale Optimization Algorithm. Experimental results and statistical comparisons prove the effectiveness and efficiency of SO on different landscapes with respect to exploration-exploitation balance and convergence curve speed. The source code is available via https://se.mathworks.com/matlabcentral/fileexchange/106465-snake-optimizer
This paper proposes a new metaheuristic algorithm called dwarf mongoose optimization algorithm (DMO) to solve the classical and CEC 2020 benchmark functions and 12 continuous/discrete engineering optimization problems. The DMO mimics the foraging behavior of the dwarf mongoose. The restrictive mode of prey capture (feeding) has dramatically affected the mongooses’ social behavior and ecological adaptations to compensate for efficient family nutrition. The compensatory behavioral adaptations of the mongoose are prey size, space utilization, group size, and food provisioning. Three social groups of the dwarf mongoose are used in the proposed algorithm, the alpha group, babysitters, and the scout group. The family forage as a unit, and the alpha female initiates foraging, determines the foraging path, the distance covered, and the sleeping mounds. A certain number of the mongoose population (usually a mixture of males and females) serve as the babysitters. They remain with the young until the group returns at midday or evening. The babysitters are exchanged for the first to forage with the group (exploitation phase). The dwarf mongooses do not build a nest for their young; they move them from one sleeping mound to another and do not return to the previously foraged site. The dwarf mongoose has adopted a seminomadic way of life in a territory large enough to support the entire group (exploration phase). The nomadic behavior prevents overexploitation of a particular area. It also ensures exploration of the whole territory because no previously visited sleeping mound is returned. The performance of the proposed DMO algorithm is compared with seven other algorithms to show its effectiveness in terms of different performance metrics and statistics. In most cases, the near-optimal solutions achieved by the DMO are better than the best solutions obtained by the current state-of-the-art algorithms. Matlab codes of DMO are available at https://www.mathworks.com/matlabcentral/fileexchange/105125-dwarf-mongoose-optimization-algorithm.
A new bio-inspired optimization algorithm called artificial hummingbird algorithm (AHA) is proposed in this work to solve optimization problems. The AHA algorithm simulates the special flight skills and intelligent foraging strategies of hummingbirds in nature. Three kinds of flight skills utilized in foraging strategies, including axial, diagonal, and omnidirectional flights, are modeled. In addition, guided foraging, territorial foraging, and migrating foraging are implemented, and a visit table is constructed to model the memory function of hummingbirds for food sources. AHA is validated using two sets of numerical test functions, and the results are compared with those obtained from various algorithms. The comparisons demonstrate that AHA is more competitive than other meta-heuristic algorithms and determine high-quality solutions with fewer control parameters. Additionally, the performance of AHA is validated on ten challenging engineering design cases studies. The results show the superior effectiveness of AHA in terms of computational burden and solution precision compared with the existing optimization techniques in literature. The study also explores the application of AHA in hydropower operation design to further demonstrate its potential in practice. The source code of AHA is publicly available at https://seyedalimirjalili.com/aha and https://www.mathworks.com/matlabcentral/fileexchange/101133-artificial-hummingbird-algorithm?s_tid=srchtitle.
This paper proposes a novel nature-inspired meta-heuristic optimizer, called Reptile Search Algorithm (RSA), motivated by the hunting behaviour of Crocodiles. Two main steps of Crocodile behaviour are implemented, such as encircling, which is performed by high walking or belly walking, and hunting, which is performed by hunting coordination or hunting cooperation. The mentioned search methods of the proposed RSA are unique compared to other existing algorithms. The performance of the proposed RSA is evaluated using twenty-three classical test functions, thirty CEC2017 test functions, ten CEC2019 test functions, and seven real-world engineering problems. The obtained results of the proposed RSA are compared to various existing optimization algorithms in the literature. The results of the tested three benchmark functions revealed that the proposed RSA achieved better results than the other competitive optimization algorithms. The results of the Friedman ranking test proved that the RSA is a significantly superior method than other comparative methods. Finally, the results of the examined engineering problems showed that the RSA obtained better results compared to other various methods.
The topological structure of the search agents in the swarm is a key factor in diversifying the knowledge between the population and balancing the designs of the exploration and intensification stages. Marine Predator Algorithm (MPA) is a recently introduced algorithm that mimics the interaction between the prey and predator in ocean. MPA has a vital issue in its structure. This drawback related to the number of iterations that is divided into the algorithm phases, hence the agents don’t have the adequate number of tries to discover the search landscape and exploit the optimal solutions. This situation affects the search process. Therefore, in this paper, the principle of the comprehensive learning strategy and memory perspective of the fractional calculus have been incorporated into MPA. They help to achieve an efficient sharing for the best knowledge and the historical experiences between the agents with the aim of escaping from the local solutions and avoiding the immature convergence. The developed fractional-order comprehensive learning MPA (FOCLMPA) has been examined with several multidimensional benchmarks from the CEC2017 and CEC2020 as challenging tested functions in the numerical validation part. For real-world applications, four engineering problems have been employed and a set of eighteen UCI datasets have been used to demonstrate the developed performance for feature selection optimization problem. The FOCLMPA has been compared with several well-regarded optimization algorithms via numerous statistical and non-parametric analyses to provide unbiased recommendation. The comparisons confirm the superiority and stability of FOCLMPA in handling the series of experiments with high qualified results and remarkable convergence curves.
Whale optimization algorithm was developed based on the prey-catching characteristics of the humpback whales. Due to its simple structure and efficiency, the researchers employed the algorithm to address numerous disciplines’ numerous problems. The profound analysis of the whale optimization algorithm discloses that the algorithm suffers from low exploration ability, leaser accuracy, and early convergence. Additionally, performance of the whale optimization algorithm and most of its variants in high-dimensional optimization problems is not satisfactory. This study proposes a new variant with several modifications to the basic whale optimization algorithm to solve high-dimensional problems. A unique selection parameter is introduced in the whale optimization algorithm to balance the algorithm’s global and local search phase. The co-efficient vectors A and C are modified and used effectively to explore and exploit the search region better. In the exploration phase, random movement is allowed to reduce the computational burden of the algorithm. An inertia weight is introduced in the exploitation phase for exhaustive search nearby the best solution. The proposed algorithm evaluates twenty-five benchmark functions using dimensions 100, 500, 1000, and 2000 and compared the results with the whale optimization algorithm and its variants. The estimated outcomes are also compared with seven basic metaheuristic algorithms. Finally, statistical analysis, complexity analysis, and convergence analysis are performed to establish the algorithm’s efficacy. All the test result suggests better performance of the proposed algorithm on higher-dimensional problems.
Recently, the numerical optimization field has attracted the research community to propose and develop various metaheuristic optimization algorithms. This paper presents a new metaheuristic optimization algorithm called Honey Badger Algorithm (HBA). The proposed algorithm is inspired from the intelligent foraging behavior of honey badger, to mathematically develop an efficient search strategy for solving optimization problems. The dynamic search behavior of honey badger with digging and honey finding approaches are formulated into exploration and exploitation phases in HBA. Moreover, with controlled randomization techniques, HBA maintains ample population diversity even towards the end of the search process. To assess the efficiency of HBA, 24 standard benchmark functions, CEC'17 test-suite, and four engineering design problems are solved. The solutions obtained using the HBA have been compared with ten well-known metaheuristic algorithms including Simulated annealing (SA), Particle Swarm Optimization (PSO), Covariance Matrix Adaptation Evolution Strategy (CMA-ES), Success-History based Adaptive Differential Evolution variants with linear population size reduction (L-SHADE), Moth-flame Optimization (MFO), Elephant Herding Optimization (EHO), Whale Optimization Algorithm (WOA), Grasshopper Optimisation Algorithm (GOA), Thermal Exchange Optimization (TEO) and Harris hawks optimization (HHO). The experimental results, along with statistical analysis, reveal the effectiveness of HBA for solving optimization problems with complex search-space, as well as, its superiority in terms of convergence speed and exploration-exploitation balance, as compared to other methods used in this study. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/98204-honey-badger-algorithm
Coverage Optimization is one of the most essential pre-requisites in Wireless Sensor Networks (WSNs) which plays a significant and impactful role in the field of environmental monitoring, surveillance, socio-economic Cyber-networkings, etc. The Whale Optimization Algorithm (WOA) is a swarm intelligence based Search-Algorithm while browsing for an optimal solution, but, it suffers from the poor & inconsistent exploration problem and that causes trapping of local optima in randomly deployed nodes that fail to guarantee network coverage. To resolve the issue, an innovative study has been researched which presents an embedded coverage optimization WSN and is based on Levy Flight mechanism with WOA (LWOA) .This updates the current search of location for positioning the sensors in the field. This mechanism can enhance and balance the exploration ability of WOA, which allows trapping of the local optima. This thichnically enhanced and updated proposal LWOA is validated by 25 benchmark optimization functions and is compared with existing Particle Swarm Optimization and WOA. From the experimental results, it can be construed and proved that the performance of Levy WOA (LWOA) has significantly improved the global search capacity and increase the efficiency of convergence, which immensely enhances the efficacy of coverage of nodes inturn amplifying the overall performance of the network. Finally, by using the K-Nearest Neighbour KNN(centroid) approach nearly 33% of nodes were optimized.
As an efficient and simple optimization algorithm, particle swarm optimization (PSO) has been widely applied to solve various real optimization problems. However, avoiding premature convergence and balancing the global exploration and local exploitation capabilities of the PSO remains two crucial problems. To overcome these drawbacks of PSO, a hybrid particle swarm optimization with crisscross learning strategy (PSO-CL) algorithm is proposed in this paper. In PSO-CL, in order to well balance the global exploration and local exploitation capabilities of PSO, a search direction adjustment mechanism based on subpopulation division operation is proposed. Meantime, to avoid the premature convergence and enhance the global search ability, a crossover-based comprehensive learning strategy (CCL) is adopted. Additionally, a stochastic example learning strategy (SEL) is introduced, which can assist collective information to be spread among separate sub-swarms, improve the local exploitation ability of the algorithm. 15 classic benchmark functions, CEC2017 test suite and two real-world optimization problems are utilized to verify the promising performance of PSO-CL, experimental results and statistical analysis indicate that PSO-CL has competitive performance compared with state-of-the-art PSO variants.
The shape optimization of developable surfaces is a pivotal and knotty technique in CAD/CAM and used in many product manufacturing planning operations, e.g., for ships, aircraft wing, automobiles, garments, etc. In this paper, an improved marine predators algorithm (MPA) is used to optimize the shape of shape-adjustable generalized cubic developable Ball (SGCD-Ball, for short) surfaces. Firstly, to solve the problems of shape adjustment and optimization for developable surfaces, we present a class of novel shape-adjustable generalized cubic Ball basis functions, and then construct the SGCD-Ball surfaces with shape parameters by using the presented basis functions. The shapes of the surfaces can be adjusted and optimized expediently by using the shape parameters. Secondly, the shape optimization of developable surfaces is mathematically an optimization problem that can be effectively dealt with by swarm intelligence algorithm. In this regard, by incorporating a quasi-opposition strategy and a differential evolution algorithm to the MPA, an improved MPA called ODMPA is developed to increase the population diversity and enhance its capability of jumping out of the local minima. Furthermore, the superiority of the proposed ODMPA is verified by comparing with standard MPA , modified MPA and several well-known intelligent algorithms on 23 classical benchmark functions, the CEC'17 test suite and three engineering optimization problems, respectively. Finally, by minimizing the energy of the SGCD-Ball surfaces as the evaluation standard, the shape optimization models of the corresponding enveloping and spine curve developable surfaces are established. The ODMPA is utilized to solve the shape optimization models, and the SGCD-Ball surfaces with minimum energy are obtained. Some representative numerical examples demonstrate the superiority of the proposed ODMPA in effectively solving the shape optimization models in terms of precision and robustness.
Recently, many intelligent algorithms have been proposed to find the best solution for complex engineering problems. These algorithms can search volatile and multi-dimensional solution spaces and find optimal answers timely. In this paper, a new meta-heuristic method is proposed that inspires the behavior of the swarm of birds called Coot. The Coot algorithm imitates two different modes of movement of birds on the water surface: in the first phase, the movement of birds is irregular, and in the second phase, the movements are regular. The swarm moves towards a group of leading leaders to reach a food supply; the movement of the end of the swarm is in the form of a chain of coots, each of coot which moves behind its front coots. The algorithm then runs on a number of test functions, and the results are compared with well-known optimization algorithms. In addition, to solve several real problems, such as Tension/Compression spring, Pressure vessel design, Welded Beam Design, Multi-plate disc clutch brake, Step-cone pulley problem, Cantilever beam design, reducer design problem, and Rolling element bearing problem this algorithm is used to confirm the applicability of this algorithm. The results show that this algorithm is capable to outperform most of the other optimization methods. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/89102-coot-optimization-algorithm
This paper proposes a novel population-based optimization method, called Aquila Optimizer (AO), which is inspired by the Aquila’s behaviors in nature during the process of catching the prey. Hence, the optimization procedures of the proposed AO algorithm are represented in four methods; selecting the search space by high soar with the vertical stoop, exploring within a diverge search space by contour flight with short glide attack, exploiting within a converge search space by low flight with slow descent attack, and swooping by walk and grab prey. To validate the new optimizer’s ability to find the optimal solution for different optimization problems, a set of experimental series is conducted. For example, during the first experiment, AO is applied to find the solution of well-known 23 functions. The second and third experimental series aims to evaluate the AO’s performance to find solutions for more complex problems such as thirty CEC2017 test functions and ten CEC2019 test functions, respectively. Finally, a set of seven real-world engineering problems are used. From the experimental results of AO that compared with well-known meta-heuristic methods, the superiority of the developed AO algorithm is observed.
This paper formulates the optimal power flow (OPF) problem with the consideration of minimizing many objective functions including the basic fuel cost, fuel cost with valve-point effects, transmission active power loss, basic fuel cost with transmission active power loss as well as basic fuel cost with voltage deviation. To solve the OPF problem, a novel crisscross search based grey wolf optimizer (CS-GWO) is proposed, in which the hunting operation in GWO is firstly modified by introducing a greedy mechanism and then the horizontal crossover operator is added to refine the first three ranking wolves. In addition, the vertical crossover operator is applied to maintain the population diversity so as to prevent the premature convergence, which provides a unique mechanism for GWO to get rid of dimensional local optimum. The cooperation of last two operators can accelerate convergence speed and avoid falling into dimensional local optimum of hunting process. The proposed CS-GWO is validated on IEEE 30-bus system and IEEE 118-bus system. The experimental results demonstrate the CS-GWO has obvious advantage over the original GWO and the other state-of-art heuristic algorithms, especially in large-scale system.
This paper proposes a new meta-heuristic algorithm inspired by horses’ herding behavior for high-dimensional optimization problems. This method, called the Horse herd Optimization Algorithm (HOA), imitates the social performances of horses at different ages using six important features: grazing, hierarchy, sociability, imitation, defense mechanism and roam. The HOA algorithm is created based on these behaviors, which has not existed in the history of studies so far. A sensitivity analysis is also performed to obtain the best values of coefficients used in the algorithm. HOA has a very good performance in solving complex problems in high dimensions, due to the large number of control parameters based on the behavior of horses at different ages. The proposed algorithm is compared with popular nature-inspired optimization algorithms, including grasshopper optimization algorithm (GOA), sine cosine algorithm (SCA), multi-verse optimizer (MVO), moth-flame optimizer (MFO), dragonfly algorithm (DA), and grey wolf optimizer (GWO). Solving several high-dimensional benchmark functions (up to 10,000 dimensions) shows that the proposed algorithm is highly efficient for high-dimensional global optimization problems. The HOA algorithm also outperforms the mentioned popular optimization algorithms for the case of accuracy and efficiency with lowest computational cost and complexity.
To solve constrained portfolio selection model effectively, an improved quantum-behaved particle swarm optimization algorithm(LQPSO) is presented. Firstly, considering its practicality in real dealing process, a class of fuzzy portfolio models with transaction costs and background risk is established. Then in the design of improved algorithm, Lévy flight strategy and contraction–expansion coefficient with nonlinear structure are taken into account for enhancing particle’s exploration ability, and premature prevention mechanism is used to increase population diversity. According to the following performance test, LQPSO demonstrates better convergence and robustness than PSO with inertia weight, QPSO and QPSO with a hybrid probability distribution in 12 benchmark functions. Furthermore, experimental results indicate that LQPSO outperforms several metaheuristics when seeking optimal solution for the fuzzy portfolio model with constraints.