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Image segmentation methods have received widespread attention in face image recognition, which can divide each pixel in the image into different regions and effectively distinguish the face region from the background for further recognition. Threshold segmentation, a common image segmentation method, suffers from the problem that the computational complexity shows exponential growth with the increase in the segmentation threshold level. Therefore, in order to improve the segmentation quality and obtain the segmentation thresholds more efficiently, a multi-threshold image segmentation framework based on a meta-heuristic optimization technique combined with Kapur's entropy is proposed in this study. A meta-heuristic optimization method based on an improved grey wolf optimizer variant is proposed to optimize the 2D Kapur's entropy of the greyscale and nonlocal mean 2D histograms generated by image computation. In order to verify the advancement of the method, experiments compared with the state-of-the-art method on IEEE CEC2020 and face image segmentation public dataset were conducted in this paper. The proposed method has achieved better results than other methods in various tests at 18 thresholds with an average feature similarity of 0.8792, an average structural similarity of 0.8532, and an average peak signal-to-noise ratio of 24.9 dB. It can be used as an effective tool for face segmentation. [ABSTRACT FROM AUTHOR]

The determination of photovoltaic (PV) parameters is of great importance for the reliability of solar system operation, continuity of the load power consumption, and control management of the energy source. Therefore, this study proposes an advanced backtracking search optimization algorithm (BSA) equipped with teaching and learning‐based optimization (TLBO), named TLBOBSA, to accurately simulate the PV model. During the evaluation of the proposed algorithm, the concept of teaching from TLBO is introduced into the BSA to guide optimal individuals, thus improving the convergence rate of the algorithm. The learning behavior among individuals in the student phase of TLBO facilitates interindividual learning and provides beneficial information for its evolution, which is introduced into the BSA to ensure the diversity of the population. The comprehensive test results of different PV module models in different environmental conditions show that the proposed algorithm is more advantageous for parameter extraction than other existing algorithms. This can be seen in the simulation experiments of two commercial PV models, where the simulated current is consistent with the measured current at each measured voltage. This demonstrates that the proposed TLBOBSA is an accurate and reliable tool for evaluating unknown parameters of PV models. [ABSTRACT FROM AUTHOR]

Moth-flame optimization is a typical meta-heuristic algorithm, but it has the shortcomings of low-optimization accuracy and a high risk of falling into local optima. Therefore, this paper proposes an enhanced moth-flame optimization algorithm named HMCMMFO, which combines the mechanisms of hybrid mutation and chemotaxis motion, where the hybrid-mutation mechanism can enhance population diversity and reduce the risk of stagnation. In contrast, chemotaxis-motion strategy can better utilize the local-search space to explore more potential solutions further; thus, it improves the optimization accuracy of the algorithm. In this paper, the effectiveness of the above strategies is verified from various perspectives based on IEEE CEC2017 functions, such as analyzing the balance and diversity of the improved algorithm, and testing the optimization differences between advanced algorithms. The experimental results show that the improved moth-flame optimization algorithm can jump out of the local-optimal space and improve optimization accuracy. Moreover, the algorithm achieves good results in solving five engineering-design problems and proves its ability to deal with constrained problems effectively. [ABSTRACT FROM AUTHOR]

Measurement data based on current and voltage of photovoltaic (PV) systems and the establishment of more accurate and stable solar system models are of typical significance for the design, control, evaluation and optimization of PV systems. Accurate and stable parameter evaluation for PV systems needs to be based on more efficient optimization techniques to achieve efficient energy conversion from solar energy. Therefore, this paper proposes a novel and efficient optimization technique enhanced colony predation algorithm to solve the complex PV parameter identification problem named ECPA. By fusing extremal optimization strategy and Nelder–Mead simplex method enables ECPA to further develop in the neighborhood of potential optimal solutions while improving the position of inferior agent candidates, and finally has the ability to search globally beyond the local optimum. To verify the optimization efficiency of ECPA, the first part verifies the efficiency of ECPA in solving complex high‐dimensional and multimodal problems by conducting competitive comparison experiments at the IEEE CEC 2020 benchmark case. In the second part, ECPA is compared with nine similar published state‐of‐the‐art algorithms, and competitive tests for PV parameter identification under single diode model, double diode model, triple diode model and PV module model (PV) are conducted. Finally, we focused on three different commercial PV models (thin film ST40, monocrystalline SM55, and multicrystalline KC200GT) to test the accuracy of ECPA in evaluating PV parameters. The test results show that ECPA is able to maintain a high level of accuracy and stability when dealing with commercial PV models in complex environments. The experimental results demonstrate that ECPA outperforms other algorithms in terms of data fitting, stability, convergence speed and convergence accuracy. All the competitive experimental results show that ECPA can be a novel technique with the best performance for identifying the parameters to be determined in solar PV systems. [ABSTRACT FROM AUTHOR]

In recent years, a range of novel and pseudonovel optimization algorithms has been proposed for solving engineering problems. Swarm intelligence optimization algorithms (SIAs) have become popular methods, and the whale optimization algorithm (WOA) is one of the highly discussed SIAs. However, regardless of novelty concerns about this method, the basic WOA is a weak method compared to top differential evolutions and particle swarm variants, and it suffers from the problem of poor initial population quality and slow convergence speed. Accordingly, in this paper, to increase the diversity of WOA versions and enhance the performance of WOA, a new WOA variant, named LXMWOA, is proposed, and based on the L'evy initialization strategy, the directional crossover mechanism, and the directional mutation mechanism. Specifically, the introduction of the L'evy initialization strategy allows initial populations to be dynamically distributed in the search space and enhances the global search capability of the WOA. Meanwhile, the directional crossover mechanism and the directional mutation mechanism can improve the local exploitation capability of the WOA. To evaluate its performance, using a series of functions and three models of engineering optimization problems, the LXMWOA was compared with a broad array of competitive optimizers. The experimental results demonstrate that the LXMWOA is significantly superior to its exploration and exploitation capability peers. Therefore, the proposed LXMWOA has great potential to be used for solving engineering problems. [ABSTRACT FROM AUTHOR]

• An enhanced political optimizer (QNMPO) is proposed to realize the extraction of photovoltaic models parameters. • The performance of the proposed QNMPO algorithm is compared with some well-known competing algorithms. • The stability performance of QNMPO was tested on three commercial PV models at different temperature levels and irradiation levels. • QNMPO exhibits better convergence speed and accuracy. Evaluating the PV system parameters is crucial for the more efficient utilization of sustainable solar energy. Due to PV systems' nonlinear and multimodal nature, efficient evaluation of PV system parameters is still a very challenging task. This paper proposes an improved political optimization algorithm, namely the QNMPO algorithm, which combines quantum rotation gate and Nelder-Mead simplex (NMs). It can be used to evaluate unknown parameters of PV systems and solar cells efficiently. In QNMPO, the quantum rotation gate method can rotate the population of agents to a more favorable position for finding the optimal solution, making the individuals in the middle of the population communicate more frequently and enhancing the population's diversity. In addition, the NMs method can improve the solution quality by better searching the neighborhoods near the optimal solution and then strengthen the advantage of local development of the algorithm so that it can converge to the global optimal solution faster. The developed QNMPO algorithm extracts the unknown parameters for single diode, double diode, triple diode and photovoltaic modules in this study. It is compared with some other representative algorithms. The experimental results show that QNMPO outperforms similar algorithms in convergence speed, solution accuracy, and better solution performance. QNMPO was then used to successfully extract the best parameter values for three real PV models (three commercial PV models (thin-film ST40, monocrystalline SM55, and multi crystalline KC200GT)) at different temperatures and different irradiance levels. The results also show that QNMPO performs consistently and accurately enough under varying temperatures and irradiation. Therefore, the QNMPO algorithm proposed in this paper can be a promising parameter extraction method for solar PV systems with good performance. [ABSTRACT FROM AUTHOR]

Random Weight Networks have been extensively used in many applications in the last decade because it has many strong features such as fast learning and good generalization performance. Most of the traditional training techniques for Random Weight Networks randomly select the connection weights and hidden biases and thus suffer from local optima stagnation and degraded convergence. The literature shows that stochastic population-based optimization techniques are well regarded and reliable alternative for Random Weight Networks optimization because of high local optima avoidance and flexibility. In addition, many practitioners and non-expert users find it difficult to set the other parameters of the network like the number of hidden neurons, the activation function, and the regularization factor. In this paper, an approach for training Random Weight Networks is proposed based on a recent variant of particle swarm optimization called competitive swarm optimization. Unlike most of Random Weight Networks training techniques, which are used to optimize only the input weights and hidden biases, the proposed approach will automatically tune the weights, biases, the number of hidden neurons, and regularization factor as well as the embedded activation function in the network, simultaneously. The goal is to help users to effectively identify a proper structure and hyperparameter values to their applications while obtaining reasonable prediction results. Twenty benchmark classification datasets are used to compare the proposed approach with different types of basic and hybrid Random Weight Network-based models. The experimental results on the benchmark datasets show that the reasonable classification results can be obtained by automatically tuning the hyperparameters using the proposed approach. [ABSTRACT FROM AUTHOR]

This study develops an improved moth-flame optimization algorithm, which is a recently proposed optimizer based on moth behavior in nature. It has achieved favorable results in medical science, educational evaluation, and other fields. However, the convergence rate of the original moth-flame optimization algorithm is too fast in the running process, and it is prone to fall into local optimum, which leads to the failure to produce the high-quality optimal result. Accordingly, this paper proposes a reinforced technique for the moth-flame optimization algorithm. Firstly, the simulated annealing strategy is introduced into the moth-flame optimization algorithm to boost the advantage of the algorithm in the local exploitation process. Then, the idea of the quantum rotation gate is integrated to enhance the global exploration ability of the algorithm and ameliorate the diversity of the moth. These two steps maintain the relationship between exploitation and exploration as well as strengthen the performance of the algorithm in both phases. After that, the method is compared with ten well-regarded and ten alternative algorithms on benchmark functions to verify the effectiveness of the approach. Also, the Wilcoxon signed rank and Friedman assessment were performed to verify the significance of the proposed method against other counterparts. The simulation results reveal that the two introduced strategies significantly improve the exploration and exploitation capacity of moth-flame optimization algorithm. Finally, the algorithm is utilized to feature selection and two engineering problems, including pressure vessel design and multiple disk clutch brake problems. In these practical applications, the novel algorithm also achieves particularly notable results, which also illustrates that the algorithm is qualified is an effective auxiliary appliance in solving complex optimization problems. [ABSTRACT FROM AUTHOR]

Whale optimization algorithm (WOA) is a recent nature-inspired metaheuristic that mimics the cooperative life of humpback whales and their spiral-shaped hunting mechanism. In this research, it is first argued that the exploitation tendency of WOA is limited and can be considered as one of the main drawbacks of this algorithm. In order to mitigate the problems of immature convergence and stagnation problems, the exploitative and exploratory capabilities of modified WOA in conjunction with a learning mechanism are improved. In this regard, the proposed WOA with associative learning approaches is combined with a recent variant of hill climbing local search to further enhance the exploitation process. The improved algorithm is then employed to tackle a wide range of numerical optimization problems. The results are compared with different well-known and novel techniques on multi-dimensional classic problems and new CEC 2017 test suite. The extensive experiments and statistical tests show the superiority of the proposed BMWOA compared to WOA and several well-established algorithms. [ABSTRACT FROM AUTHOR]

Water cycle algorithm (WCA) is a new population-based meta-heuristic technique. It is originally inspired by idealized hydrological cycle observed in natural environment. The conventional WCA is capable to demonstrate a superior performance compared to other well-established techniques in solving constrained and also unconstrained problems. Similar to other meta-heuristics, premature convergence to local optima may still be happened in dealing with some specific optimization tasks. Similar to chaos in real water cycle behavior, this article incorporates chaotic patterns into stochastic processes of WCA to improve the performance of conventional algorithm and to mitigate its premature convergence problem. First, different chaotic signal functions along with various chaotic-enhanced WCA strategies (totally 39 meta-heuristics) are implemented, and the best signal is preferred as the most appropriate chaotic technique for modification of WCA. Second, the chaotic algorithm is employed to tackle various benchmark problems published in the specialized literature and also training of neural networks. The comparative statistical results of new technique vividly demonstrate that premature convergence problem is relieved significantly. Chaotic WCA with sinusoidal map and chaotic-enhanced operators not only can exploit high-quality solutions efficiently but can outperform WCA optimizer and other investigated algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a continuous harmony search (HS) approach is investigated for tackling the Uncapacitated Facility Location (UFL) task. This article proposes an efficient modified HS-based optimizer to improve the performance of HS on complex spatial tasks like UFL problems. For this aim, opposition-based learning (OBL) and chaotic patterns are utilized. The proposed technique is examined against several UFL benchmark challenges in specialized literature. Then, the modified HS is substantiated in detail and compared to the basic HS and some other methods. The results showed that new opposition-based chaotic HS (OBCHS) algorithm not only can exploit better solutions competently but it is able to outperform HS in solving UFL problems. [ABSTRACT FROM AUTHOR]

• A novel weighted mean of vectors (INFO) is proposed for global optimization. • The performance of INFO is verified by comparison against other competitive algorithms. • INFO has faster convergence speed and accuracy compared with others. • INFO was validated on 48 functions and four remarkable engineering test cases. • Excellent results have been obtained in engineering experiments. This study presents the analysis and principle of an innovative optimizer named weIghted meaN oF vectOrs (INFO) to optimize different problems. INFO is a modified weight mean method, whereby the weighted mean idea is employed for a solid structure and updating the vectors' position using three core procedures: updating rule , vector combining , and a local search. The updating rule stage is based on a mean-based law and convergence acceleration to generate new vectors. The vector combining stage creates a combination of obtained vectors with the updating rule to achieve a promising solution. The updating rule and vector combining steps were improved in INFO to increase the exploration and exploitation capacities. Moreover, the local search stage helps this algorithm escape low-accuracy solutions and improve exploitation and convergence. The performance of INFO was evaluated in 48 mathematical test functions, and five constrained engineering test cases including optimal design of 10-reservoir system and 4-reservoir system. According to the literature, the results demonstrate that INFO outperforms other basic and advanced methods in terms of exploration and exploitation. In the case of engineering problems, the results indicate that the INFO can converge to 0.99% of the global optimum solution. Hence, the INFO algorithm is a promising tool for optimal designs in optimization problems, which stems from the considerable efficiency of this algorithm for optimizing constrained cases. The source codes of INFO algorithm are publicly available at https://imanahmadianfar.com. and https://aliasgharheidari.com/INFO.html. [ABSTRACT FROM AUTHOR]

The seagull optimization algorithm (SOA) is a novel swarm intelligence algorithm proposed in recent years. The algorithm has some defects in the search process. To overcome the problem of poor convergence accuracy and easy to fall into local optimality of seagull optimization algorithm, this paper proposed a new variant SOA based on individual disturbance (ID) and attraction-repulsion (AR) strategy, called IDARSOA, which employed ID to enhance the ability to jump out of local optimum and adopted AR to increase the diversity of population and make the exploration of solution space more efficient. The effectiveness of the IDARSOA has been verified using representative comprehensive benchmark functions and six practical engineering optimization problems. The experimental results show that the proposed IDARSOA has the advantages of better convergence accuracy and a strong optimization ability than the original SOA. [ABSTRACT FROM AUTHOR]

• A novel global optimization algorithm, rime optimization algorithm (RIME), is proposed. • RIME simulates the growth and crossover behavior of the rime-particle population. • The performance of RIME is adequately discussed based on benchmark functions. • RIME has better convergence accuracy and speed compared to other methods. • RIME is applied to solving five practical engineering optimization problems. This paper proposes an efficient optimization algorithm based on the physical phenomenon of rime-ice, called the RIME. The RIME algorithm implements the exploration and exploitation behaviors in the optimization methods by simulating the soft-rime and hard-rime growth process of rime-ice and constructing a soft-rime search strategy and a hard-rime puncture mechanism. Meanwhile, the greedy selection mechanism in the algorithm is improved, and the population is updated in the stage of selecting the optimal solution to enhance the exploitation capability of the RIME. In the experimental, this paper conducts qualitative analysis experiments on the RIME to clarify the characteristics of the algorithm in the process of finding the optimal solution. The performance of RIME is then tested on a total of 42 functions in the classic IEEE CEC2017 and the latest IEEE CEC2022 test sets. The proposed algorithm is compared with 10 well-established algorithms and 10 latest improved algorithms to verify its performance advantage. In addition, this paper designs experiments for the parametric analysis of RIME to discuss the potential of the algorithm in running different parameters and handling different problems. Finally, this paper applies RIME to five practical engineering problems to verify its effectiveness and superiority in real-world problems. The statistical and comparison results show that the RIME is a strong and competitive algorithm. The source code of the RIME 1 1 Source codes of RIME algorithm are also available at: https://codeocean.com/capsule/4472937/tree and https://www.mathworks.com/matlabcentral/fileexchange/124610-rime-a-physics-based-optimization and https://github.com/aliasgharheidaricom/RIME-A-physics-based-optimization. algorithm and associated files are publicly accessible at https://aliasgharheidari.com/RIME.html. [ABSTRACT FROM AUTHOR]

The optimization field suffers from the metaphor-based " pseudo-novel " or " fancy " optimizers. Most of these cliché methods mimic animals' searching trends and possess a small contribution to the optimization process itself. Most of these cliché methods suffer from the locally efficient performance, biased verification methods on easy problems, and high similarity between their components' interactions. This study attempts to go beyond the traps of metaphors and introduce a novel metaphor-free population-based optimization method based on the mathematical foundations and ideas of the Runge Kutta (RK) method widely well-known in mathematics. The proposed RUNge Kutta optimizer (RUN) was developed to deal with various types of optimization problems in the future. The RUN utilizes the logic of slope variations computed by the RK method as a promising and logical searching mechanism for global optimization. This search mechanism benefits from two active exploration and exploitation phases for exploring the promising regions in the feature space and constructive movement toward the global best solution. Furthermore, an enhanced solution quality (ESQ) mechanism is employed to avoid the local optimal solutions and increase convergence speed. The RUN algorithm's efficiency was evaluated by comparing with other metaheuristic algorithms in 50 mathematical test functions and four real-world engineering problems. The RUN provided very promising and competitive results, showing superior exploration and exploitation tendencies, fast convergence rate, and local optima avoidance. In optimizing the constrained engineering problems, the metaphor-free RUN demonstrated its suitable performance as well. The authors invite the community for extensive evaluations of this deep-rooted optimizer as a promising tool for real-world optimization. The source codes, supplementary materials, and guidance for the developed method will be publicly available at different hubs at http://imanahmadianfar.com and http://aliasgharheidari.com/RUN.html. [ABSTRACT FROM AUTHOR]

This paper presents an enhanced Harris Hawks Optimizer (HHO) to tackle global optimization and determine the optimal threshold values for multi-level image segmentation problems. HHO is a new swarm-based metaheuristic technique that simulates the behaviors of Harris hawks during the process of catching the rabbits. The HHO established its strong performance as a swarm-based optimization technique. However, population-based HHO still may face some limitations in dealing with more multi-modal and composition problems. For example, this optimizer may be stagnated to local optima and turned to immature convergence when performing phases of exploration and exploitation. To mitigate these drawbacks, an improved HHO is proposed that considers the salp swarm algorithm (SSA) as a competitive method to enhance the balance between its exploration and exploitation trends. Firstly, a set of solutions is generated. Then, we divide those solutions into two halves, where the exploratory and exploitative phases of HHO will be applied to the first half, and the searching stages of SSA will be used to update the solutions in the second half. Thereafter, the best solutions from the union sub-populations are selected to continue the iterative process. According to the improved HHO, which is called HHOSSA, an effective multi-level image segmentation approach is also developed in this research. A comprehensive set of experiments are performed using 36 IEEE CEC 2005 benchmark functions and 11 natural gray-scale images. Extensive results and comparisons show the high ability of the SSA to improve the HHO's performance since the proposed HHOSSA achieves a more stable performance compared to HHO, SSA, and many other well-known methods. • This paper presents an enhanced Harris Hawks Optimizer (HHO). • A comprehensive experiment is performed using more than forty five benchmark problems. • Extensive results show the more stable performance of the proposed variant of HHO. [ABSTRACT FROM AUTHOR]

• This paper proposes a boosted MFO for global search and kernel extreme learning machines. • Two strategies have been introduced into MFO for a more stable balance. • The extensive results on benchmark problems and real datasets have been performed. • A hybrid kernel extreme learning machine model is established for financial stress prediction. Image, graphical abstract Moth-flame optimization algorithm (MFO) is a new nature-inspired meta-heuristic based on the navigation routine of moths in the environment known as transverse orientation. For some complex optimization tasks, especially high dimensional and multimodal problems, the conventional MFO may face problems in the convergence trends or be trapped into the local and deceptive optima. Therefore, in this study, two strategies have been introduced into the conventional MFO to get a more stable sense of balance between the exploration and exploitation propensities. First, Gaussian mutation is employed to increase the population diversity of MFO. Then, a chaotic local search is applied to the flame updating process of MFO for better exploiting the locality of the solutions. The proposed CLSGMFO approach was compared against a wide range of well-known classical metaheuristic algorithms (MAs) and various advanced MAs using 23 classical benchmark functions. It was shown that the designed CLSGMFO can outperform most of the popular MAs in terms of solution quality and convergence speed. Moreover, based on CLSGMFO, a hybrid kernel extreme learning machine model, which is called CLSGMFO-KELM, is established to deal with financial stress prediction scenarios. To investigate the effectiveness of the CLSGMFO-KELM model, the proposed hybrid system was tested on two widely used financial datasets and compared against a broad array of popular classifiers. The results demonstrate that the proposed learning scheme can offer a superior kernel extreme learning machine model with excellent predictive performance. Accordingly, the proposed CLSGMFO can serve as an effective and efficient computer-aided tool for financial prediction. [ABSTRACT FROM AUTHOR]

• A multi-strategy boosted mutative WOA is proposed for global optimization. • A chaotic initialization strategy, a chaotic local search and Gaussian mutation are incorporated into WOA. • The extensive results on benchmark problems and three classical engineering design problems reveal the excellent performance. Image, graphical abstract This paper presents an improved Whale Optimization Algorithm (WOA) for global optimization. WOA is a recently introduced meta-heuristic algorithm mimicking the hunting behavior of humpback whales. Owing to its simplicity in exploratory and exploitative operators and the satisfactory efficacy, this algorithm has found its place among the well-established population-based approach utilized in many engineering and science areas. However, this method is easy to fall into local optimum when dealing with some optimization cases. In order to further enhance its exploratory and exploitative performance, three strategies are incorporated into the original method to keep a better balance between exploitation and exploration tendencies. First, the chaotic initialization phase is introduced into the optimizer to initiate the swarm of chaos-triggered whales. Then, Gaussian mutation is employed to intensify the diversity level of the evolving population. At last, a chaotic local search with a 'shrinking' strategy is used to enhance the exploitative leanings of the basic optimizer. In order to verify the effectiveness of the improved WOA, it is compared to four meta-heuristic and state-of-the-art evolutionary algorithms on representative benchmark functions. Trial results and simulations reveal that not only the proposed improved WOA is significantly better than those basic algorithms including original WOA but also it is superior to compared state-of-the-art approaches. Moreover, the proposed algorithm is successfully applied to realize three constrained engineering test cases, which the results suggest that the improved WOA can effectively deal with the constrained functions as well. [ABSTRACT FROM AUTHOR]

Fruit fly optimization algorithm (FOA) is a well-known optimization algorithm with a well-designed structure and superiority of fewer parameters, more effortless adjustment, and competitive and fast computation time. Up till now, FOA has been effectively applied to numerous fields, such as financial forecast and medicine, and it achieves favorable results. However, some aspects need to be enhanced when dealing with some function optimization cases. This method is inclined to falling into local optima with a slow convergence. In this paper, the following behavior-driven multi-population FOA is proposed to relieve these drawbacks, which combines the following mechanism of artificial fish swarm algorithm with the unique searching ability of different types of fruit flies. The chaotic global disturbance is introduced to improve the global exploration ability of the original FOA and reduce the probability of advanced FOA falling into the local extreme. The proposed FOA, it is compared with the advanced FOA with several well-established algorithms and the latest improved optimizers in different dimensions horizontally and vertically to substantiate the effectiveness of the. It is also applied advanced FOA to two practical engineering optimization projects. Systematic analysis and experimental data indicate that the advanced FOA variant outperforms the original FOA and the latest improved algorithms. An online repository will support this research at http://aliasgharheidari.com for any communication and guidance for future works. [ABSTRACT FROM AUTHOR]

• An improved Fruit Fly Optimization Algorithm (WFOA) is proposed. • Whale hunting strategy is integrated into the original FOA. • The greater performance of WFOA is verified over a set of advanced algorithms. • WFOA is rigorously validated on CEC2014 and CEC2011 functions. Fruit fly optimization algorithm (FOA) is a well-established meta-heuristic method with a clear core concept, a straightforward computation, and a code framework that is easy to build. In the case of large scale and multifaceted practical problems, the optimization effect of FOA may be unsatisfactory, and it is prone to stagnation. In this paper, to enrich the exploration and exploitation capability of the classic FOA, an effective whale-inspired hunting strategy is introduced to replace the random search plan of the original FOA, which we named it as WFOA. The proposed WFOA is compared with 9 state-of-the-art FOA's variants on a comprehensive set of 23 benchmark set and 30 IEEE CEC 2014 functions and advanced algorithms on a set of 21 test functions to validate its effectiveness. In addition, the effectiveness of WFOA is also verified on 20 IEEE CEC 2011 benchmark problems for tackling real-world problems. The statistical data shows that developed components effectively expand the exploration and exploitation capacity of the original FOA. [ABSTRACT FROM AUTHOR]

• This paper proposes an enhanced whale optimizer (WOA) for global search. • Strategy of random replacement is created to enhance the convergence speed of WOA. • Strategy of double adaptive weight is introduced to improve the ability of global search of WOA. • The excellent performance is validated on benchmark problems and engineering problems. Whale optimization algorithm (WOA) is a newly developed meta-heuristic algorithm, which is mainly based on the predation behavior of humpback whales in the ocean. In this paper, a reinforced variant called RDWOA is proposed to alleviate the central shortcomings of the original method that converges slowly, and it is easy to fall into local optimum when dealing with multi-dimensional problems. Two strategies are introduced into the original WOA. One is the strategy of random spare or random replacement to enhance the convergence speed of this algorithm. The other method is the strategy of double adaptive weight, which is introduced to improve the exploratory searching trends during the early stages and exploitative behaviors in the later stages. The combination of the two strategies significantly improves the convergence speed and the overall search ability of the algorithm. The advantages of the proposed RDWOA are deeply analyzed and studied by using typical benchmark examples such as unimodal, multi-modal, and fixed multi-modal functions, and three famous engineering design problems. The experimental results show that the exploratory and exploitative tendencies of WOA and its convergence mode have been significantly improved. The RDWOA developed in this paper is a promising improved WOA variant, and it has better efficacy compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Searching for the optimal subset of features is known as a challenging problem in feature selection process. To deal with the difficulties involved in this problem, a robust and reliable optimization algorithm is required. In this paper, Grasshopper Optimization Algorithm (GOA) is employed as a search strategy to design a wrapper-based feature selection method. The GOA is a recent population-based metaheuristic that mimics the swarming behaviors of grasshoppers. In this work, an efficient optimizer based on the simultaneous use of the GOA, selection operators, and Evolutionary Population Dynamics (EPD) is proposed in the form of four different strategies to mitigate the immature convergence and stagnation drawbacks of the conventional GOA. In the first two approaches, one of the top three agents and a randomly generated one are selected to reposition a solution from the worst half of the population. In the third and fourth approaches, to give a chance to the low fitness solutions in reforming the population, Roulette Wheel Selection (RWS) and Tournament Selection (TS) are utilized to select the guiding agent from the first half. The proposed GOA_EPD approaches are employed to tackle various feature selection tasks. The proposed approaches are benchmarked on 22 UCI datasets. The comprehensive results and various comparisons reveal that the EPD has a remarkable impact on the efficacy of the GOA and using the selection mechanism enhanced the capability of the proposed approach to outperform other optimizers and find the best solutions with improved convergence trends. Furthermore, the comparative experiments demonstrate the superiority of the proposed approaches when compared to other similar methods in the literature. [ABSTRACT FROM AUTHOR]

• This paper proposes an enhanced SCA algorithm variant, called ARSCA. • ARSCA improves the convergence accuracy and avoids premature convergence. • This paper compares ARSCA with classical algorithms, variations of other algorithms. • ARSCA is applied to six engineering design problems and its results are satisfactory. 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. [ABSTRACT FROM AUTHOR]

Grey wolf optimizer (GWO) is a widespread metaphor-based algorithm based on the enhanced variants of velocity-free particle swarm optimizer with proven defects and shortcomings in performance. Regardless of the proven defect and lack of novelty in this algorithm, the GWO has a simple algorithm and it may face considerable unbalanced exploration and exploitation trends. However, GWO is easy to be utilized, and it has a low capacity to deal with multi-modal functions, and it quickly falls into the optima trap or fails to find the global optimal solution. To improve the shortcomings of the basic GWO, this paper proposes an improved GWO called multi-stage grey wolf optimizer (MGWO). By dividing the search process into three stages and using different population updating strategies at each stage, the MGWO's optimization ability is improved while maintaining a certain convergence speed. The MGWO cannot easily fall into premature convergence and has a better ability to get rid of the local optima trap than GWO. Meanwhile, the MGWO achieves a better balance of exploration and exploitation and has a rough balance curve. Hence, the proposed MGWO can obtain a higher-quality solution. Based on verification on the thirty benchmark functions of IEEE CEC2017 as the objective functions, the simulation experiments in which MGWO compared with some swarm-based optimization algorithms and the balance and diversity analysis were conducted. The results verify the effectiveness and superiority of MGWO. Finally, the MGWO was applied to the multi-threshold image segmentation of Leaf Spot Diseases on Maize at four different threshold levels. The segmentation results were analysed by comparing each comparative algorithm's PSNR, SSIM, and FSIM. The results proved that the MGWO has noticeable competitiveness, and it can be used as an effective optimizer for multi-threshold image segmentation. • An improved multi-stage grey wolf optimizer (MGWO) is proposed. • The multi-stage strategy is used to balance exploration and exploitation. • A part of salp swarm algorithm strategy is introduced into GWO. • The greater performance of MGWO is verified over some advanced algorithms. • MGWO is tested on multi-threshold image segmentation of Leaf Spot Diseases on Maize. [ABSTRACT FROM AUTHOR]

• We propose an elite evolution strategy to be integrated with HHO. • The proposed modified HHO algorithm is named EESHHO. • We evaluate EESHHO by solving 29 mathematical optimization cases. • EESHHO is used to solve the QoS web service composition problem. Harris hawks optimization (HHO) is one of the leading optimization approaches due to its efficacy and multi-choice structure with time-varying components. The HHO has been applied in various areas due to its simplicity and outstanding performance. However,the original HHO can be improved and evolved in terms of convergence trends, and it is prone to local optimization under certain circumstances. Therefore, the performance and robustness of the algorithm need to be further improved. In our research, based on the core principle of evolutionary methods, we first developed an elite evolutionary strategy (EES) and then utilized it to advance HHO's convergence speed and ability to jump out of the local optimum. We named such an enhanced hybrid algorithm EESHHO in this paper. To verify the effectiveness and robustness of the EESHHO, we tested it on 29 numerical optimization test functions, including 23 classic basic test functions and 6 composite test functions from the IEEE CEC2017 special session. Moreover, we apply the EESHHO on resource-constrained project scheduling and QoS-aware web service composition problems to further validate the effectiveness of EESHHO. The experimental results show that proposed EESHHO has faster convergence speed and better optimization performance by comparing it with other mainstream algorithms. The supplementary info and answers to possible queries will be publicly available at https://aliasgharheidari.com/publications/EESHHO.html. Also, the codes and info of HHO are available at: https://aliasgharheidari.com/HHO.html. [ABSTRACT FROM AUTHOR]

Whale Optimization Algorithm (WOA) is a popular swarm-based algorithm with some spotted defects in its generated patterns during the searching phases. In this study, an enhanced WOA-based method is proposed in order to overcome the drawbacks of slow convergence speed and easy falling of WOA into the local optimum. The designed variant is called enhanced WOA (EWOA), which combines two strategies at the same time. First, a new communication mechanism (CM) is embedded into the basic WOA to promote the global optimal search ability and the exploitation tendency of the WOA. Then, the Biogeography-based Optimization (BBO) algorithm is partially utilized to harmonize the exploration and exploitation trends. A representative set of comprehensive benchmark cases and three engineering cases are utilized to verify the advantages of the proposed EWOA. The experimental results show that the exploration ability, exploitation ability, state of the balance, and convergence style of the algorithm has been improved significantly. Based on results, the proposed EWOA is a promising and excellent algorithm, and it has achieved better solution quality and faster convergence rate compared with other most advanced algorithms. For access to material and guide for users of this paper, we host an online page at https://aliasgharheidari.com. [ABSTRACT FROM AUTHOR]

• BFGSOLMFO is proposed for global optimization and real-world problems. • OL is used to enhance exploitation and exploration ability of MFO. • BFGS is employed to further excavate the potential global best solution. As a typical emergent swarm intelligence algorithm, Moth-Flame Optimization (MFO) has been created to deal with global optimization problems. Since the introduction, it has been applied to various optimization problems. However, MFO may have the trouble of getting into the local best, and the convergence rate cannot be satisfying when handling the high-dimensional and some multimodal problems. In this work, an enhanced MFO integrated with orthogonal learning (OL) and Broyden-Fletcher-Goldfarb-Shanno (BFGS), which we called BFGSOLMFO, is proposed to alleviate the stagnation shortcomings and accelerate the performance of well-regarded MFO. In the BFGSOLMFO, OL is used to construct a better candidate solution for each moth and then guide the whole population to a reasonable potential area. Meanwhile, in each iteration, after the evolution of population finished and the global optima are obtainable, BFGS is employed to further excavate the potential of the global best moth in the current population. With the aim of evaluating the efficacy of the BFGSOLMFO, first of all, the IEEE CEC2014 benchmark set is utilized to measure the performance in solving function optimizations with high-dimensional and multimodal characteristics. Both sets of the IEEE CEC2011 real-world benchmark problems and the three constrained engineering optimization problems are adopted to estimate the performance of BFGSOLMFO in tackling practical scenarios. In all the experiments, the developed BFGSOLMFO is compared with state-of-the-art advanced algorithms. Experimental results and statistical tests demonstrate that the proposed method outperforms the basic MFO and a comprehensive set of advanced algorithms. [ABSTRACT FROM AUTHOR]

• Gaussian mutation operator was introduced into FOA to avoid the premature convergence. • Chaotic local search method was adopted for enhancing the local search ability of FOA. • Extensive benchmark problems were used to verify the method. Image, graphical abstract To cope with the potential shortcomings of classical fruit fly optimization algorithm (FOA), a new version of FOA with Gaussian mutation operator and the chaotic local search strategy (MCFOA) is proposed in this research. First, the Gaussian mutation operator is introduced into the basic FOA to avoid premature convergence and improve the exploitative tendencies in the algorithm (MFOA). Then, chaotic local search method is adopted for enhancing the local searching ability of the swarm of agents (CFOA). To substantiate the efficiency of three proposed methods, a comprehensive comparison has been completed using 23 benchmark functions with different characteristics. The best version of FOA among them is the MCFOA, which is extensively compared with the notable swarm-intelligence algorithms like bat algorithm (BA), particle swarm optimization algorithm (PSO), and several advanced FOA-based methods such as chaotic FOA (CIFOA), improved FOA (IFOA), multi-swarm FOA (swarm_MFOA) and differential evolution based FOA (DFOA). Numerical results show that two embedded strategies will effectively boost the performance of FOA for optimization tasks. In addition, MCFOA is also applied to feature selection problems. The results also prove that MCFOA can obtain the optimal classification accuracy. [ABSTRACT FROM AUTHOR]