Modified prairie dog optimization algorithm for global optimization and constrained engineering problems.

The prairie dog optimization (PDO) algorithm is a metaheuristic optimization algorithm that simulates the daily behavior of prairie dogs. The prairie dog groups have a unique mode of information exchange. They divide into several small groups to search for food based on special signals and build caves around the food sources. When encountering natural enemies, they emit different sound signals to remind their companions of the dangers. According to this unique information exchange mode, we propose a randomized audio signal factor to simulate the specific sounds of prairie dogs when encountering different foods or natural enemies. This strategy restores the prairie dog habitat and improves the algorithm's merit-seeking ability. In the initial stage of the algorithm, chaotic tent mapping is also added to initialize the population of prairie dogs and increase population diversity, even use lens opposition-based learning strategy to enhance the algorithm's global exploration ability. To verify the optimization performance of the modified prairie dog optimization algorithm, we applied it to 23 benchmark test functions, IEEE CEC2014 test functions, and six engineering design problems for testing. The experimental results illustrated that the modified prairie dog optimization algorithm has good optimization performance.

Hybrid Slime Mold and Arithmetic Optimization Algorithm with Random Center Learning and Restart Mutation.

The slime mold algorithm (SMA) and the arithmetic optimization algorithm (AOA) are two novel meta-heuristic optimization algorithms. Among them, the slime mold algorithm has a strong global search ability. Still, the oscillation effect in the later iteration stage is weak, making it difficult to find the optimal position in complex functions. The arithmetic optimization algorithm utilizes multiplication and division operators for position updates, which have strong randomness and good convergence ability. For the above, this paper integrates the two algorithms and adds a random central solution strategy, a mutation strategy, and a restart strategy. A hybrid slime mold and arithmetic optimization algorithm with random center learning and restart mutation (RCLSMAOA) is proposed. The improved algorithm retains the position update formula of the slime mold algorithm in the global exploration section. It replaces the convergence stage of the slime mold algorithm with the multiplication and division algorithm in the local exploitation stage. At the same time, the stochastic center learning strategy is adopted to improve the global search efficiency and the diversity of the algorithm population. In addition, the restart strategy and mutation strategy are also used to improve the convergence accuracy of the algorithm and enhance the later optimization ability. In comparison experiments, different kinds of test functions are used to test the specific performance of the improvement algorithm. We determine the final performance of the algorithm by analyzing experimental data and convergence images, using the Wilcoxon rank sum test and Friedman test. The experimental results show that the improvement algorithm, which combines the slime mold algorithm and arithmetic optimization algorithm, is effective. Finally, the specific performance of the improvement algorithm on practical engineering problems was evaluated.

An improved fused feature residual network for 3D point cloud data.

Point clouds have evolved into one of the most important data formats for 3D representation. It is becoming more popular as a result of the increasing affordability of acquisition equipment and growing usage in a variety of fields. Volumetric grid-based approaches are among the most successful models for processing point clouds because they fully preserve data granularity while additionally making use of point dependency. However, using lower order local estimate functions to close 3D objects, such as the piece-wise constant function, necessitated the use of a high-resolution grid in order to capture detailed features that demanded vast computational resources. This study proposes an improved fused feature network as well as a comprehensive framework for solving shape classification and segmentation tasks using a two-branch technique and feature learning. We begin by designing a feature encoding network with two distinct building blocks: layer skips within, batch normalization (BN), and rectified linear units (ReLU) in between. The purpose of using layer skips is to have fewer layers to propagate across, which will speed up the learning process and lower the effect of gradients vanishing. Furthermore, we develop a robust grid feature extraction module that consists of multiple convolution blocks accompanied by max-pooling to represent a hierarchical representation and extract features from an input grid. We overcome the grid size constraints by sampling a constant number of points in each grid using a simple K-points nearest neighbor (KNN) search, which aids in learning approximation functions in higher order. The proposed method outperforms or is comparable to state-of-the-art approaches in point cloud segmentation and classification tasks. In addition, a study of ablation is presented to show the effectiveness of the proposed method.

An improved multi-strategy beluga whale optimization for global optimization problems.

This paper presents an improved beluga whale optimization (IBWO) algorithm, which is mainly used to solve global optimization problems and engineering problems. This improvement is proposed to solve the imbalance between exploration and exploitation and to solve the problem of insufficient convergence accuracy and speed of beluga whale optimization (BWO). In IBWO, we use a new group action strategy (GAS), which replaces the exploration phase in BWO. It was inspired by the group hunting behavior of beluga whales in nature. The GAS keeps individual belugas whales together, allowing them to hide together from the threat posed by their natural enemy, the tiger shark. It also enables the exchange of location information between individual belugas whales to enhance the balance between local and global lookups. On this basis, the dynamic pinhole imaging strategy (DPIS) and quadratic interpolation strategy (QIS) are added to improve the global optimization ability and search rate of IBWO and maintain diversity. In a comparison experiment, the performance of the optimization algorithm (IBWO) was tested by using CEC2017 and CEC2020 benchmark functions of different dimensions. Performance was analyzed by observing experimental data, convergence curves, and box graphs, and the results were tested using the Wilcoxon rank sum test. The results show that IBWO has good optimization performance and robustness. Finally, the applicability of IBWO to practical engineering problems is verified by five engineering problems.

Modified reptile search algorithm with multi-hunting coordination strategy for global optimization problems.

The reptile search algorithm (RSA) is a bionic algorithm proposed by Abualigah. et al. in 2020. RSA simulates the whole process of crocodiles encircling and catching prey. Specifically, the encircling stage includes high walking and belly walking, and the hunting stage includes hunting coordination and cooperation. However, in the middle and later stages of the iteration, most search agents will move towards the optimal solution. However, if the optimal solution falls into local optimum, the population will fall into stagnation. Therefore, RSA cannot converge when solving complex problems. To enable RSA to solve more problems, this paper proposes a multi-hunting coordination strategy by combining Lagrange interpolation and teaching-learning-based optimization (TLBO) algorithm's student stage. Multi-hunting cooperation strategy will make multiple search agents coordinate with each other. Compared with the hunting cooperation strategy in the original RSA, the multi-hunting cooperation strategy has been greatly improved RSA's global capability. Moreover, considering RSA's weak ability to jump out of the local optimum in the middle and later stages, this paper adds the Lens pposition-based learning (LOBL) and restart strategy. Based on the above strategy, a modified reptile search algorithm with a multi-hunting coordination strategy (MRSA) is proposed. To verify the above strategies' effectiveness for RSA, 23 benchmark and CEC2020 functions were used to test MRSA's performance. In addition, MRSA's solutions to six engineering problems reflected MRSA's engineering applicability. It can be seen from the experiment that MRSA has better performance in solving test functions and engineering problems.

Improved Reptile Search Algorithm by Salp Swarm Algorithm for Medical Image Segmentation.

This study proposes a novel nature-inspired meta-heuristic optimizer based on the Reptile Search Algorithm combed with Salp Swarm Algorithm for image segmentation using gray-scale multi-level thresholding, called RSA-SSA. The proposed method introduces a better search space to find the optimal solution at each iteration. However, we proposed RSA-SSA to avoid the searching problem in the same area and determine the optimal multi-level thresholds. The obtained solutions by the proposed method are represented using the image histogram. The proposed RSA-SSA employed Otsu's variance class function to get the best threshold values at each level. The performance measure for the proposed method is valid by detecting fitness function, structural similarity index, peak signal-to-noise ratio, and Friedman ranking test. Several benchmark images of COVID-19 validate the performance of the proposed RSA-SSA. The results showed that the proposed RSA-SSA outperformed other metaheuristics optimization algorithms published in the literature.

Modified Harris Hawks Optimization Algorithm with Exploration Factor and Random Walk Strategy.

One of the most popular population-based metaheuristic algorithms is Harris hawks optimization (HHO), which imitates the hunting mechanisms of Harris hawks in nature. Although HHO can obtain optimal solutions for specific problems, it stagnates in local optima solutions. In this paper, an improved Harris hawks optimization named ERHHO is proposed for solving global optimization problems. Firstly, we introduce tent chaotic map in the initialization stage to improve the diversity of the initialization population. Secondly, an exploration factor is proposed to optimize parameters for improving the ability of exploration. Finally, a random walk strategy is proposed to enhance the exploitation capability of HHO further and help search agent jump out the local optimal. Results from systematic experiments conducted on 23 benchmark functions and the CEC2017 test functions demonstrated that the proposed method can provide a more reliable solution than other well-known algorithms.

An Improved Teaching-Learning-Based Optimization Algorithm with Reinforcement Learning Strategy for Solving Optimization Problems.

This paper presents an improved teaching-learning-based optimization (TLBO) algorithm for solving optimization problems, called RLTLBO. First, a new learning mode considering the effect of the teacher is presented. Second, the Q-Learning method in reinforcement learning (RL) is introduced to build a switching mechanism between two different learning modes in the learner phase. Finally, ROBL is adopted after both the teacher and learner phases to improve the local optima avoidance ability of RLTLBO. These two strategies effectively enhance the convergence speed and accuracy of the proposed algorithm. RLTLBO is analyzed on 23 standard benchmark functions and eight CEC2017 test functions to verify the optimization performance. The results reveal that proposed algorithm provides effective and efficient performance in solving benchmark test functions. Moreover, RLTLBO is also applied to solve eight industrial engineering design problems. Compared with the basic TLBO and seven state-of-the-art algorithms, the results illustrate that RLTLBO has superior performance and promising prospects for dealing with real-world optimization problems. The source codes of the RLTLBO are publicly available at https://github.com/WangShuang92/RLTLBO.

An improved remora optimization algorithm with autonomous foraging mechanism for global optimization problems.

The remora optimization algorithm (ROA) is a newly proposed metaheuristic algorithm for solving global optimization problems. In ROA, each search agent searches new space according to the position of host, which makes the algorithm suffer from the drawbacks of slow convergence rate, poor solution accuracy, and local optima for some optimization problems. To tackle these problems, this study proposes an improved ROA (IROA) by introducing a new mechanism named autonomous foraging mechanism (AFM), which is inspired from the fact that remora can also find food on its own. In AFM, each remora has a small chance to search food randomly or according to the current food position. Thus the AFM can effectively expand the search space and improve the accuracy of the solution. To substantiate the efficacy of the proposed IROA, twenty-three classical benchmark functions and ten latest CEC 2021 test functions with various types and dimensions were employed to test the performance of IROA. Compared with seven metaheuristic and six modified algorithms, the results of test functions show that the IROA has superior performance in solving these optimization problems. Moreover, the results of five representative engineering design optimization problems also reveal that the IROA has the capability to obtain the optimal results for real-world optimization problems. To sum up, these test results confirm the effectiveness of the proposed mechanism.

An improved arithmetic optimization algorithm with forced switching mechanism for global optimization problems.

Arithmetic optimization algorithm (AOA) is a newly proposed meta-heuristic method which is inspired by the arithmetic operators in mathematics. However, the AOA has the weaknesses of insufficient exploration capability and is likely to fall into local optima. To improve the searching quality of original AOA, this paper presents an improved AOA (IAOA) integrated with proposed forced switching mechanism (FSM). The enhanced algorithm uses the random math optimizer probability (RMOP) to increase the population diversity for better global search. And then the forced switching mechanism is introduced into the AOA to help the search agents jump out of the local optima. When the search agents cannot find better positions within a certain number of iterations, the proposed FSM will make them conduct the exploratory behavior. Thus the cases of being trapped into local optima can be avoided effectively. The proposed IAOA is extensively tested by twenty-three classical benchmark functions and ten CEC2020 test functions and compared with the AOA and other well-known optimization algorithms. The experimental results show that the proposed algorithm is superior to other comparative algorithms on most of the test functions. Furthermore, the test results of two training problems of multi-layer perceptron (MLP) and three classical engineering design problems also indicate that the proposed IAOA is highly effective when dealing with real-world problems.

Enhanced Aquila optimizer algorithm for global optimization and constrained engineering problems.

The Aquila optimizer (AO) is a recently developed swarm algorithm that simulates the hunting behavior of Aquila birds. In complex optimization problems, an AO may have slow convergence or fall in sub-optimal regions, especially in high complex ones. This paper tries to overcome these problems by using three different strategies: restart strategy, opposition-based learning and chaotic local search. The developed algorithm named as mAO was tested using 29 CEC 2017 functions and five different engineering constrained problems. The results prove the superiority and efficiency of mAO in solving many optimization issues.

Enhanced Slime Mould Algorithm for Multilevel Thresholding Image Segmentation Using Entropy Measures.

Image segmentation is a fundamental but essential step in image processing because it dramatically influences posterior image analysis. Multilevel thresholding image segmentation is one of the most popular image segmentation techniques, and many researchers have used meta-heuristic optimization algorithms (MAs) to determine the threshold values. However, MAs have some defects; for example, they are prone to stagnate in local optimal and slow convergence speed. This paper proposes an enhanced slime mould algorithm for global optimization and multilevel thresholding image segmentation, namely ESMA. First, the Levy flight method is used to improve the exploration ability of SMA. Second, quasi opposition-based learning is introduced to enhance the exploitation ability and balance the exploration and exploitation. Then, the superiority of the proposed work ESMA is confirmed concerning the 23 benchmark functions. Afterward, the ESMA is applied in multilevel thresholding image segmentation using minimum cross-entropy as the fitness function. We select eight greyscale images as the benchmark images for testing and compare them with the other classical and state-of-the-art algorithms. Meanwhile, the experimental metrics include the average fitness (mean), standard deviation (Std), peak signal to noise ratio (PSNR), structure similarity index (SSIM), feature similarity index (FSIM), and Wilcoxon rank-sum test, which is utilized to evaluate the quality of segmentation. Experimental results demonstrated that ESMA is superior to other algorithms and can provide higher segmentation accuracy.

An improved hybrid Aquila Optimizer and Harris Hawks Optimization for global optimization.

This paper introduces an improved hybrid Aquila Optimizer (AO) and Harris Hawks Optimization (HHO) algorithm, namely IHAOHHO, to enhance the searching performance for global optimization problems. In the IHAOHHO, valuable exploration and exploitation capabilities of AO and HHO are retained firstly, and then representative-based hunting (RH) and opposition-based learning (OBL) strategies are added in the exploration and exploitation phases to effectively improve the diversity of search space and local optima avoidance capability of the algorithm, respectively. To verify the optimization performance and the practicability, the proposed algorithm is comprehensively analyzed on standard and CEC2017 benchmark functions and three engineering design problems. The experimental results show that the proposed IHAOHHO has more superior global search performance and faster convergence speed compared to the basic AO and HHO and selected state-of-the-art meta-heuristic algorithms.

A Hybrid SSA and SMA with Mutation Opposition-Based Learning for Constrained Engineering Problems.

Based on Salp Swarm Algorithm (SSA) and Slime Mould Algorithm (SMA), a novel hybrid optimization algorithm, named Hybrid Slime Mould Salp Swarm Algorithm (HSMSSA), is proposed to solve constrained engineering problems. SSA can obtain good results in solving some optimization problems. However, it is easy to suffer from local minima and lower density of population. SMA specializes in global exploration and good robustness, but its convergence rate is too slow to find satisfactory solutions efficiently. Thus, in this paper, considering the characteristics and advantages of both the above optimization algorithms, SMA is integrated into the leader position updating equations of SSA, which can share helpful information so that the proposed algorithm can utilize these two algorithms' advantages to enhance global optimization performance. Furthermore, Levy flight is utilized to enhance the exploration ability. It is worth noting that a novel strategy called mutation opposition-based learning is proposed to enhance the performance of the hybrid optimization algorithm on premature convergence avoidance, balance between exploration and exploitation phases, and finding satisfactory global optimum. To evaluate the efficiency of the proposed algorithm, HSMSSA is applied to 23 different benchmark functions of the unimodal and multimodal types. Additionally, five classical constrained engineering problems are utilized to evaluate the proposed technique's practicable abilities. The simulation results show that the HSMSSA method is more competitive and presents more engineering effectiveness for real-world constrained problems than SMA, SSA, and other comparative algorithms. In the end, we also provide some potential areas for future studies such as feature selection and multilevel threshold image segmentation.

Multilevel thresholding using a modified ant lion optimizer with opposition-based learning for color image segmentation.

Multilevel thresholding has important research value in image segmentation and can effectively solve region analysis problems of complex images. In this paper, Otsu and Kapur's entropy are adopted among thresholding segmentation methods. They are used as the objective functions. When the number of threshold increases, the time complexity increases exponentially. In order to overcome this drawback, a modified ant lion optimizer algorithm based on opposition-based learning (MALO) is proposed to determine the optimum threshold values by the maximization of the objective functions. By introducing the opposition-based learning strategy, the search accuracy and convergence performance are increased. In addition to IEEE CEC 2017 benchmark functions validation, 11 state-of-the-art algorithms are selected for comparison. A series of experiments are conducted to evaluate the segmentation performance of the algorithm. The evaluation metrics include: fitness value, peak signal-to-noise ratio, structural similarity index, feature similarity index, and computational time. The experimental data are analyzed and discussed in details. The experimental results significantly demonstrate that the proposed method is superior over others, which can be considered as a powerful and efficient thresholding technique.

A hybrid equilibrium optimizer algorithm for multi-level image segmentation.

Threshlod image segmentation is a classic method of color image segmentation. In this paper, we propose a hybrid equilibrium optimizer algorithm for multi-level image segmentation. When multi-level threshold method calculates the neighborhood mean and median of color image, it takes huge challenge to find the optimal threshold. We use the proposed method to optimize the multi-level threshold method and get the optimal threshold from the color image. In order to test the performance of the proposed method, we select the CEC2015 dataset as the benchmark function. The result shows that the proposed method improves the optimization ability of the original algorithm. And then, the classic images and wood fiber images are taken as experimental objects to analyze the segmentation result. The experimental results show that the proposed method has a good performance in Uniformity measure, Peak Signal-to-Noise Ratio and Feature Similarity Index and CPU time.

Improved barnacles mating optimizer algorithm for feature selection and support vector machine optimization.

With the rapid development of computer technology, data collection becomes easier, and data object presents more complex. Data analysis method based on machine learning is an important, active, and multi-disciplinarily research field. Support vector machine (SVM) is one of the most powerful and fast classification models. The main challenges SVM faces are the selection of feature subset and the setting of kernel parameters. To improve the performance of SVM, a metaheuristic algorithm is used to optimize them simultaneously. This paper first proposes a novel classification model called IBMO-SVM, which hybridizes an improved barnacle mating optimizer (IBMO) with SVM. Three strategies, including Gaussian mutation, logistic model, and refraction-learning, are used to improve the performance of BMO from different perspectives. Through 23 classical benchmark functions, the impact of control parameters and the effectiveness of introduced strategies are analyzed. The convergence accuracy and stability are the main gains, and exploration and exploitation phases are more properly balanced. We apply IBMO-SVM to 20 real-world datasets, including 4 extremely high-dimensional datasets. Experimental results are compared with 6 state-of-the-art methods in the literature. The final statistical results show that the proposed IBMO-SVM achieves a better performance than the standard BMO-SVM and other compared methods, especially on high-dimensional datasets. In addition, the proposed model also shows significant superiority compared with 4 other classifiers.

Kapur's Entropy for Color Image Segmentation Based on a Hybrid Whale Optimization Algorithm.

In this paper, a new hybrid whale optimization algorithm (WOA) called WOA-DE is proposed to better balance the exploitation and exploration phases of optimization. Differential evolution (DE) is adopted as a local search strategy with the purpose of enhancing exploitation capability. The WOA-DE algorithm is then utilized to solve the problem of multilevel color image segmentation that can be considered as a challenging optimization task. Kapur's entropy is used to obtain an efficient image segmentation method. In order to evaluate the performance of proposed algorithm, different images are selected for experiments, including natural images, satellite images and magnetic resonance (MR) images. The experimental results are compared with state-of-the-art meta-heuristic algorithms as well as conventional approaches. Several performance measures have been used such as average fitness values, standard deviation (STD), peak signal to noise ratio (PSNR), structural similarity index (SSIM), feature similarity index (FSIM), Wilcoxon's rank sum test, and Friedman test. The experimental results indicate that the WOA-DE algorithm is superior to the other meta-heuristic algorithms. In addition, to show the effectiveness of the proposed technique, the Otsu method is used for comparison.

A Chaotic Electromagnetic Field Optimization Algorithm Based on Fuzzy Entropy for Multilevel Thresholding Color Image Segmentation.

Multilevel thresholding segmentation of color images is an important technology in various applications which has received more attention in recent years. The process of determining the optimal threshold values in the case of traditional methods is time-consuming. In order to mitigate the above problem, meta-heuristic algorithms have been employed in this field for searching the optima during the past few years. In this paper, an effective technique of Electromagnetic Field Optimization (EFO) algorithm based on a fuzzy entropy criterion is proposed, and in addition, a novel chaotic strategy is embedded into EFO to develop a new algorithm named CEFO. To evaluate the robustness of the proposed algorithm, other competitive algorithms such as Artificial Bee Colony (ABC), Bat Algorithm (BA), Wind Driven Optimization (WDO), and Bird Swarm Algorithm (BSA) are compared using fuzzy entropy as the fitness function. Furthermore, the proposed segmentation method is also compared with the most widely used approaches of Otsu's variance and Kapur's entropy to verify its segmentation accuracy and efficiency. Experiments are conducted on ten Berkeley benchmark images and the simulation results are presented in terms of peak signal to noise ratio (PSNR), mean structural similarity (MSSIM), feature similarity (FSIM), and computational time (CPU Time) at different threshold levels of 4, 6, 8, and 10 for each test image. A series of experiments can significantly demonstrate the superior performance of the proposed technique, which can deal with multilevel thresholding color image segmentation excellently.