Classical Benchmark Functions Research Articles

Comprehensive Optimization of PID Controller Parameters for DC Motor Speed Management Using a Modified Jellyfish Search Algorithm

ABSTRACTThe proportional integral derivative (PID) controller plays a crucial role in various industrial applications. However, conventional methods often fail to provide optimal parameter values. Therefore, this study proposes a novel version of the jellyfish search (JS) algorithm, the modified jellyfish search (mJS) algorithm, for optimally tuning PID controllers to regulate the speed of a direct current (DC) motor. The original JS algorithm is known for its nature‐inspired approach; however, it has limitations in terms of exploitation power. To address these issues, the proposed mJS incorporates quasi‐dynamic opposed‐based learning and a Weibull probability distribution. The objective function minimizes the integral of the time‐weighted absolute error (ITAE). The effectiveness of mJS was validated by solving the 23rd classical benchmark function, followed by a comparative analysis with contemporary optimization algorithms using stringent statistical criteria. Then mJS is then applied to optimize the PID parameters of three different DC motor models. Results show that the mJS outperforms the standard JS, gray wolf optimization (GWO), JAYA, and golden jackal optimization (GJO) for various performance indicators. Specifically, the best ITAE values were 3.274e6 for DC motor 1 using the JS algorithm, 0.002737 for DC motor 2 using the GJO algorithm, and 0.02785 for DC motor 3 using the mJS algorithm. Additionally, the mJS and JS algorithms reduced the settling time to 0.005 s for DC motor 1, whereas the best settling time of 0.325 s for DC motor 2 was achieved by the mJS algorithm, and a settling time of 1.19 s was recorded for DC motor 3 using both the mJS and JS algorithms. These findings underscore the practical importance of the developed optimizer in engineering applications and its significant contribution to the literature.

Q-Learning-Based Dumbo Octopus Algorithm for Parameter Tuning of Fractional-Order PID Controller for AVR Systems

The tuning of fractional-order proportional-integral-derivative (FOPID) controllers for automatic voltage regulator (AVR) systems presents a complex challenge, necessitating the solution of real-order integral and differential equations. This study introduces the Dumbo Octopus Algorithm (DOA), a novel metaheuristic inspired by machine learning with animal behaviors, as an innovative approach to address this issue. For the first time, the DOA is invented and employed to optimize FOPID parameters, and its performance is rigorously evaluated against 11 existing metaheuristic algorithms using 23 classical benchmark functions and CEC2019 test sets. The evaluation includes a comprehensive quantitative analysis and qualitative analysis. Statistical significance was assessed using the Friedman’s test, highlighting the superior performance of the DOA compared to competing algorithms. To further validate its effectiveness, the DOA was applied to the FOPID parameter tuning of an AVR system, demonstrating exceptional performance in practical engineering applications. The results indicate that the DOA outperforms other algorithms in terms of convergence accuracy, robustness, and practical problem-solving capability. This establishes the DOA as a superior and promising solution for complex optimization problems, offering significant advancements in the tuning of FOPID for AVR systems.

Exponential-trigonometric optimization algorithm for solving complicated engineering problems

This article presents an innovative optimization algorithm called the Exponential-Trigonometric Optimization (ETO) algorithm, which is based on a sophisticated combination of exponential and trigonometric functions. The ETO algorithm is structured to strike a balance between two important stages: exploration and exploitation, a challenge that many other optimization algorithms have also sought to address. ETO incorporates several additional random and adaptive variables, resulting in better performance compared to existing algorithms. The algorithm's performance and potential were validated through three phases of testing. First, the ETO algorithm is evaluated against seven other meta-heuristic algorithms, including SCHO, SCA, AOA, GWO, HHO, HGS, and GJO, using 23 classical benchmark functions of varying sizes. These benchmark functions are categorized into three main groups: "unimodal" (F1 to F7), "multi-modal" (F8 to F13), and "fixed-dimension" (F14 to F23). Next, the ETO algorithm was tested on CEC2019 and CEC2020 functions and compared with 7 algorithms mentioned above to evaluate performance. In addition, the ETO algorithm is tested on the CEC2017 benchmark functions with dimensions of 10-D, 30-D, and 50-D. It is then compared and evaluated against other potential algorithms, such as SHADE, LSHADE, and JADE, using the Wilcoxon rank-sum test. Finally, the ETO algorithm is utilized to tackle five intricate engineering problems to show its robustness, including optimizing the shape of aircraft wings to increase lift. These results have demonstrated the effectiveness and potential of the ETO algorithm, yielding outstanding results and ranking first among other algorithms. Notably, the optimization of the improved aircraft wing increased the lift force from 0.797055 to 0.951817, signaling promising prospects for advancing optimization problems in the future. Source codes of ETO is publicly available at https://ceats.ou.edu.vn/us/exponential-trigonometric-optimization-algorithm-.html.

Ameliorated Fick’s law algorithm based multi-threshold medical image segmentation

Medical image segmentation is a critical and demanding step in medical image processing, which provides a solid foundation for subsequent medical image data extraction and analysis. Multi-threshold image segmentation, one of the most commonly used and specialized image segmentation techniques, limits its application to medical images because it requires demanding computational performance and is difficult to produce satisfactory segmentation results. To overcome the above problems, an ameliorated Fick's law algorithm (MsFLA) for multi-threshold image segmentation is developed in this paper. First, an optimized sine–cosine strategy is introduced to extend the molecular diffusion process to alleviate the problem of easily falling into local optima, thus improving the convergence accuracy of the Fick's law algorithm (FLA). Secondly, the introduction of local minimal value avoidance enriches the individual molecular information and enhances the local search ability, thus improving computational accuracy. In addition, the optimal neighborhood learning strategy is added to ensure a more careful and reasonable reliance on the optimal solution, thus reducing the chance of convergence of a local solution. The efficient optimization capability of MsFLA is comprehensively validated by comparing MsFLA with the original FLA and other algorithms in 23 classical benchmark functions. Finally, MsFLA is applied to image segmentation of grayscale images of COVID-19 and brain and color images of Lung and Colon cancer histopathology by using Cross entropy to validate its segmentation capability. The experimental results show that the MsFLA obtains the best segmentation results in three medical image cases compared to other comparison algorithms, which indicates that MsFLA can effectively solve the multi-threshold medical image segmentation problem.Graphical abstract

Enhanced Prairie Dog Optimization with Differential Evolution for solving engineering design problems and network intrusion detection system

This paper introduces a novel hybrid optimization algorithm, PDO-DE, which integrates the Prairie Dog Optimization (PDO) algorithm with the Differential Evolution (DE) strategy. This research aims to develop an algorithm that efficiently addresses complex optimization problems in engineering design and network intrusion detection systems. Our method enhances the PDO's search capabilities by incorporating the DE's principal mechanisms of mutation and crossover, facilitating improved solution exploration and exploitation. We evaluate the effectiveness of the PDO-DE algorithm through rigorous testing on 23 classical benchmark functions, five engineering design problems, and a network intrusion detection system (NIDS). The results indicate that PDO-DE outperforms several state-of-the-art optimization algorithms regarding convergence speed and accuracy, demonstrating its robustness and adaptability across different problem domains. The PDO-DE algorithm's potential applications extend to engineering challenges and cybersecurity issues, where efficient and reliable solutions are critical; for example, the NIDS results show significant results in detection rate, false alarm, and accuracy with 98.1%, 2.4%, and 96%, respectively. The innovative integration of PDO and DE contributes significantly to stochastic optimization and swarm intelligence, offering a promising new tool for tackling diverse optimization problems. In conclusion, the PDO-DE algorithm represents a significant scientific advancement in hybrid optimization techniques, providing a more effective approach for solving real-world problems that require high precision and optimal resource utilization.

An improved prairie dog optimization algorithm integrating multiple strategies and its application

Aiming at the problems in prairie dog optimization (PDO), such as uneven population distribution at initialization, slow convergence, imbalance between global exploration and local exploitation, and the tendency to get trapped in the local optimum, this study proposes an Improved prairie dog optimisation algorithm integrating multiple strategies (IMSPDO). Firstly, the population is initialized using spatial pyramid matching (SPM) chaotic mapping combined with improved random opposition-based learning (IROL) to solve the problems of uneven distribution and poor diversity of the population. Secondly, the prey escapes energy formula mentioned in the harris hawks optimization (HHO) is introduced to achieve the smooth transition between the exploration phase and the exploitation phase, balancing the algorithm’s global exploration capability and local exploitation capability. Additionally, the idea of the particle swarm optimization (PSO) is applied to enhance the global optimization capability of the algorithm. Finally, the ideas of simulated annealing (SA), polynomial mutation and Cauchy mutation are also introduced to improve the ability that individuals to jump out of the local optimum. The performance of the improved algorithm is verified on a set of 21 classical benchmark functions and 8 CEC2020 test functions. The proposed IMSPDO is also evaluated against original PDO, and six other commonly used algorithms. The result of the Wilcoxon rank-sum test shows that there is a significant difference between the selected algorithms and IMSPDO. Furthermore, 3 engineering examples are used to further test the superiority of IMSPDO in dealing with real-world problems.

Improved Osprey Optimization Algorithm Based on Two-Color Complementary Mechanism for Global Optimization and Engineering Problems.

Aiming at the problem that the Osprey Optimization Algorithm (OOA) does not have high optimization accuracy and is prone to falling into local optimum, an Improved Osprey Optimization Algorithm Based on a Two-Color Complementary Mechanism for Global Optimization (IOOA) is proposed. The core of the IOOA algorithm lies in its unique two-color complementary mechanism, which significantly improves the algorithm's global search capability and optimization performance. Firstly, in the initialization stage, the population is created by combining logistic chaos mapping and the good point set method, and the population is divided into four different color groups by drawing on the four-color theory to enhance the population diversity. Secondly, a two-color complementary mechanism is introduced, where the blue population maintains the OOA core exploration strategy to ensure the stability and efficiency of the algorithm; the red population incorporates the Harris Hawk heuristic strategy in the development phase to strengthen the ability of local minima avoidance; the green group adopts the strolling and wandering strategy in the searching phase to add stochasticity and maintain the diversity; and the orange population implements the optimized spiral search and firefly perturbation strategies to deepen the exploration and effectively perturb the local optimums, respectively, to improve the overall population diversity, effectively perturbing the local optimum to improve the performance of the algorithm and the exploration ability of the solution space as a whole. Finally, to validate the performance of IOOA, classical benchmark functions and CEC2020 and CEC2022 test sets are selected for simulation, and ANOVA is used, as well as Wilcoxon and Friedman tests. The results show that IOOA significantly improves convergence accuracy and speed and demonstrates high practical value and advantages in engineering optimization applications.

An improved transient search optimization algorithm for building energy optimization and hybrid energy sizing applications

In this paper, a new algorithm named the improved transient search optimization algorithm (ITSOA) is utilized to solve classical test functions, optimize the consumption of building energy, and optimize hybrid energy system production. The conventional TSOA draws inspiration from the fleeting behavior of electrical circuits with energy storage components. Rosenbrock’s direct rotation technique is used to improve the traditional TSOA performance against exploration and exploitation unbalance. First, the ITSOA performance is investigated in solving 23 classical benchmark functions, and the outcomes have shown the superior capability of the recommended algorithm in comparison with the conventional TSOA, DMO, SHO, GA, MRFO, and PSO methods. Also, the ITSOA proficiency is verified in solving the building energy optimization (BEO) problem for minimizing the energy usage of two simple and detailed buildings. The optimization results showed that the optimized solutions of ITSOA in single and multi-objective optimizations compared to conventional TSOA, DMO, SHO, GA, MRFO, and PSO obtained a lower value of the cost function. Also, the superiority of ITSOA has been confirmed to solve the BEO compared to previous methods. Moreover, the multi-objective optimization results have shown that ITSOA is able to determine the ultimate solution among the Pareto front set based on the fuzzy decision-making approach and building energy utilization decisions.

A multi-strategy improved sparrow search algorithm for mobile robots path planning

Abstract Path planning for mobile robots plays a vital role in task execution, given the constraints imposed by environments and energy resources. It poses a significant challenge for mobile robots, requiring them to find a feasible path between the start point and target point that is obstacle-free and as short as possible. To address the challenge of path planning, a multi-strategy improved sparrow search algorithm with crazy operator (CMISSA) is proposed. Firstly, Tent chaos mapping and reverse learning are introduced into the population initialization of sparrow search algorithm (SSA) to enhance the uniformity and effectiveness of the initial population distribution. Secondly, adaptive parameters are applied in SSA to maintain a balance between exploitation and exploration. Thirdly, to prevent SSA from getting trapped in local optima, the crazy operator is used to perturb the population position. Finally, a novel adaptive boundary control strategy is introduced to handle the location of individuals that have crossed the boundary. In addition, the experimental results on 15 classical benchmark functions show that CMISSA has better optimization performance than other 10 comparison algorithms. Furthermore, in the path planning experimental results, the results of comparing CMISSA with 5 comparison algorithms on 5 different environments reveal CMISSA's average path shortening rates were 34.90%, 20.11%, 29.01%, 51.97%, 37.42%, respectively. It is further demonstrated that CMISSA has superior availability for solving mobile robots path planning.

A Multi-strategy Improved Grasshopper Optimization Algorithm for Solving Global Optimization and Engineering Problems

This paper presents a multi-strategy improved grasshopper optimization algorithm (MSIGOA), which aims to address the shortcomings of the grasshopper optimization algorithm (GOA), including its slow convergence, vulnerability to trapping into local optima, and low accuracy. Firstly, to improve the uniformity of the population distribution in the search space, the MSIGOA uses circle mapping for the population initialization. A nonlinear decreasing coefficient is utilized instead of an original linear decreasing coefficient to improve the local exploitation and global exploration capabilities. Then, the modified golden sine mechanism is added during the position update stage to change the single position update mode of GOA and enhance the local exploitation capability. The greedy strategy is added to greedily select the new and old positions of the individual to retain a better position and increase the speed of convergence. Finally, the quasi-reflection-based learning mechanism is utilized to construct new populations to improve population multiplicity and the capability to escape from the local optima. This paper verifies the efficacy of MSIGOA by comparing it with other advanced algorithms on six engineering design problems, CEC2017 test functions, and 12 classical benchmark functions. The experimental results show that MSIGOA performs better than the original GOA and other compared algorithms and has stronger comprehensive optimization capabilities.

Blood-sucking leech optimizer

In this paper, a new meta-heuristic optimization algorithm motivated by the foraging behaviour of blood-sucking leeches in rice fields is presented, named Blood-Sucking Leech Optimizer (BSLO). BSLO is modelled by five hunting strategies, which are the exploration of directional leeches, exploitation of directional leeches, switching mechanism of directional leeches, search strategy of directionless leeches, and re-tracking strategy. BSLO and ten comparative meta-heuristic optimization algorithms are used for optimizing twenty-three classical benchmark functions, CEC 2017, and CEC 2019. The strong robustness and optimization efficiency of BSLO are confirmed via four qualitative analyses, two statistical tests and convergence curves. Furthermore, the superiority of BSLO for real-world problems under constraints is demonstrated using five classical engineering problems. Finally, a BSLO-based Artificial Neural Network (ANN) predictive model for diameter prediction of melt electrospinning writing fibre is proposed, which further verifies BSLO's applicability for real-world problems. Therefore, BSLO is a potential optimizer for optimizing various problems. Source codes of BSLO are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/163106-blood-sucking-leech-optimizer.

Greater cane rat algorithm (GCRA): A nature-inspired metaheuristic for optimization problems

This paper introduces a new metaheuristic technique known as the Greater Cane Rat Algorithm (GCRA) for addressing optimization problems. The optimization process of GCRA is inspired by the intelligent foraging behaviors of greater cane rats during and off mating season. Being highly nocturnal, they are intelligible enough to leave trails as they forage through reeds and grass. Such trails would subsequently lead to food and water sources and shelter. The exploration phase is achieved when they leave the different shelters scattered around their territory to forage and leave trails. It is presumed that the alpha male maintains knowledge about these routes, and as a result, other rats modify their location according to this information. Also, the males are aware of the breeding season and separate themselves from the group. The assumption is that once the group is separated during this season, the foraging activities are concentrated within areas of abundant food sources, which aids the exploitation. Hence, the smart foraging paths and behaviors during the mating season are mathematically represented to realize the design of the GCR algorithm and carry out the optimization tasks. The performance of GCRA is tested using twenty-two classical benchmark functions, ten CEC 2020 complex functions, and the CEC 2011 real-world continuous benchmark problems. To further test the performance of the proposed algorithm, six classic problems in the engineering domain were used. Furthermore, a thorough analysis of computational and convergence results is presented to shed light on the efficacy and stability levels of GCRA. The statistical significance of the results is compared with ten state-of-the-art algorithms using Friedman's and Wilcoxon's signed rank tests. These findings show that GCRA produced optimal or nearly optimal solutions and evaded the trap of local minima, distinguishing it from the rival optimization algorithms employed to tackle similar problems. The GCRA optimizer source code is publicly available at: https://www.mathworks.com/matlabcentral/fileexchange/165241-greater-cane-rat-algorithm-gcra.

Research on Multi-Objective Process Parameter Optimization Method in Hard Turning Based on an Improved NSGA-II Algorithm

To address the issue of local optima encountered during the multi-objective optimization process with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm, this paper introduces an enhanced version of the NSGA-II. This improved NSGA-II incorporates polynomial and simulated binary crossover operators into the genetic algorithm’s crossover phase to refine its performance. For evaluation purposes, the classic ZDT benchmark functions are employed. The findings reveal that the enhanced NSGA-II algorithm achieves higher convergence accuracy and surpasses the performance of the original NSGA-II algorithm. When applied to the machining of the high-hardness material 20MnCrTi, four algorithms were utilized: the improved NSGA-II, the conventional NSGA-II, NSGA-III, and MOEA/D. The experimental outcomes show that the improved NSGA-II algorithm delivers a more optimal combination of process parameters, effectively enhancing the workpiece’s surface roughness and material removal rate. This leads to a significant improvement in the machining quality of the workpiece surface, demonstrating the superiority of the improved algorithm in optimizing machining processes.

Adaptive mutation sparrow search algorithm-Elman-AdaBoost model for predicting the deformation of subway tunnels

A novel coupled model integrating Elman-AdaBoost with adaptive mutation sparrow search algorithm (AM-SSA), called AMSSA-Elman-AdaBoost, is proposed for predicting the existing metro tunnel deformation induced by adjacent deep excavations in soft ground. The novelty is that the modified SSA proposes adaptive adjustment strategy to create a balance between the capacity of exploitation and exploration. In AM-SSA, firstly, the population is initialized by cat mapping chaotic sequences to improve the ergodicity and randomness of the individual sparrow, enhancing the global search ability. Then the individuals are adjusted by Tent chaotic disturbance and Cauchy mutation to avoid the population being too concentrated or scattered, expanding the local search ability. Finally, the adaptive producer-scrounger number adjustment formula is introduced to balance the ability to seek the global and local optimal. In addition, it leads to the improved algorithm achieving a better accuracy level and convergence speed compared with the original SSA. To demonstrate the effectiveness and reliability of AM-SSA, 23 classical benchmark functions and 25 IEEE Congress on Evolutionary Computation benchmark test functions (CEC2005), are employed as the numerical examples and investigated in comparison with some well-known optimization algorithms. The statistical results indicate the promising performance of AM-SSA in a variety of optimization with constrained and unknown search spaces. By utilizing the AdaBoost algorithm, multiple sets of weak AMSSA-Elman predictor functions are restructured into one strong predictor by successive iterations for the tunnel deformation prediction output. Additionally, the on-site monitoring data acquired from a deep excavation project in Ningbo, China, were selected as the training and testing sample. Meanwhile, the predictive outcomes are compared with those of other different optimization and machine learning techniques. In the end, the obtained results in this real-world geotechnical engineering field reveal the feasibility of the proposed hybrid algorithm model, illustrating its power and superiority in terms of computational efficiency, accuracy, stability, and robustness. More critically, by observing data in real time on daily basis, the structural safety associated with metro tunnels could be supervised, which enables decision-makers to take concrete control and protection measures.

BinDMO: a new Binary Dwarf Mongoose Optimization algorithm on based Z-shaped, U-shaped, and taper-shaped transfer functions for CEC-2017 benchmarks

Intelligent swarm optimization algorithms have become increasingly common due to their success in solving real-world problems. Dwarf Mongoose Optimization (DMO) algorithm is a newly proposed intelligent swarm optimization algorithm in recent years. It was developed for continuous optimization problem solutions in its original paper. But real-world problems are not always problems that take continuously variable values. Real-world problems are often problems with discrete variables. Therefore, heuristic algorithms proposed for continuous optimization problems need to be updated to solve discrete optimization problems. In this study, DMO has been updated for binary optimization problems and the Binary DMO (BinDMO) algorithm has been proposed. In binary optimization, the search space consists of binary variable values. Transfer functions are often used in the conversion of continuous variable values to binary variable values. In this study, twelve different transfer functions were used (four Z-shaped, four U-shaped, and four Taper-shaped). Thus, twelve different BinDMO variations were obtained (BinDMO1, BinDMO2, …, BinDMO12). The achievements of BinDMO variations were tested on thirteen different unimodal and multimodal classical benchmark functions. The effectiveness of population sizes on the effectiveness of BinDMO was also investigated. When the results were examined, it was determined that the most successful BinDMO variation was BinDMO1 (with Z1-shaped transfer function). The most successful BinDMO variation was compared with three different binary heuristic algorithms selected from the literature (SO, PDO, and AFT) on CEC-2017 benchmark functions. According to the average results, BinDMO was the most successful binary heuristic algorithm. This has proven that BinDMO can be chosen as an alternative algorithm for binary optimization problems.

The Pine Cone Optimization Algorithm (PCOA).

The present study introduces a novel nature-inspired optimizer called the Pine Cone Optimization algorithm (PCOA) for solving science and engineering problems. PCOA is designed based on the different mechanisms of pine tree reproduction, including pollination and pine cone dispersal by gravity and animals. It employs new and powerful operators to simulate the mentioned mechanisms. The performance of PCOA is analyzed using classic benchmark functions, CEC017 and CEC2019 as mathematical problems and CEC2006 and CEC2011 as engineering design problems. In terms of accuracy, the results show the superiority of PCOA to well-known algorithms (PSO, DE, and WOA) and new algorithms (AVOA, RW_GWO, HHO, and GBO). The results of PCOA are competitive with state-of-the-art algorithms (LSHADE and EBOwithCMAR). In terms of convergence speed and time complexity, the results of PCOA are reasonable. According to the Friedman test, PCOA's rank is 1.68 and 9.42 percent better than EBOwithCMAR (second-best algorithm) and LSHADE (third-best algorithm), respectively. The authors recommend PCOA for science, engineering, and industrial societies for solving complex optimization problems.

Optimization of numerical and engineering problems using altered differential evolution algorithm

In this study, an altered differential evolution (ADE) is presented for numerical and engineering problem optimization. It incorporates innovative mutation strategy with new control parameters using the perception of particle swarm optimization (PSO) process, to enhance exploration and exploitation activities extra profusely and increase the global search capacity. Also, a new crossover rate is employed in ADE, to attain higher convergence accuracy and quality optimal solutions. Finally, a novel selection strategy is introduced in ADE, to facilitate information sharing as well as for escaping local minima and keeps progressing. To investigate the suggested ADE performance, a collection of 13 classical benchmark functions, CEC2014 and CEC2017 benchmark suite are solved. Furthermore, the superiority and applicability of the ADE algorithm are further demonstrated through experimentation on six famous real-life engineering problems. The experimental and statistical test outcomes, collectively indicate that compared to other modern optimization algorithms, overall ADE exhibits superior performance. Also, comparison results show that ADE has powerful exploration and exploitation capabilities, excellent convergence performance, and strong ability for gaining high quality solution.

An enhanced Equilibrium Optimizer for solving complex optimization problems

Equilibrium Optimizer (EO), despite its acceptable performance in several complex problems, suffers from low exploitation ability with unbalanced exploration, stagnation in local optima and poor convergence rate. To enhance the performance of the EO, the authors infused the intelligence of quasi-opposite numbers and chaotic-maps into the EO and proposed a Quasi-Oppositional Chaotic Equilibrium Optimizer (QOCEO) that consists of Quasi-Opposition based learning for improving the scalability, Chaotic Time Parameter for ensuring a proper balance between exploration and exploitation, and Chaotic Local Search for reducing the local stagnation. The performance of QOCEO and several contemporary metaheuristics have been evaluated on 96 benchmark functions (including classical benchmark, CEC-2017, CEC-2019, CEC-2020 and CEC-2022) and six constrained engineering optimization problems employing several statistical tests. The average rank Friedman test confirms that for all 96 benchmark functions, QOCEO outperforms CMA-ES, OBTLEO, m-EO, EO, LSHADE-SPACMA, SPS_L_SHADE_EIG, SHADE by 88%, 83%, 49%, 35%, 27%, 18% and 5%, respectively. Comparing the results of Bonferroni-Dunn and Holm’s tests, QOCEO outperforms PSO, GWO, EO, HGSO, SSA, and GSA for classical benchmark functions with 30, 100, 300, and 500 dimensions. Further, QOCEO outperform CMA-ES, OBTLEO, m-EO, EO, LSHADE-SPACMA for all 96 benchmark functions and statistically similar to SPS_L_SHADE_EIG, SHADE and EBOwithCMAR.

A multi-strategy improved snake optimizer and its application to SVM parameter selection

<p>Support vector machine (SVM) is an effective classification tool and maturely used in various fields. However, its performance is very sensitive to parameters. As a newly proposed swarm intelligence algorithm, snake optimizer algorithm (SO) can help to solve the parameter selection problem. Nevertheless, SO has the shortcomings of weak population initialization, slow convergence speed in the early stage, and being easy to fall into local optimization. To address these problems, an improved snake optimizer algorithm (ISO) was proposed. The mirror opposition-based learning mechanism (MOBL) improved the population quality to enhance the optimization speed. The novel evolutionary population dynamics model (NEPD) was beneficial for searching accurately. The differential evolution strategy (DES) helped to reduce the probability of falling into local optimal value. The experimental results of classical benchmark functions and CEC2022 showed that ISO had higher optimization precision and faster convergence rate. In addition, it was also applied to the parameter selection of SVM to demonstrate the effectiveness of the proposed ISO.</p>

Reinforcement learning guided Spearman dynamic opposite Gradient-based optimizer for numerical optimization and anchor clustering

Abstract As science and technology advance, the need for novel optimization techniques has led to an increase. The recently proposed metaheuristic algorithm, Gradient-based optimizer (GBO), is rooted in the gradient-based Newton's method. GBO has a more concrete theoretical foundation. However, gradient search rule (GSR) and local escaping operator (LEO) operators in GBO still have some shortcomings. The insufficient updating method and the simple selection process limit the search performance of the algorithm. In this paper, an improved version is proposed to compensate for the above shortcomings, called RL-SDOGBO. First, during the GSR phase, the Spearman rank correlation coefficient is used to determine weak solutions on which to perform dynamic opposite learning. This operation assists the algorithm to escape from local optima and enhance exploration capability. Secondly, to optimize the exploitation capability, reinforcement learning is used to guide the selection of solution update modes in the LEO operator. RL-SDOGBO is tested on 12 classical benchmark functions and 12 CEC2022 benchmark functions with seven representative metaheuristics, respectively. The impact of the improvements, the scalability and running time of the algorithm, and the balance of exploration and exploitation are analyzed and discussed. Combining the experimental results and some statistical results, RL-SDOGBO exhibits excellent numerical optimization performance and provides high-quality solutions in most cases. In addition, RL-SDOGBO is also used to solve the anchor clustering problem for small target detection, making it a more potential and competitive option.