CEC2005 Benchmark Functions Research Articles

A vector-encirclement-model-based sparrow search algorithm for engineering optimization and numerical optimization problems

Sparrow search algorithm (SSA) is a new global optimization tool with high performance. In order to further improve its global and local search abilities, in this paper, an improved SSA (ISSA) is put forward where the main novelties lie in the producer centralization strategy, the vector encirclement model and the direction selection strategy. The producer centralization strategy is designed to update the position of producer with the hope of improving the global search ability of the producer, while the vector encirclement model and the direction selection strategy are proposed to update the position of scrounger for the purpose of improving the local search ability of scrounger. For the comparison purpose, the performances of the proposed ISSA and the existing excellent algorithms are tested in CEC2017 benchmark functions and 30 real-world constrained optimization problems. The experimental results demonstrate that the proposed ISSA substantially improves the convergence rate, optimization accuracy, stability of the SSA and can solve a wide range of real-world constrained optimization problems successfully with satisfactory performances. Finally, the proposed ISSA is successfully applied in the trajectory optimization of mechanical arms.

An Improved Sea Lion Optimization for Workload Elasticity Prediction with Neural Networks

The work in this paper presents a study into nature-inspired optimization applied to workload elasticity prediction using neural networks. Currently, the trend is for proactive decision support in increasing or decreasing the available resource in cloud computing. The aim is to avoid overprovision leading to resource waste and to avoid resource under-provisioning. The combination of optimization and neural networks has potential for the performance, accuracy, and stability of the prediction solution. In this context, we initially proposed an improved variant of sea lion optimization (ISLO) to boost the efficiency of the original in solving optimization problems. The designed optimization results are validated against eight well-known metaheuristic algorithms on 20 benchmark functions of CEC’2014 and CEC’2015. After that, improved sea lion optimization (ISLO) is used to train a hybrid neural network. Finally, the trained neural model is used for resource auto-scaling based on workload prediction with 4 real and public datasets. The experiments show that our neural network model provides improved results in comparison with other models, especially in comparison with neural networks trained using the original sea lion optimization. The proposed ISLO proved efficiency and improvement in solving problems ranging from global optimization with swarm intelligence to the prediction of workload elasticity.

A novel metaheuristic optimisation approach for text sentiment analysis

Automated sentiment analysis is considered an area in natural language processing research that seeks to understand a text author's mood, thoughts, and feelings. New opportunities and challenges have arisen in this field due to the popularity and accessibility of a variety of resources of ideas, such as online review websites, personal blogs, and social media. Feature selection, which can be conducted using metaheuristic algorithms, is one of the steps of sentiment analysis. It is crucial to use high-performing algorithms for feature selection. This paper applies the Horse herd Optimisation Algorithm (HOA) for feature selection in text sentiment analysis. HOA is a metaheuristic algorithm and uses six key behaviours to simulate the social performance of horses of various ages, to solve high-dimensional optimisation problems. In order to improve HOA, this paper adds another behaviour of horses to the basic algorithm; thus, the new algorithm uses seven key behaviours of horses of different ages to imitate their social performance. It is then discretised and converted to a multi-objective algorithm. The improved algorithm's performance is evaluated using 15 CEC benchmark functions, and the results are compared to the Binary Social Spider Algorithm, the Binary Grey Wolf Optimizer, and the Binary Butterfly Optimization Algorithm. The new algorithm, the Multi-objective Binary Horse herd Optimisation Algorithm (MBHOA), excels at solving high-dimensional complex problems. To evaluate the algorithm's performance in feature selection, as a practical example, it is employed in text sentiment analysis and examined on various data sets. The simulation results indicate that MBHOA has a better performance in analysing sentiment compared to similar approaches.

An evolutionary machine learning for multiple myeloma using Runge Kutta Optimizer from multi characteristic indexes

Multiple myeloma (MM) is a malignant plasma cell disease that is the second most prevalent hematological malignancy in high-income nations and accounts for around 1.8% of all cancers and 18% of hematologic malignancies in the United States. In this research, we try to design a machine learning framework for MM diagnosis from multi characteristic indexes using slime mould Runge Kutta Optimizer (MSRUN) and kernel extreme learning machine, which is called as MSRUN-KELM. An efficient slime mould learning operator is introduced to the initial Runge Kutta Optimizer in MSRUN, ensuring that the trade-off between intensity and diversity is satisfied. The MSRUN was evaluated using IEEE CEC2014 benchmark functions, and the statistical results indicate a significant increase in the search performance of MSRUN. In MSRUN-KELM, kernel extreme machine learning is constructed on MM from multi-characteristic indexes with MSRUN, parameter optimization, and feature selection synchronized by MSRUN. The results of MSRUN-KELM on MM are accuracy of 93.88%, a Matthews correlation coefficient of 0.922677, and sensitivities of 93.41% and 93.19%. The suggested MSRUN-KELM may be utilized to analyze MM from multi-characteristic indexes well, and it can be treated as a potential tool for MM diagnosis.

A Modified Reptile Search Algorithm for Numerical Optimization Problems.

The reptile search algorithm (RSA) is a swarm-based metaheuristic algorithm inspired by the encirclement and hunt mechanisms of crocodiles. Compared with other algorithms, RSA is competitive but still suffers from low population diversity, unbalanced exploitation and exploration, and the tendency to fall into local optima. To overcome these shortcomings, a modified variant of RSA, named MRSA, is proposed in this paper. First, an adaptive chaotic reverse learning strategy is employed to enhance the population diversity. Second, an elite alternative pooling strategy is proposed to balance exploitation and exploration. Finally, a shifted distribution estimation strategy is used to correct the evolutionary direction and improve the algorithm performance. Subsequently, the superiority of MRSA is verified using 23 benchmark functions, IEEE CEC2017 benchmark functions, and robot path planning problems. The Friedman test, the Wilcoxon signed-rank test, and simulation results show that the proposed MRSA outperforms other comparative algorithms in terms of convergence accuracy, convergence speed, and stability.

A Modified Gorilla Troops Optimizer for Global Optimization Problem

The Gorilla Troops Optimizer (GTO) is a novel Metaheuristic Algorithm that was proposed in 2021. Its design was inspired by the lifestyle characteristics of gorillas, including migration to a known position, migration to an undiscovered position, moving toward the other gorillas, following silverback gorillas and competing with silverback gorillas for females. However, like other Metaheuristic Algorithms, the GTO still suffers from local optimum, low diversity, imbalanced utilization, etc. In order to improve the performance of the GTO, this paper proposes a modified Gorilla Troops Optimizer (MGTO). The improvement strategies include three parts: Beetle-Antennae Search Based on Quadratic Interpolation (QIBAS), Teaching–Learning-Based Optimization (TLBO) and Quasi-Reflection-Based Learning (QRBL). Firstly, QIBAS is utilized to enhance the diversity of the position of the silverback. Secondly, the teacher phase of TLBO is introduced to the update the behavior of following the silverback with 50% probability. Finally, the quasi-reflection position of the silverback is generated by QRBL. The optimal solution can be updated by comparing these fitness values. The performance of the proposed MGTO is comprehensively evaluated by 23 classical benchmark functions, 30 CEC2014 benchmark functions, 10 CEC2020 benchmark functions and 7 engineering problems. The experimental results show that MGTO has competitive performance and promising prospects in real-world optimization tasks.

Multi-Population-Based Algorithm with an Exchange of Training Plans Based on Population Evaluation

Abstract Population Based Algorithms (PBAs) are excellent search tools that allow searching space of parameters defined by problems under consideration. They are especially useful when it is difficult to define a differentiable evaluation criterion. This applies, for example, to problems that are a combination of continuous and discrete (combinatorial) problems. In such problems, it is often necessary to select a certain structure of the solution (e.g. a neural network or other systems with a structure usually selected by the trial and error method) and to determine the parameters of such structure. As PBAs have great application possibilities, the aim is to develop more and more effective search formulas used in them. An interesting approach is to use multiple populations and process them with separate PBAs (in a different way). In this paper, we propose a new multi-population-based algorithm with: (a) subpopulation evaluation and (b) replacement of the associated PBAs subpopulation formulas used for their processing. In the simulations, we used a set of typical CEC2013 benchmark functions. The obtained results confirm the validity of the proposed concept.

An enhanced artificial hummingbird algorithm and its application in truss topology engineering optimization

In view of the shortcomings such as slow search speed, low optimization precision and premature convergence of artificial hummingbird algorithm, an enhanced artificial hummingbird algorithm based on golden sine factor named DGSAHA is proposed. Firstly, chaos mapping is used to generate the initial candidate solution to increase the diversity of the population, which lays the foundation for the global search. Then, perturb the individuals by means of the differential variation between individuals on the group, thereby enhancing the diversity of the population, preserving the excellent individuals, eliminating the inferior individuals, and guiding the search process to approach the global optimal solution, avoiding the phenomenon of premature convergence. Finally, the golden sine factor were introduced in the guided foraging stage is conducive to the full exploration of the global optimal solution, reducing the search space for individuals to approach the optimal solution. And, it facilitates the balance between “exploration” and “exploitation” of algorithm. Thereby, the accuracy and speed of the DGSAHA can be improved to a certain extent. 25 classic functions, the CEC2014 and CEC2019 benchmark functions were tested, and several representative meta-heuristic algorithms and its improved algorithm are compared for evaluate the validity of DGSAHA. Meanwhile, the dimensional scalability of the variable-dimensional test function is discussed. The results of non-parametric statistical analysis and performance index show that DGSAHA in this paper has better comprehensive optimization performance, significantly improves the search speed and convergence precision, and has strong ability to get rid of the local optimal solution. Finally, the performance of DGSAHA and the practicability of truss structure are answered by three engineering examples of plane and space truss topology optimization problem. This optimization problem considers not only the static constraints such as stress, displacement and buckling, but also the dynamic constraints of frequency and motion stability. In order to avoid singularity and unnecessary analysis, the stiffness, mass and load matrices are reconstructed in finite element analysis. A lighter truss structure than the existing solution is obtained. The validity, extensibility and practicability of the algorithm are further illustrated.

Moving-Distance-Minimized PSO for Mobile Robot Swarm.

Particle swarm optimizer (PSO) and mobile robot swarm are two typical swarm techniques. Many applications emerge separately along both of them while the similarity between them is rarely considered. When a solution space is a certain region in reality, a robot swarm can replace a particle swarm to explore the optimal solution by performing PSO. In this way, a mobile robot swarm should be able to efficiently explore an area just like the particle swarm and uninterruptedly work even under the shortage of robots or in the case of unexpected failure of robots. Furthermore, the moving distances of robots are highly constrained because energy and time can be costly. Inspired by such requirements, this article proposes a moving-distance-minimized PSO (MPSO) for a mobile robot swarm to minimize the total moving distance of its robots while performing optimization. The distances between the current robot positions and the particle ones in the next generation are utilized to derive paths for robots such that the total distance that robots move is minimized, hence minimizing the energy and time for a robot swarm to locate the optima. Experiments on 28 CEC2013 benchmark functions show the advantage of the proposed method over the standard PSO. By adopting the given algorithm, the moving distance can be reduced by more than 66% and the makespan can be reduced by nearly 70% while offering the same optimization effects.

Individual disturbance and neighborhood mutation search enhanced whale optimization: performance design for engineering problems

AbstractThe whale optimizer is a popular metaheuristic algorithm, which has the problems of weak global exploration, easy falling into local optimum, and low optimization accuracy when searching for the optimal solution. To solve these problems, this paper proposes an enhanced whale optimization algorithm (WOA) based on the worst individual disturbance (WD) and neighborhood mutation search (NM), named WDNMWOA, which employed WD to enhance the ability to jump out of local optimum and global exploration, adopted NM to enhance the possibility of individuals approaching the optimal solution. The superiority of WDNMWOA is demonstrated by representative IEEE CEC2014, CEC2017, CEC2019, and CEC2020 benchmark functions and four engineering examples. The experimental results show that thes WDNMWOA has better convergence accuracy and strong optimization ability than the original WOA.

An Efficient Improved Greedy Harris Hawks Optimizer and Its Application to Feature Selection.

To overcome the lack of flexibility of Harris Hawks Optimization (HHO) in switching between exploration and exploitation, and the low efficiency of its exploitation phase, an efficient improved greedy Harris Hawks Optimizer (IGHHO) is proposed and applied to the feature selection (FS) problem. IGHHO uses a new transformation strategy that enables flexible switching between search and development, enabling it to jump out of local optima. We replace the original HHO exploitation process with improved differential perturbation and a greedy strategy to improve its global search capability. We tested it in experiments against seven algorithms using single-peaked, multi-peaked, hybrid, and composite CEC2017 benchmark functions, and IGHHO outperformed them on optimization problems with different feature functions. We propose new objective functions for the problem of data imbalance in FS and apply IGHHO to it. IGHHO outperformed comparison algorithms in terms of classification accuracy and feature subset length. The results show that IGHHO applies not only to global optimization of different feature functions but also to practical optimization problems.

Adolescent Identity Search Algorithm Based on Fast Search and Balance Optimization for Numerical and Engineering Design Problems.

This paper proposed a fast convergence and balanced adolescent identity search algorithm (FCBAISA) for numerical and engineering design problems. The main contributions are as follows. Firstly, a hierarchical optimization strategy is proposed to balance the exploration and exploitation better. Secondly, a fast search strategy is proposed to avoid the local optimization and improve the accuracy of the algorithm; that is, the current optimal solution combines with the random disturbance of Brownian motion to guide other adolescents. Thirdly, the Chebyshev functional-link network (CFLN) is improved by recursive least squares estimation (RSLE), so as to find the optimal solution more effectively. Fourthly, the terminal bounce strategy is designed to avoid the algorithm falling into local optimization in the later stage of iteration. Fifthly, FCBAISA and comparison algorithms are tested by CEC2017 and CEC2022 benchmark functions, and the practical engineering problems are solved by algorithms above. The results show that FCBAISA is superior to other algorithms in all aspects and has high precision, fast convergence speed, and excellent performance.

Opposition-mutual learning differential evolution with hybrid mutation strategy for large-scale economic load dispatch problems with valve-point effects and multi-fuel options

The economic load dispatch (ELD) problem plays a crucial role in power system operation. In practice, the ELD problem becomes a non-convex, multi-constraint, non-linear optimization problem when considering the valve point effects, the prohibited operation zones, the ramp rate limit, and the multi-fuel options. To effectively solve this problem, this paper puts forward an improved differential evolution (DE) named OMLIDE based on opposition-mutual learning, hybrid mutation strategy, and parameters adaptive mechanism. OMLIDE differs from the traditional DE in that: (1) an opposition-mutual learning strategy is employed for population initialization to increase the probability of finding an optimal solution; (2) two novel mutation operators named DE/elite-to-ordinary/1 and DE/elite-to-ordinary/2 are hybridized and a selection probability is introduced to regulate them adaptively at different evolutionary stages; and (3) a parameters adaptive mechanism is presented to adjust the scaling factor and crossover rate. The proposed OMLIDE is first validated by the numerical benchmark functions of CEC 2014. Then it is applied to five non-convex ELD problems with valve-point effects and multi-fuel options. Simulation results demonstrate that OMLIDE provides better or highly competitive results in different terms compared with other peer algorithms.

Dandelion Optimizer: A nature-inspired metaheuristic algorithm for engineering applications

This paper proposes a novel swarm intelligence bioinspired optimization algorithm, called the Dandelion Optimizer (DO), for solving continuous optimization problems. DO simulates the process of dandelion seed long-distance flight relying on wind, which is divided into three stages. In the rising stage, seeds raise in a spiral manner due to the eddies from above or drift locally in communities according to different weather conditions. In the descending stage, flying seeds steadily descend by constantly adjusting their direction in global space. In the landing stage, seeds land in randomly selected positions so that they grow. The moving trajectory of a seed in the descending stage and landing stage are described by Brownian motion and a Levy random walk. CEC2017 benchmark functions are utilized to evaluate the performance of DO, including the optimization accuracy, stability, convergence, and scalability, through a comparison with 9 well-known nature-inspired metaheuristic algorithms. Finally, the applicability of DO is verified by solving 4 real-world optimization problems. The experimental results indicate that the proposed DO method is a higher performing optimizer with outstanding iterative optimization and strong robustness compared with well-established algorithms. Source codes of DO are publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/114680-dandelion-optimizer.

Improved DV-Hop based on parallel and compact whale optimization algorithm for localization in wireless sensor networks

AbstractImproving localization performance is one of the critical issues in Wireless Sensor Networks (WSN). As a range-free localization algorithm, Distance Vector-Hop(DV-Hop) is well-known for its simplicity but is hindered by its low accuracy and poor stability. Therefore, it is necessary to improve DV-Hop to achieve a competitive performance. However, the comprehensive performance of WSN is limited by computing and storage capabilities of sensor nodes. In this paper, we propose an algorithm with parallel and compact techniques based on Whale Optimization Algorithm (PCWOA) to improve DV-Hop performance. The compact technique saves memory consumption by reducing the original population. The parallel techniques enhance the ability to jump out of local optimization and improve the solution accuracy. The proposed algorithm is tested on CEC2013 benchmark functions and compared with some popular algorithms and compact algorithms. Experimental results show that the improved algorithm achieves competitive results over compared algorithms. Finally, simulation research is conducted to verify the localization performance of our proposed algorithm.

Boosted machine learning model for predicting intradialytic hypotension using serum biomarkers of nutrition

Intradialytic hypotension (IDH) is a serious complication of hemodialysis (HD), with an incidence of more than 20%. IDH induces ischemic organ damage and even reduces the ultrafiltration and duration of HD sessions. Frequent attacks of IDH are a risk factor for death in HD patients. Malnutrition is common in HD patients and is also associated with mortality. Although the link between IDH episodes and malnutrition has been observed in practice, it has not been supported by the data. To study the relationship, we propose a promising hybrid model called BSCWJAYA_KELM, which is a wrapper feature selection method based on a variant of the JAYA optimization algorithm (SCWJAYA) and Kernel extreme learning machine (KELM). In this paper, we verify the optimization capability of the SCWJAYA algorithm in the model by comparing experiments with some state-of-the-art methods for IEEE CEC2014, IEEE CEC2017, and IEEE CEC2019 benchmark functions. The prediction accuracy of BSCWJAYA_KELM is validated by the public datasets and the HD dataset. In the experiments on the HD dataset, 1940 HD sessions of 178 HD patients are analyzed by the developed BSCWJAYA_KELM model. The key indicators selected from vast amounts of data are serum uric acid, dialysis vintage, age, diastolic pressure, and albumin. The BSCWJAYA_KELM method is a stable and excellent prediction model that can achieve a more accurate prediction of IDH.

Population interaction network in representative differential evolution algorithms: Power-law outperforms Poisson distribution

Differential evolution is a classical and effective evolutionary algorithm. In recent years, many differential evolution variants have been proposed and achieved good results on many problems. To investigate their inherent characteristics, this paper uses the population interaction network. Six representative differential evolution algorithms including DE, JADE, CJADE, SHADE, L-SHADE, and EBLSHADE are analyzed from the perspective of information interaction among individuals. The cumulative distribution function of degrees of nodes obtained from the population interaction network on thirty IEEE CEC2017 benchmark functions is fitted by seven distribution models. Results show that the cumulative distribution function of differential evolution is the Poisson distribution whereas the other variants meet the Power-law distribution. The Power-law distribution influences their performance and depends on the population size. These remarkable findings suggest that the Power-law distribution widely exists in best-performing differential evolution algorithms, which gives empirical evidence for designing Power-law distribution-based differential evolution algorithms.

Development and Applications of Augmented Whale Optimization Algorithm

Metaheuristics are proven solutions for complex optimization problems. Recently, bio-inspired metaheuristics have shown their capabilities for solving complex engineering problems. The Whale Optimization Algorithm is a popular metaheuristic, which is based on the hunting behavior of whale. For some problems, this algorithm suffers from local minima entrapment. To make WOA compatible with a number of challenging problems, two major modifications are proposed in this paper: the first one is opposition-based learning in the initialization phase, while the second is inculcation of Cauchy mutation operator in the position updating phase. The proposed variant is named the Augmented Whale Optimization Algorithm (AWOA) and tested over two benchmark suits, i.e., classical benchmark functions and the latest CEC-2017 benchmark functions for 10 dimension and 30 dimension problems. Various analyses, including convergence property analysis, boxplot analysis and Wilcoxon rank sum test analysis, show that the proposed variant possesses better exploration and exploitation capabilities. Along with this, the application of AWOA has been reported for three real-world problems of various disciplines. The results revealed that the proposed variant exhibits better optimization performance.

A new metaheuristic optimization based on K-means clustering algorithm and its application to structural damage identification

This paper develops a new metaheuristic optimization algorithm named K-means Optimizer (KO) to solve a wide range of optimization problems from numerical functions to real-design challenges. First, the centroid vectors of clustering regions are established at each iteration using K-means algorithm, then KO proposes two movement strategies to create a balance between the ability of exploitation and exploration. The decision on the movement strategy for exploration or exploitation at each iteration depends on a parameter that will be designed to recognize if each search agent is too long in the region visited with no self-improvement. To demonstrate the effectiveness and reliability of KO, twenty-three classical benchmark functions, CEC2005 and CEC2014 benchmark functions, are employed as a first example and compared with other algorithms. Then, three well-known engineering problems are also considered and their results are compared to the results obtained by the other algorithms. Finally, KO is applied to structural damage identification (SDI) problem of a complex 3D concrete structure including seven stories building having a 25.2 m total height. For this purpose, SAP2000 is used to solve the finite element (FE) model of this structure. Then, for the first time, we successfully developed a sub-program that allows two-way data exchange between SAP2000 and MATLAB through the Open Application Programming Interface (OAPI) library to update the FE model. From the results, we found that KO has the best performance for the considered benchmark functions based on the Wilcoxon rank-sum test and Friedman ranking test. The results obtained in this work have proved the effectiveness and reliability of KO in solving optimization problems, especially for SDI. Source codes of KO is publicly available at http://goldensolutionrs.com/codes.html.

Optimal foraging algorithm with direction prediction and Gaussian oscillation for constrained optimization problems

Optimal foraging algorithm (OFA) is a newly stochastic optimization technique and is famous for its computational accuracy. However, the high computational accuracy leads to slow convergence speed. Experimental results demonstrate that OFA is good at unimodal functions but poor at multimodal functions. To improve these drawbacks, in this paper a novel modified OFA with direction prediction and Gaussian oscillation, named OFA/P&G is introduced. In OFA/P&G, a transition matrix is constructed when a new global optimum is found to generate the candidate individuals. If the current global optimum does not change, the Gaussian oscillation is employed in a low probability and OFA update method is used in a high probability to generate the candidate individuals. The superior performance of OFA/P&G is verified on the 12 CEC2017 benchmark functions, 13 constrained benchmark functions and 5 engineering problems. Experimental results demonstrate that OFA/P&G outperforms other comparative algorithms. Finally, a real-world problem, drilling path optimization, is solved by OFA/P&G.