Search

Population diversity holds significant importance in determining the success of any evolutionary algorithm. It helps the algorithm in efficiently exploring the search space and identifying the promising region(s) containing global optimal solution(s). However, during the optimization procedure the population may lose its diversity, causing premature convergence in the algorithm and resulting in approximations to the sub-optimal solution(s). This paper proposes a Voronoi Tessellations based Simple Optimizer (VTSO) algorithm that utilizes a niche concept of Voronoi Tessellations (VTs) from the field of computational geometry to ensure a well-distributed population throughout the optimization procedure. It proposed an elite sampling mechanism that utilizes Lévy flights to aggressively explore the search space for locating potential optimal region(s), and the Differential Evolution (DE) algorithm to exploit these regions in order to approximate the global optimal solution(s). In addition, a population diameter-based switch is devised which activates itself when the algorithm detects premature convergence in the algorithm. Experiments are conducted on CEC14 and CEC17 benchmark test suit, and the proposed algorithm is compared with the existing state-of-the-art evolutionary algorithms. The results are competitive to recommend the VTSO algorithm as a new efficient and accurate optimizer for handling complex optimization problems. • This paper proposed a computational geometry approach for improving population diversity in evolutionary algorithms. • This includes a novel Voronoi Tessellations-based population generation method. • A levy flight and Differential Evolution assisted approach for updating population in the search space. • In addition, a population diameter-based switch is proposed to check the stagnation or premature convergence. [ABSTRACT FROM AUTHOR]

Surrogate-assisted evolutionary algorithms (SAEAs) have gained considerable attention owing to their ability of tackling expensive optimization problems (EOPs). The surrogate model can be used to replace real fitness value with approximated one, thus greatly reducing computational cost in expensive function evaluations. However, most existing SAEAs are designed for expensive optimization with low or medium dimensions owing to the curse of dimensionality. To improve the performance for solving high-dimensional expensive optimization problems (HEOPs), a surrogate-assisted Differential Evolution with fitness-independent parameter adaptation (SADE-FI) is proposed in the paper. The SADE-FI algorithm consists of a global surrogate-assisted prescreening strategy (GSA-PS) and a local surrogate-assisted DE with fitness-independent parameter adaptation (LSA-FIDE). The main highlights of the paper can be summarized as follows: First, both global and local surrogates are employed to approximate the fitness value of candidate offspring in GSA-PS and LSA-FIDE, respectively. Second, a fitness-independent parameter adaptation mechanism is firstly incorporated into the framework of surrogate-assisted DE as an efficient parameter adaptation for surrogate-assisted search. Third, both the kernel space determination mechanism and linear population size reduction strategy are implemented to enhance the exploitation capability of LSA-FIDE. To validate the performance of SADE-FI, it was tested on expensive benchmark functions on 30D, 50D, 100D, and 200D, as well as a real-world antenna array design problem. The optimization results were compared with state-of-the-art algorithms, and the results indicate that SADE-FI has a significant performance advantage in solving HEOPs. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is an efficient and powerful population-based search algorithm for solving numerical optimization problems in continuous spaces. It has been proven that multi-strategy DE algorithms are more effective than single-strategy DE algorithms in addressing benchmark and real-world problems. However, most multi-strategy DE variants focus on maintaining population diversity and balancing exploitation and exploration, ignoring the dynamic allocation of computational resources. Moreover, the success of these algorithms often depends on additional designed techniques, leading to increased computational complexity. In this paper, the Collaborative Resource Allocation-based Differential Evolution (CRADE) is introduced. It involves a collaborative resource allocation mechanism that utilizes the historical performance ranking of three mutation strategies to automatically allocate computational resources to various subpopulations during the search process. The parameter adaptation technique is used to adjust the associated control parameters of different mutation strategies. As a result, the most efficient mutation strategy consumes the majority of computational resources at different search stages to mitigate inefficient search under constrained resources. The performance of CRADE is evaluated on the well-known CEC2013 benchmark function set. The paper also investigates its application in the parameter identification of photovoltaic solar cells and modules. The overall results show that CRADE exhibits superior and competitive performance compared to other state-of-the-art algorithms. Consequently, CRADE has emerged as a novel and effective approach for addressing numerical optimization problems, distinguished by its excellence, practicality, and unwavering reliability. [ABSTRACT FROM AUTHOR]

In this paper, an efficient method for solving multiple knapsack problem (MKP) using discrete differential evolution is proposed. Firstly, an integer programming model of MKP suitable for discrete evolutionary algorithm is established. Secondly, a new method for discretizing continuous evolutionary algorithm is proposed based on the combination of transfer function and modulo operation. Therefrom, a new discrete differential evolution algorithm (named TMDDE) is proposed. Thirdly, the algorithm GROA is proposed to eliminate infeasible solutions of MKP. On this basis, a new method for solving MKP using TMDDE is proposed. Finally, the performance of TMDDE using S-shaped, U-shaped, V-shaped, and Taper-shaped transfer functions combined with modulo operation is compared, respectively. It is pointed out that T3-TMDDE which used Taper-shaped transfer function T3 is the best. The comparison results of solving 30 MKP instances show that the performance of T3-TMDDE is better than five advanced evolutionary algorithms. It not only indicates that TMDDE is more competitive for solving MKP, but also demonstrates that the proposed discretization method is an effective method. [ABSTRACT FROM AUTHOR]

Surrogate-Assisted Evolutionary Algorithms (SAEAs) integrate Evolutionary Algorithms (EAs) with surrogate models to reduce the actual number of expensive function evaluations and have been widely used in solving Expensive Optimization Problems (EOPs). However, because of the insufficient diversity of new solutions, SAEAs often fall into local optima and result in evolutionary stagnation when dealing with complex problems. To improve the diversity of new solutions, this paper introduces a S urrogate- A ssisted evolutionary F ramework with an ensemble of T eaching-learning and D ifferential evolution (SAF-TD), which successfully integrates the strengths of both EAs to produce more diverse and effective solutions. The main contributions are summarized as follows: First, a novel framework that effectively integrates two distinct EAs using a radial basis function surrogate model and strategic sampling is introduced. Second, a mutation strategy with a supervisory mechanism is proposed to enhance mutation effectiveness and avoid stagnation. Third, a volatility index derived from dimensional improvements is incorporated into parameter control to address fitness-dependent weaknesses. Experiments on five expensive optimization functions and the CEC2017 test suite across multiple dimensions were conducted to evaluate the performance of SAF-TD. The results demonstrate that SAF-TD is highly competitive compared with state-of-the-art SAEAs and exhibits excellent performance in solving EOPs. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is a simple but powerful population based evolutionary algorithm, which was widely used to solve various complex optimization problems. However, even recently proposed state-of-the-art DE variants tend to get trapped in local minima due to insufficient population diversity in the later stages of evolution. In this paper, an A daptive C luster D ivision D ifferential E volution (ACD-DE) algorithm was proposed to mitigate population diversity deficiency. The main highlights are summarized as follows: Firstly, a novel cluster division based mutation strategy was proposed to enhance the diversity of difference vectors during the mutation operation. Secondly, a population diversity detection indicator was used to assess the stagnation level of individuals, enabling stagnation management to be launched based on different stagnation levels. Thirdly, an effective evolution guidance mechanism was proposed by adjusting certain parameters in the D -dimensional vectors of outlier individuals that significantly deviate from the current population. Fourthly, novel parameter adaptations were employed to dynamically adjust the control parameters, including the scale factor F , crossover rate CR , and population size PS , during evolution. To validate the ACD-DE algorithm, extensive experiments were conducted on 88 benchmark functions from the CEC2013, CEC2014, and CEC2017 test suites, focusing on the optimization accuracy, convergence speed, time complexity, and component effectiveness. The results demonstrate the superiority of our ACD-DE algorithm compared to state-of-the-art DE variants. [ABSTRACT FROM AUTHOR]

Multimodal multi-objective optimization problems (MMOPs), which aim to identify as many optimal solutions as possible and exhibit multiple equivalent Pareto optimal solution sets (PSs) that correspond to the same Pareto optimal front (PF), commonly arise in a wide range of optimization problems in the real world. However, some dominated solutions that exhibit greater diversity in the decision space may be substituted by non-dominated solutions with a higher level of decision space crowding. To tackle this issue, this paper proposes a multimodal multi-objective differential evolution with series-parallel combination and dynamic neighbor strategy (MMODE_SPDN), which can balance convergence, objective space diversity and decision space diversity. Specifically, two archives are initially updated serially followed by the overall update of the parallel structure, in which the serial-first approach can enhance population diversity and the parallel structure can greatly reduce the amount of calculation. In addition, a dynamic neighbor strategy which utilizes adaptive selection among neighbors to generate difference vectors in the decision space and objective space and then adopts the main and auxiliary parent method during the mutation process is proposed. Furthermore, the utilization of an auxiliary archive and the clustering-based special crowding distance (CSCD) method are employed to facilitate the updating of the archive, thereby enhancing diversity. MMODE_SPDN is compared with other multimodal multi-objective optimization evolutionary algorithms (MMOEAs) on numerous test problems and the experimental results demonstrate that MMODE_SPDN exhibits superior performance. • The series-parallel combination strategy is proposed. • The dynamic neighbor based mutation strategy is proposed. • The CSCD-Based archive update method is proposed. • A ranking method is used in the series-parallel combination strategy. • The environmental selection approach introduced in the SPEA2 is employed in MMODE_SPDN. [ABSTRACT FROM AUTHOR]

Constrained multimodal multi-objective optimization problems (CMMOPs) consist of multiple equivalent constrained Pareto sets (CPSs) that have the identical constrained Pareto front (CPF). It is challenging for primary multimodal multi-objective evolutionary algorithms (MMEAs) to solve CMMOPs since they do not consider constraints. To tackle this challenge, a dynamic speciation-based differential evolution with ring topology, termed DSRDE, for solving CMMOPs is developed in this paper. To search for multiple equivalent CPSs in CMMOPs, the dynamic speciation-based niche strategy is developed. The dynamic speciation-based niche strategy divides the population into multiple species, each of which searches for diverse and equivalent CPSs in different regions. Particularly, the species number is dynamically decreased to explore the equivalent CPSs with good convergence. Then, a ring topology is constructed among multiple species and their neighbors to balance the diversity, convergence, and feasibility of solutions. Continuously, each species interacts information with its neighbors and searches for equivalent CPSs. DSRDE adopts the popular constrained dominance principle to handle constraints and uses the differential evolutionary algorithm to locate diverse CPSs in the ring topology. It is compared with several state-of-the-art algorithms in two CMMOPs test suites for evaluating the performance of the proposed DSRDE. The experimental results confirm that DSRDE is competitive and has the ability to find multiple CPSs when tackling CMMOPs. DSRDE is also implemented in a real-world CMMOP and obtains superior performance. [ABSTRACT FROM AUTHOR]

Multimodal multi-objective optimization problem (MMOP) is a variant of the multi-objective problem (MOP), which has multiple optimal Pareto sets (PSs) mapping to the same or similar Pareto front (PF) from the decision space to the objective space. As algorithms must obtain multiple Pareto Sets, addressing MMOPs presents greater challenges for algorithms. To address the issue, the paper proposes a novel multimodal multi-objective differential evolution algorithm named MMODE_SDNR. Firstly, the algorithm sorts the population using the fast non-dominated sorting method and the Shortest Distance (SD) values. SD represents the shortest Euclidean distance between an individual and its nearest neighboring individual, calculated jointly in the decision space and the objective space. Secondly, a definition of the similarity between an individual and its neighbors in both spaces is provided, based on which a novel environmental selection strategy for the algorithm, called the nearest Neighbor-Repulsion (nNR) is devised. The strategy removes the individuals that have similarity with one another to maximize the retention of different individuals. Moreover, it keeps the diversity of PSs in the decision space and retains more solutions that exhibit a similar or same PF in the objective space. Finally, the proposed MMODE_SDNR has undergone several tests on the benchmark functions from CEC 2019 and CEC 2020 to assess its performance. The experimental results indicate that MMODE_SDNR excels in three metrics, outperforming other several state-of-the-art MMO algorithms. Its strong convergence and focus on decision space quality ensure competitiveness. [ABSTRACT FROM AUTHOR]

Solving nonlinear equation systems (NESs) is one of the most important tasks in numerical computing. The NESs usually have multiple roots, and quickly locating their roots in a single algorithm run with a limited number of iterations has always been the algorithm improvement direction. In order to further enhance the efficiency of the existing methods, a density clustering-based differential evolution algorithm (DCDE) for the NESs problem solving is proposed in this paper. Firstly, density-based spatial clustering of applications with noise (DBSCAN) is used to divide the population into clusters and noises, which provides a better direction for population evolution. Secondly, a cluster evaluation factor is proposed, which not only divides the clusters into excellent clusters and non-excellent clusters, but also prevents the migration of excellent clusters and maintain the diversity of populations. Then, a migration strategy and individual generation mechanism are proposed to guide non-excellent clusters to migrate to promising regions. Finally, combined with an archive technique, the individuals which satisfy the solution requirements are archived and randomly initialized to further improve population diversity. To verify the effectiveness of the proposed algorithm, comparative experimental results of the propsoed DCDE with other state-of-the-art algorithms for thirty NESs problems solving show that the proposed DCDE is the most effective algorithm to locate more roots in a single run. [ABSTRACT FROM AUTHOR]

• An improved gaining-sharing knowledge-based algorithm named MSGSK is proposed. • A parameter adjustment strategy is developed to adjust relative parameters of MSGSK. • A backtracking differential mutation strategy is designed to enrich the population diversity. • A strategy selection mechanism is presented to integrate the former two strategies. • MSGSK extracts more accurate parameters for five PV models. The determination of photovoltaic (PV) model parameters has essential theoretical and practical significance for the performance evaluation, power monitoring, and power generation efficiency calculation of PV systems. In this paper, a multi-strategy gaining-sharing knowledge-based algorithm (MSGSK) is developed to determine these parameters. In our previous work, it has been demonstrated that gaining-sharing knowledge-based algorithm (GSK) is well suited for solving the concerned problem. To enhance its performance, a parameter adjustment strategy is developed to adjust the knowledge rate and knowledge ratio of GSK. Besides, a backtracking differential mutation strategy by combining the mutation scheme of differential evolution and the updating scheme of backtracking search optimization algorithm is developed to enrich the population diversity. Furthermore, a strategy selection mechanism is introduced to integrate the former two strategies to balance exploration and exploitation in different stages of the evolutionary process. The suggested MSGSK algorithm is applied to five PV cases (SDM, DDM, Photowatt-PW201, STM6-40/36, and STP6-120/36). From the experimental data, it can be observed that MSGSK extracts the PV model parameters more precisely than the basic GSK. Furthermore, it exhibits faster convergence speed and higher accuracy compared to other advanced algorithms found in the literature. [ABSTRACT FROM AUTHOR]

• Analyze DE algorithm two key issues: parameter sensitivity and search imbalance. • A complementary mutation strategy based on complementary symmetric selection and a Gaussian distribution mutation is proposed. • Data fusion-based parameter adaptation method proposed for parameter rationalization. • A novel variant of DE called DACDE is designed and results shown competitive edge. As an excellent optimization algorithm widely used to solve various practical problems, differential evolution (DE) algorithm has few parameters, yet its performance is significantly affected by these parameters. To address this issue, this paper presents a novel variant of DE called DACDE, which utilizes data fusion-based parameter adaptation and a complementary mutation strategy. Most parameter adaptation methods based on successful history only analyze the mean of parameters and ignore their degree of dispersion. In DACDE, the successful parameter distribution is recorded and described by both the mean and variance. Data fusion is then used to combine records and generate an estimated distribution, which is applied to a Gaussian distribution to generate new parameters. Inspired by opposition-based learning, we introduce a complementary mutation strategy. This strategy employs a symmetric selection mechanism to adapt to the varying search abilities required by the algorithm at different stages. The new variant is verified on 32 single-objective functions from CEC 2011 and 2014 benchmark suites, and the results show that DACDE is competitive compared to other 29 evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Crypto-currency markets are known to exhibit inefficiencies, which presents opportunities for profitable cyclic transactions or arbitrage, where one currency is traded for another in a way that results in a net gain without incurring any risk. Quantum computing has shown promise in financial applications, particularly in resolving optimization problems like arbitrage. In this paper, we introduce a differential evolution (DE) optimization algorithm for Variational Quantum Eigensolver (VQE) using Qiskit framework. We elucidate the application of crypto-currency arbitrage using different VQE optimizers. Our findings indicate that the proposed DE-based method effectively converges to the optimal solution in scenarios where other commonly used optimizers, such as COBYLA, struggle to find the global minimum. We further test this procedure's feasibility on IBM's real quantum machines up to 127 qubits. With a scenario of three currencies, the algorithm converged in 417 steps over a 12 hour period on the "ibm_geneva" machine. These results suggest the potential to achieve a quantum advantage in solving increasingly complex problems. • We introduce a differential evolution (DE) optimization algorithm for Variational Quantum Eigensolver (VQE) using Qiskit. • We validate this method using crypto-currency arbitrage, as an example of problem with many local minima. • We test this procedure's feasibility on IBM's real quantum machines up to 127 qubits. [ABSTRACT FROM AUTHOR]

Various variants have been proposed to improve the search ability and efficiency of Differential Evolution (DE). However, the variants ignore the impact caused by the use of accumulated historical information, resulting in unpromising performance of the search. Furthermore, the global exploration and local exploitation ability of population is affected by the population number (NP), which commonly adapts with little adaptive control or with linear descendent only. To utilize more historical population information, we propose in this paper a novel adaptive population size-based DE (APSDE) by mining historical population information, to balance global exploration and local exploitation ability. APSDE uses historical population information to mine population distribution and extract information to assign parameters to the current population. Moreover, an archive is utilized to store the historical population information, where historical successful parameter information consists of scaling factor (F), crossover rate (CR) and NP for better balancing the search ability of population. To evaluate the performance of APSDE, we conduct experiments both on the 28 benchmark functions of CEC2017, the 10 benchmark functions of CEC2020, and a real-world application - the path planning of unmanned aerial vehicles (UAVs). The experimental results have demonstrated that APSDE achieves the promising performance in both convergence accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

In this paper, a new differential evolution (DE) algorithm is presented for solving global optimization problems by guiding the individuals adaptively to explore different decision regions and setting the control parameters properly for individuals. To consolidate algorithm efficiency and preserve population diversity, we first introduce a proration-based mutation strategy. This strategy dynamically selects promising individuals from population as guiders and proportionately allocates the individuals following them based on their fitness values and unsuccessful updates. Besides, we design a multi-segment mixed parameter setting to provide suitable parameters for individuals, considering feedback information from the population, individual requirements, and parameters' interaction. Additionally, we devise an adaptive population maintaining mechanism to refresh the population by replacing individuals with higher unsuccessful updates and removing those with poor fitness values. Unlike previous DE versions, our new algorithm dynamically and appropriately explores promising areas, refines parameter suitability, and accelerates convergence by updating and removing unpromising individuals. This enhances the algorithm search efficiency and achieves a good balance between exploration and exploitation. Finally, we evaluate the proposed algorithm's performance by comparing it with 17 typical or state-of-the-art algorithms on IEEE CEC2014 and CEC2017 test suites. Experimental results indicate that the proposed algorithm is a more promising optimizer. [ABSTRACT FROM AUTHOR]

Filter pruning has been successfully applied in convolutional neural networks (CNN) to reduce model redundancy and speed up inference. Current pruning algorithms require setting a target value for a pruned model, which is not conducive to the rapid implementation in practical application. Firstly, for a target model, it may be necessary to pay attention to multiple performances at the same time, but it is hard to keep the best trade-off among indicators. Secondly, it is time-consuming to find a suitable model by pruning in a trial-and-error way. Therefore, this paper attempts to combine the most concerning indicators into a search target, rather than producing a model that only contains some pre-defined constraint. Specifically, the multi-object differential evolution algorithm is introduced into the search process, which is used to obtain a set of sparse structures that have taken all useful indicators into account. Then select proper sub-network to retrain from search results according to actual requirements. Experiments on multiple advanced CNN networks show that our algorithm can compress different indicators while keeping comparable or better performance than prior works. On ImageNet, pruning based on ResNet50 reduces FLOPs by 60.4%, while the accuracy of top-1 and top-5 only loses 1.09% and 0.57%, respectively. [ABSTRACT FROM AUTHOR]

Over the past few years, many evolutionary algorithms have been developed to find multiple roots of the nonlinear equation system (NES). However, they can only solve one NES in a single run, ignoring the potentially useful information and solving experience derived from different NESs. To this end, an evolutionary multitasking NES optimization framework called MTNES, is proposed for the first time in this paper for solving multiple NESs simultaneously. Specifically, we first initialize multiple NES tasks in a 0-1 unified search space to establish an implicit relationship between NESs to facilitate knowledge transfer. Then, combining differential evolution and neighborhood technique, a neighborhood knowledge transfer is presented to reduce negative knowledge transfer and thus help find more roots. In addition, a novel resource reallocation mechanism is developed to release the found roots, thereby improving population diversity as well as aiding the search for more promising areas. Numerous empirical results reveal that the proposed approach can achieve a higher root rate and success rate when compared with several well-established algorithms on eighteen complex NESs. Moreover, experimental results on two real-world applications further show the potential practicability of the proposed multitasking NES-solving framework. • An evolutionary multitasking NES-solving framework MTNES is proposed. • A 0-1 unified search space is introduced to narrows the search scope and facilitate knowledge transfer. • A neighborhood knowledge transfer is presented to reduce negative knowledge transfer. • A novel resource reallocation mechanism is proposed to release the found roots. [ABSTRACT FROM AUTHOR]

Effective gas system scheduling is vital for ensuring the safe operation and energy efficiency of steel production. However, the dynamic and cyclical nature of gas generation and consumption leads to fluctuations in gas network pressure and gas holder levels. To address this issue, this paper proposes a novel strategy for gas system scheduling based on multi-objective differential evolution. The originality lies in fully considering the workload of operators, effectively reducing the workload while ensuring gas network stability. We analyze the composition of the gas system and design a scheduling scheme. Subsequently, a novel gas holder level model based on mechanism analysis is established, which calculates the gas holder level by analyzing the volume and pressure of the gas. Then, a gas system scheduling model with a new objective function based on a multi-objective differential evolution algorithm is provided. By comparing with the two recent methods, this method reduced the number of adjustments by 13.9% and 9.75%, respectively, effectively reducing the workload while ensuring gas system stability. Through statistical analysis for eight consecutive months, the results show that this method can reduce the gas emission rate from 1.34% to 0.88%, demonstrating its correctness and effectiveness. [ABSTRACT FROM AUTHOR]

In many comparison papers Evolutionary Algorithms are stopped after a pre-defined number of function calls, which is a code-independent measure of computational time. This number of function calls is either defined by the inventors of particular benchmark problems, or set subjectively by the user for the specific problem. The question how much improvement could be achieved by Evolutionary Algorithms if they were given much more time is surprisingly rarely asked. In the present study we analyze improvements obtained by thirty Evolutionary Algorithms on four different benchmark sets, including one composed of 22 real-world problems, when the allowed number of function calls is extended ten times with respect to the values defined in the comparison criteria for the specific benchmark sets. We analyze how the prolonged search would affect the ranking of algorithms, how much improvement could be obtained by Evolutionary Algorithms in general, on what kind of problems the improvement will be achieved, and which type of algorithms would benefit most from such an extended search. We show that the improvements obtained in prolonged search are higher for real-world problems than for mathematical functions, and such improvements are mainly achieved by similar kinds of adaptive algorithms proposed relatively recently. Many metaheuristics fail to benefit from the extended search on most benchmark problems, or benefit only marginally. [ABSTRACT FROM AUTHOR]

Researchers at Federal University Juiz De Fora in Brazil have conducted a study on the use of thermal analysis for the clinical diagnosis of breast tumors. They propose using metaheuristics to estimate the geometric parameters of multicentric breast tumors through thermography. The study compares three algorithms - differential evolution, genetic algorithm, and self-adaptive differential evolution - and finds that the self-adaptive differential evolution approach outperforms the others. The research suggests that this approach could be a suitable alternative for solving this type of inverse problem. [Extracted from the article]

A new report from Northeastern University in Shenyang, China discusses the importance of selecting critical features from microarray data as biomarkers for disease diagnosis and drug development. The report proposes a hybrid feature-selection algorithm that combines the Max Relevance and Min Redundancy (mRMR) method with differential evolution. This algorithm improves the quantization functions of mRMR to accommodate the continuous nature of microarray data attributes and utilizes an enhanced differential evolution algorithm to further filter the features. The research concludes that this hybrid algorithm improves the performance and efficiency of feature selection for microarray data analysis. [Extracted from the article]

A study conducted at the National Yunlin University of Science and Technology in Taiwan explores the identification of fractional Hammerstein models for electrical stimulated muscle. The researchers propose a parameter estimation technique based on a fuzzy-weighted differential evolution algorithm for these models, which are important for the rehabilitation of spinal cord injury patients. The results show that the algorithm is effective in accurately identifying the parameters of the models, with high precision, stability, and reliability. This research has been peer-reviewed and published in Biomedical Signal Processing and Control. [Extracted from the article]