Terminal Conditions Research Articles

A class of supercritical/critical singular stochastic PDEs: Existence, non-uniqueness, non-Gaussianity, non-unique ergodicity

We study the surface quasi-geostrophic equation with an irregular spatial perturbation∂tθ+u⋅∇θ=−ν(−Δ)γ/2θ+ζ,u=∇⊥(−Δ)−1θ, on [0,∞)×T2, with ν⩾0, γ∈[0,3/2) and ζ∈B∞,∞−2+κ(T2) for some κ>0. This covers the case of ζ=(−Δ)α/2ξ for α<1 and ξ a spatial white noise on T2. Depending on the relation between γ and α, our setting is subcritical, critical or supercritical in the language of Hairer's regularity structures [38]. Based on purely analytical tools from convex integration and without the need of any probabilistic arguments including renormalization, we prove existence of infinitely many analytically weak solutions in Llocp(0,∞;B∞,1−1/2)∩Cb([0,∞);B∞,1−1/2−δ)∩Cb1([0,∞);B∞,1−3/2−δ) for all p∈[1,∞) and δ>0. We are able to prescribe an initial as well as a terminal condition at a finite time T>0, and to construct steady state, i.e. time independent, solutions. In all cases, the solutions are non-Gaussian, but we may as well prescribe Gaussianity at some given times. Moreover, a coming down from infinity with respect to the perturbation and the initial condition holds. Finally, we show that our solutions generate statistically stationary solutions as limits of ergodic averages, and we obtain existence of infinitely many non-Gaussian time dependent ergodic stationary solutions. We also extend our results to a more general class of singular SPDEs.

Factorized squared Smith method for large-scale Stein equations with high-rank terms

Solving large-scale Stein equations with high-ranked coefficient and constant terms is relatively difficult since the solution is no longer numerically low-ranked and its storage and outputting are nontrivial. This paper presents a factorized squared Smith method (FSS) that consists of banded and low-ranked parts to overcome this obstacle when the coefficient and the constant matrices are banded-plus-low-ranked. The deflation process as well as the partial truncation and compression are presented to control the growth of the columns of the low-ranked factors, effectively reducing the complexity of the FSS method. The convergence of the banded and the low-ranked parts is established and the banded part is shown being always numerically banded under some assumptions. The residual computation as well as the termination condition have been redesigned. Numerical examples indicate that for large-scale problems, the proposed FSS algorithm outperforms the Smith method with hierarchical HODLR structured toolkit on CPU time.

Neuromorphic Circuit Implementation of Operant Conditioning Based on Emotion Generation and Modulation

In this work, an operant conditioning (OC) model and memristive circuit implementation based on emotion generation and modulation is proposed, which is inspired by neural and psychological mechanisms to simulate human behavioral decisions guided by reinforcers and emotional changes during interaction with dynamically changing environments. The OC model consists of four main modules which are the cue-synapse-action module, the reward and punishment value systems, and the emotion system. Under four conditions of reward appearance or termination, and punishment appearance or termination, the memristive circuit designed according to the OC model can realize the process of exploration, acquisition, extinction, and recovery of OC (external phenomena), and also reflect the process of change of value signals and emotion signals (internal states). In addition, the phenomena of reward fatigue and punishment adaptation are considered so that value and emotion signals gradually diminish with the repetition of invariant reinforcers. The neuromorphic circuit is verified to have good robustness and device tolerance. This work enables multi-timescale OC tasks and is expected to be applied in an emotionally intelligent robot platform to achieve humanoid functions such as real-time dynamic decision-making for interaction with the environment and emotional companionship.

Relaxed Actor-Critic With Convergence Guarantees for Continuous-Time Optimal Control of Nonlinear Systems

This paper presents the Relaxed Continuous-Time Actor-critic (RCTAC) algorithm, a method for finding the nearly optimal policy for nonlinear continuous-time (CT) systems with known dynamics and infinite horizon, such as the path-tracking control of vehicles. RCTAC has several advantages over existing adaptive dynamic programming algorithms for CT systems. It does not require the ``admissibility" of the initialized policy or the input-affine nature of controlled systems for convergence. Instead, given any initial policy, RCTAC can converge to an admissible, and subsequently nearly optimal policy for a general nonlinear system with a saturated controller. RCTAC consists of two phases: a warm-up phase and a generalized policy iteration phase. The warm-up phase minimizes the square of the Hamiltonian to achieve admissibility, while the generalized policy iteration phase relaxes the update termination conditions for faster convergence. The convergence and optimality of the algorithm are proven through Lyapunov analysis, and its effectiveness is demonstrated through simulations and real-world path-tracking tasks.

Symplectic period mode decomposition method and its application in fault diagnosis of rolling bearing

The rolling bearing fault signals are accompanied with the specific periodic impulse components in case of fault. Due to the background noise, the periodic impulse component is extremely weak and difficult to be extracted. The periodic segment matrix (PSM) has excellent singular value aggregation property and can accurately separate the periodic impulse components from the signal. Based on this, a symplectic period mode decomposition (SPMD) method is proposed. Firstly, the singular value squared difference ratio (SVSDR) spectrum is defined, and the embedded dimension of PSM is determined. Then, the symplectic geometry component matrix is obtained by symplectic geometry similarity transformation, and the first symplectic geometry period component (SPC) is obtained by periodic impact intensity (PII). Finally, the spectral L2/L1 norm (SNL2/L1) index is used as the termination condition, and the iterative decomposition is terminated when the SNL2/L1 of the residual signal decreases. The emulation and experimental signals results indicate that the SPMD method can extract periodic impulse components accurately and is an effective rolling bearing fault diagnosis method.

Robust global mantle flow trajectories and their validation via dynamic topography histories

SUMMARYThe ability to construct time-trajectories of mantle flow is crucial to move from studies of instantaneous to time-dependent earth models and to exploit geological constraints for mantle convection modelling. However mantle convection is chaotic and subject to the butterfly effect: the trajectories of two identical mantle convection models initialized with slightly different temperature fields diverge exponentially in time until they become uncorrelated. Because one may use seismic inferences about the mantle state as a starting or terminal condition to project mantle flow forward or backward in time, and because the seismic inference is invariably subject to uncertainties, this seemingly would rule out any construction of robust mantle flow trajectories. Here we build upon earlier work which showed that assimilation of the horizontal component of the surface velocity field from a known reference model allows one to overcome the butterfly effect and to construct robust mantle flow trajectories, regardless of the choice of the initial state perturbation. To this end, we use high resolution 3-D spherical mantle convection models in four end-member configurations: an isoviscous purely internally heated model, an isoviscous purely bottom heated model, a model with a radial increase in viscosity along with pure internal heating as well as a model that combines the effects of radial viscosity increase, internal and bottom heating. In order to capture the impact of seismic filtering, we perturb the initial temperature fields of these end-member models through either radial or horizontal smoothing of the temperature field or the application of the tomographic filter of seismic model S20RTS. We assess the quality of the constructed model trajectories via a number of statistical measures as well as comparisons of their dynamic topography histories. The latter is an essential step since mantle flow cannot be directly observed but has to be inferred via its surface manifestations. Importantly, linking mantle flow to surface observations yields patterns representable on a latitude–longitude grid similar to meteorological observables such as precipitation. This invites the application of meteorological quality metrics, such as the power ratio and Taylor diagram, to assess the quality of mantle flow trajectories. We introduce these metrics for the first time in the context of mantle convection and demonstrate their viability based on the compact manner in which they summarize model performance.

Dynamical decomposition and selection based evolutionary algorithm for many-objective optimization

Decomposition-based many-objective evolutionary algorithms decompose the objective space into multiple subregions, with the help of a set of predefined reference vectors. These vectors serve to guide coevolution between subproblems, and while they show potential for maintaining the diversity of solutions, they have limited exploration capabilities in complex problems and high-dimensional objective space. The main issue is that the predefined reference vectors cannot maintain uniformity of the intersection points between search directions and the irregular Pareto front (PF). To address this problem, this paper proposes a dynamical decomposition and selection strategy (DDS). In DDS, the predefined reference vectors are replaced by solutions themselves and normal-boundary directions (NBI), which guide the population to automatically adapt to the shape of PF. The subregions adapt to divide the objective space to increase diversity. Then, to adjust the relationship between diversity and convergence, a dynamical selection strategy based on the course of evolution is proposed. The process of dynamical decomposition and selection strategy is repeated until the termination condition is met. The proposed algorithm is compared with the state-of-the-art many-objective optimization algorithms on several benchmark problems with 5 to 15 objectives in evolutionary computation. Experimental results show that it outperforms other algorithms in most test instances and is less sensitive to irregular PFs.

Kepuasan Pengguna Jasa Terminal Angkutan Umum di Bangka Selatan

Toboali Public Transportation Terminal is one of the most important terminals in South Bangka Regency due to the route access of public transportation in Toboali as the capital of Bangka- Belitung Province. Each public transport to Sadai Port area and to Pangkal Pinang City will go through this terminal. The purpose of the study is to determine and analyze the level of service quality toward the users satisfaction at Toboali Terminal in South Bangka Regency. There are some main problems which are; the traffic flow continues to become denser, some terminal facilities are inadequate, the schedule of public transportation arrival in the terminal is not precise, the late response to terminal internal condition, and lame security condition in the terminal. The sample used in this study was 50 respondents. The data analysis technique used Customer Satisfaction Index method which aims to determine the level of service users satisfaction. Based on the calculation of Customer Satisfaction Index, the results obtained in the form of the level of service users satisfaction with the quality of Toboali Terminal services. The level of passenger respondents satisfaction is 67% where the value is in range of 0.66-0.80. It means that overall passenger respondents are satisfied. Reliability is the dimension of the highest level of satisfaction with the quality of service at Toboali Terminal.

Research on human resource management performance evaluation based on BP algorithm

Abstract With economic globalisation and in the face of increasingly fierce market competition, enterprises must establish an evaluation mechanism that can promote the company’s development and motivate employees to improve performance in order to achieve the company’s strategic goals. In view of the characteristics and problems of enterprise performance appraisal, a performance evaluation method based on artificial neural network (ANN) technology is proposed. This study uses BP algorithm to comprehensively evaluate the performance of enterprises and construct an evaluation network. According to the statistics of 75 power companies in the province from 2018 to 2021, the training was carried out in batches, and the 10-fold cross-validation method was used to find the smallest optimisation value of the error term (average overall relative error) of the test set. The training set is set as 70% and the test set as 30%, and the termination condition is used to end the training process when the training error is &lt;0.0001. This proves that the use of BP neural network for performance evaluation can effectively avoid the influence of subjective factors on the evaluation results, so as to establish a more objective comprehensive evaluation system.

Enhanced ANN Predictive Model for Composite Pipes Subjected to Low-Velocity Impact Loads

This paper presents an enhanced artificial neural network (ANN) to predict the displacement in composite pipes impacted by a drop weight having different velocities. The impact response of fiber-reinforced polymer composite pipes depends on several factors including thickness, stacking sequence, and the number of layers. These factors were investigated in an earlier study using sensitivity analysis, and it was found that they had the most prominent effect on the impact resistance of the composite pipes. In this present study, composite pipes with a diameter of 54 mm are considered to explore the damages induced by low-velocity impact and the influence of these damages on their strength. To evaluate the effect of low-velocity, the pipes were exposed to impacts at different velocities of 1.5, 2, 2.5, and 3 m/s, and preliminary damage was initiated. Next, we used Jaya and E-Jaya algorithms to enhance the ANN algorithm for good training and prediction. The Jaya algorithm has a basic structure and needs only two requirements, namely, population size and terminal condition. Recently, Jaya algorithm has been widely utilized to solve various problems. Due to its single learning technique and limited population information, Jaya algorithm may quickly be trapped in local optima while addressing complicated optimization problems. For better prediction, an enhanced Jaya (E-Jaya) algorithm has been presented to enhance global searchability. In this study, ANN is enhanced based on the influential parameters using E-Jaya to test its effectiveness. The results showed the effectiveness of the E-Jaya algorithm for best training and prediction compared with the original algorithm.

An efficient factoring algorithm for the quickest path multi-state flow network reliability problem

The exact evaluation of the quickest path multi-state flow network reliability parameter belongs to the family of NP-hard problems. All methods known up to date for its resolution consist of two steps. The first step generates all relevant paths with respect to the reliability under consideration. The second one, having exponential time-complexity with respect to the number of relevant paths, exploits them to compute the reliability as the probability of the union of events not mutually exclusive. As a consequence, published methods are impractical for configurations with more than thirty relevant paths. In this paper, we present a new method, called the factoring method, which finds a relevant path, and uses one of its link and the total expectation theorem for transforming the given problem on two similar ones but related to smaller multi-state flow networks. This transformation, with polynomial execution-time complexity, is then recursively applied until termination conditions are met. By illustrations on versions of NSFNet, ARPANET and complete topologies, we highlight that the proposed method allows to compute quickly the reliability of multi-state flow networks with hundreds or even thousands of relevant paths and outperforms significantly the method based on the Depth-First-Search procedure (DFS-based method), which in previous literature was established as the most efficient one.

Prism adaptation in patients with unilateral lesion of the parietal or cerebellar cortex: A pilot study on two single cases using a concurrent exposure procedure

Neuroimaging studies showed that prism adaptation (PA), a widely used tool for the rehabilitation of neglect, involves a wide network of brain regions including the parietal cortex and the cerebellum. In particular, the parietal cortex has been suggested to mediate the initial stage of PA through conscious compensatory mechanisms as a reaction to the deviation induced by PA. The cerebellum, on the other side, intervenes in sensory errors prediction to update internal models in later stages. It has been suggested that two mechanisms may underlie PA effects: recalibration, a strategic cognitive process occurring in the initial stages of PA, and realignment, a fully automatic reorganization of spatial maps emerging later and more slowly in time. The parietal lobe has been proposed to be involved mainly in the recalibration whereas the realignment would be carried over by the cerebellum. Previous studies have investigated the effects of a lesion involving either the cerebellum or the parietal lobe in PA taking into account both realignment and recalibration processes. Conversely, no studies have compared the performance of a patient with a cerebellar lesion to that of a patient with a parietal lesion. In the present study, we used a recently developed technique for digital PA to test for differences in visuomotor learning after a single session of PA in a patient with parietal and a patient with cerebellar lesions, respectively. The PA procedure, in this case, includes a digital pointing task based on a concurrent exposure technique, which allows patients to fully see their arm during the pointing task. This procedure has been shown to be as effective as the terminal exposure condition in neglect rehabilitation albeit different processes take place during concurrent exposure condition compared to the most used terminal exposure (allowing to see only the final part of the movement). Patients’ performances were compared to that of a control group. A single session of PA was administered to 1) a patient (BC) with left parieto-occipital lesion involving superior parietal lobe (SPL) and inferior parietal lobe (IPL), 2) a patient (TGM) with a stroke in the territory sub-served by the superior cerebellar artery (SCA) , and 3) 14 healthy controls (HC).The task included three conditions: before wearing prismatic goggles (pre-exposure), while wearing prisms (exposure) and after removing the goggles (post-exposure). Mean deviations were calculated for the following phases: pre-exposure, early-exposure, late-exposure, post-exposure. The presence of after-effect was calculated as the difference between pre-exposure and post-exposure conditions. For each of these conditions, patients’ performance was compared to that of the control group by using a modified Crawford t-test. We found that the patient with the parietal lesion had a significantly different performance in the late-exposure and in the post-exposure compared to both HC and the patient with the cerebellar lesion. Conversely, no differences were observed between TGM and HC across all the conditions.Our results show an increase in the magnitude of the adaptation during the late stage of PA in the patient with the parietal lesion whereas no differences in the performance between the cerebellar patient and the controls were found. These results confirm previous studies suggesting that the parietal cortex is an important node of a wider network involved in PA effect. Furthermore, results concerning the cerebellar patient suggest that visuomotor learning is not affected by lesions of the SCA territory when a concurrent exposure is used as, in such case, it less relies on sensory errors prediction to update internal models. Results are discussed considering the novelty of the applied PA technique.

Evaluation, computation and coding of iterative function using recursive approach

Iteration and recursion are very pivotal concepts in understanding the logic and building blocks of all computer programs across all programming paradigms. Although the theory of iteration together with the development and implementation of iterative algorithm is easy to grasp, that of recursion remains elusive to programmers especially novice programmers. In this research, functions composition is applied in the explanation of iteration using recursion. The method demonstrates an easy and elaborate way of writing iterative programs using recursion by identifying the significant variables in both constructs. Function composition is used to write the recursive function, the recursive variable is identified as a variable that converges towards the base case, also the base case is also identified as being the terminating point of the function call else the function call runs and fill the stack memory causing stack overflow. The recursive part is the loop update and base case the termination condition in iterative programs. The results obtained simplifies how to write iterative codes using recursion.

Optimizing Emergency Supply Location Selection in Urban Areas: A Multi-Objective Planning Model and Algorithm

The scientific location and layout of emergency material storage and rescue points in urban areas are critical aspects of emergency management. In this study, a multi-objective programming optimization model was constructed based on related theories, incorporating multiple goal combinations with different dimensions according to various disaster scenarios and urban emergency needs. The weight factors of emergency timeliness, economy, and safety were considered, and the multi-objective model optimization problem was transformed into a single-objective comprehensive optimization model problem using the weight method. The analysis decision function was utilized to study the transformation and solution method of the urban emergency rescue point location model. Heuristic optimization algorithms were employed to perform average segmentation calculations on the preset neighborhoods, constantly changing and narrowing the neighborhood range until the algorithm termination conditions were met, approaching the domain range of the optimal solution. Additionally, another precision parameter was utilized to control the accuracy of the final solution neighborhood range. The optimization of emergency vehicle scheduling was used to synergistically solve the problem of reserve rescue point location layout and optimization solution. The results of the example demonstrate the feasibility of constructing a multi-objective model with multiple combinations of different dimensions of objectives and the rationality of the Dijkstra heuristic optimization algorithm used. This study provides multiple methodologies and alternative site selection plans for decision-makers to select the required multi-objective reserve rescue point location model based on different urban disaster situations and their own emergency rescue needs.

Partial discharge signal compression reconstruction method based on transfer sparse representation and dual residual ratio threshold

AbstractPartial discharge (PD) signals have a large amount of data and a low energy proportion of pulse signals, resulting in difficult data transmission and poor reconstruction efficiency. To this end, a PD signal compression reconstruction method based on transfer sparse representation and dual residual ratio threshold (TSR‐DRRT) is proposed. TSR‐DRRT is centred on the sparse representation (SR) and accurate reconstruction of noisy signals. The intrinsic pulse of PD signals is extracted by signal decomposition, and jointly trained with different types of signals to establish the transfer SR dictionary. The compressed signal accurately retains the essential characteristics of the pulse information by improving the match between the dictionary atoms and the polymorphic PD pulses. To match the transfer SR dictionary, the inner and outer DRRT iteration termination conditions are set adaptively during the reconstruction process based on the correlation difference between the dictionary and signal frames. Independent control of PD pulse recognition and reconstruction accuracy is achieved, and its performance under noisy signals is improved. The results show that the method can achieve high ratio compression and efficient reconstruction of noisy signals. Different types of PD signals can also have high matching accuracy. This method can meet the demand for PD signals compression and transmission to the terminal for accurate reconstruction.

Regularity of optimal solutions and the optimal cost for hybrid dynamical systems via reachability analysis

For a general optimal control problem for dynamical systems with hybrid dynamics, we study the dependency of the optimal cost on perturbations to problem constraints and mappings. The former limits the allowable values for the state, input, initial and terminal condition, and the terminal time, while the latter is given by the right-hand sides of the differential/difference inclusions defining the dynamics, as well as the functions defining the cost functional We show that upper and lower semicontinuous dependence of solutions on initial conditions – properties that are captured by outer and inner well-posedness, respectively – lead to the existence of a solution to the optimal control problem and upper/lower semicontinuity of the optimal cost. In particular, by exploiting properties of finite horizon reachable sets for hybrid systems, we show that the optimal cost varies upper semicontinuously when the hybrid system is outer well-posed, and lower semicontinuously when it is inner well-posed and an additional assumption requiring partial knowledge of solutions holds. Consequently, when the system is both inner and outer well-posed and the aforementioned assumption holds, the optimal cost varies continuously, and optimal solutions vary outer/upper semicontinuously. We further show that even in the absence of this solution-based assumption, the optimal cost (respectively, solutions) can be continuously (respectively, outer/upper semicontinuously) approximated. Results are demonstrated by examples, theoretically and numerically.

Backward Deep BSDE Methods and Applications to Nonlinear Problems

We present a pathwise deep Backward Stochastic Differential Equation (BSDE) method for Forward Backward Stochastic Differential Equations with terminal conditions that time-steps the BSDE backwards and apply it to the differential rates problem as a prototypical nonlinear problem of independent financial interest. The nonlinear equation for the backward time-step is solved exactly or by a Taylor-based approximation. This is the first application of such a pathwise backward time-stepping deep BSDE approach for problems with nonlinear generators. We extend the method to the case when the initial value of the forward components X can be a parameter rather than fixed and similarly to also learn values at intermediate times. We present numerical results for a call combination and for a straddle, the latter comparing well to those obtained by Forsyth and Labahn with a specialized PDE solver.

An Iterated Population-Based Metaheuristic for Order Acceptance and Scheduling in Unrelated Parallel Machines with Several Practical Constraints

This study considers order acceptance and scheduling problems in unrelated parallel machines with several practical constraints, including order release times, sequence-dependent setup times, machines’ unequal ready times, and preventive maintenance. In a make-to-order production environment, issues with order acceptance and scheduling are mainly caused by the limited production capacity of a factory, which makes it impossible to accept all orders. Consequently, some orders must be rejected in order to maximize profits and the accepted orders must be completed by the due date or no later than the deadline. An iterated population-based metaheuristic is proposed to solve the problems. The algorithm begins with an efficient initial solution generator to generate an initial solution, and then uses the destruction and construction procedure to generate a population with multiple solutions. Then, a solution is selected from the population, and a variable neighborhood descent search algorithm with several new reduced-size neighborhood structures is applied to improve the selected solution. Following the completion of the local search, a method for updating the members of the population was devised to enhance its diversity. Finally, the metaheuristic allows the populations to evolve for several generations until the termination condition is satisfied. To evaluate the performance of the proposed metaheuristic, a heuristic rule and an iterated local search algorithm are examined and compared. The computational experimental results indicate that the presented metaheuristic outperforms the other heuristics.

An Integrated Machine Learning-Based Brain Computer Interface to Classify Diverse Limb Motor Tasks: Explainable Model

Terminal neurological conditions can affect millions of people worldwide and hinder them from doing their daily tasks and movements normally. Brain computer interface (BCI) is the best hope for many individuals with motor deficiencies. It will help many patients interact with the outside world and handle their daily tasks without assistance. Therefore, machine learning-based BCI systems have emerged as non-invasive techniques for reading out signals from the brain and interpreting them into commands to help those people to perform diverse limb motor tasks. This paper proposes an innovative and improved machine learning-based BCI system that analyzes EEG signals obtained from motor imagery to distinguish among various limb motor tasks based on BCI competition III dataset IVa. The proposed framework pipeline for EEG signal processing performs the following major steps. The first step uses a meta-heuristic optimization technique, called the whale optimization algorithm (WOA), to select the optimal features for discriminating between neural activity patterns. The pipeline then uses machine learning models such as LDA, k-NN, DT, RF, and LR to analyze the chosen features to enhance the precision of EEG signal analysis. The proposed BCI system, which merges the WOA as a feature selection method and the optimized k-NN classification model, demonstrated an overall accuracy of 98.6%, outperforming other machine learning models and previous techniques on the BCI competition III dataset IVa. Additionally, the EEG feature contribution in the ML classification model is reported using Explainable AI (XAI) tools, which provide insights into the individual contributions of the features in the predictions made by the model. By incorporating XAI techniques, the results of this study offer greater transparency and understanding of the relationship between the EEG features and the model's predictions. The proposed method shows potential levels for better use in controlling diverse limb motor tasks to help people with limb impairments and support them while enhancing their quality of life.

Glee: A granularity filter for feature selection

In the field of Granular Computing (GrC), feature selection is an attractive task. Some basics of GrC such as information granulation and granularity have well guided the explorations of feature selection technique. Nevertheless, some challenges to perform feature selection such as high computational costs of repeating information granulation and multi-granularity structure in the process of searching qualified features may also arise. In this study, to improve the efficiency and effectiveness of feature selector, a novel framework named Glee: Granularity fiLter for fEature sElection, is reported. Firstly, the value of granularity related to each feature is calculated. Secondly, all features are reordered by the corresponding values of granularity. Finally, following such a derived sequence, features will be added into the selection pool one by one until the termination condition is achieved. Glee can not only eliminate the iterative calculations of information granulation in the whole process of selecting, but also provide sequence of features which may be insensitive to data perturbation. It should also be emphasized that Glee is a general framework, and most existing termination conditions to feature selection can be embedded into it. To validate the effectiveness of Glee, it is compared with several well-established feature selection schemes in elapsed time of selecting features, stability of selected features and classification performance. Experimental results over 20 UCI datasets with both raw features and 3 different ratios of noisy features demonstrate that our framework is superior as it yields better robustness with satisfactory elapsed time.