A Two-Timescale Duplex Neurodynamic Approach to Mixed-Integer Optimization

Model design and exponential state estimation for discrete-time delayed memristive spiking neural P systems

This paper investigates the exponential state estimation of the discrete-time memristive spiking neural P system (MSNPS). The spiking neural P system (SNPS) offers algorithmic support for neural morphology computation and AI chips, boasting advantages such as high performance and efficiency. As a new type of information device, memristors have efficient computing characteristics that integrate memory and computation, and can serve as synapses in SNPS. Therefore, to leverage the combined benefits of SNPS and memristors, this study introduces an innovative MSNPS circuit design, where memristors substitute resistors in the SNPS framework. Meanwhile, MSNPS mathematical model is constructed based on circuit model. In order to be more practical, the time delays in the system are analyzed in addition to the discretization of the continuous MSNPS. Moreover, some sufficient conditions for exponential state estimation are established by utilizing a Lyapunov functional to MSNPS. Finally, a numerical simulation example is constructed to validate the main findings.

Optimal Reconstruction of Probabilistic Boolean Networks

In gene regulatory networks (GRNs), it is important to model gene regulation based on a priori information and experimental data. As a useful mathematical model, probabilistic Boolean networks (PBNs) have been widely applied in GRNs. This article addresses the optimal reconstruction problem of PBNs based on several priori Boolean functions and sampled data. When all candidate Boolean functions are known in advance, the optimal reconstruction problem is reformulated into an optimization problem. This problem can be well solved by a recurrent neural network approach which decreases the computational cost. When parts of candidate Boolean functions are known in advance, necessary and sufficient conditions are provided for the reconstruction of PBNs. In this case, two types of reconstruction problems are further proposed: one is aimed at minimizing the number of reconstructed Boolean functions, and the other one is aimed at maximizing the selection probability of the main dynamics under noises. At last, examples in GRNs are elaborated to demonstrate the effectiveness of the main results.

A Novel Swarm-Exploring Neurodynamic Network for Obtaining Global Optimal Solutions to Nonconvex Nonlinear Programming Problems

A swarm-exploring neurodynamic network (SENN) based on a two-timescale model is proposed in this study for solving nonconvex nonlinear programming problems. First, by using a convergent-differential neural network (CDNN) as a local quadratic programming (QP) solver and combining it with a two-timescale model design method, a two-timescale convergent-differential (TTCD) model is exploited, and its stability is analyzed and described in detail. Second, swarm exploration neurodynamics are incorporated into the TTCD model to obtain an SENN with global search capabilities. Finally, the feasibility of the proposed SENN is demonstrated via simulation, and the superiority of the SENN is exhibited through a comparison with existing collaborative neurodynamics methods. The advantage of the SENN is that it only needs a single recurrent neural network (RNN) interact, while the compared collaborative neurodynamic approach (CNA) involves multiple RNN runs.

A Collaborative Neurodynamic Optimization Approach to Distributed Chiller Loading

In this article, we present a collaborative neurodynamic optimization approach to distributed chiller loading in the presence of nonconvex power consumption functions and binary variables associated with cardinality constraints. We formulate a cardinality-constrained distributed optimization problem with nonconvex objective functions and discrete feasible regions, based on an augmented Lagrangian function. To overcome the difficulty caused by the nonconvexity in the formulated distributed optimization problem, we develop a collaborative neurodynamic optimization method based on multiple coupled recurrent neural networks reinitialized repeatedly using a meta-heuristic rule. We elaborate on experimental results based on two multi-chiller systems with the parameters from the chiller manufacturers to demonstrate the efficacy of the proposed approach in comparison to several baselines.

Binary matrix factorization via collaborative neurodynamic optimization

Binary matrix factorization is an important tool for dimension reduction for high-dimensional datasets with binary attributes and has been successfully applied in numerous areas. This paper presents a collaborative neurodynamic optimization approach to binary matrix factorization based on the original combinatorial optimization problem formulation and quadratic unconstrained binary optimization problem reformulations. The proposed approach employs multiple discrete Hopfield networks operating concurrently in search of local optima. In addition, a particle swarm optimization rule is used to reinitialize neuronal states iteratively to escape from local minima toward better ones. Experimental results on eight benchmark datasets are elaborated to demonstrate the superior performance of the proposed approach against six baseline algorithms in terms of factorization error. Additionally, the viability of the proposed approach is demonstrated for pattern discovery on three datasets.

LFT: Neural Ordinary Differential Equations With Learnable Final-Time

Since the last decade, deep neural networks have shown remarkable capability in learning representations. The recently proposed neural ordinary differential equations (NODEs) can be viewed as the continuous-time equivalence of residual neural networks. It has been shown that NODEs have a tremendous advantage over the conventional counterparts in terms of spatial complexity for modeling continuous-time processes. However, existing NODEs methods entail their final time to be specified in advance, precluding the models from choosing a desirable final time and limiting their expressive capabilities. In this article, we propose learnable final-time (LFT) NODEs to overcome this limitation. LFT rebuilds the NODEs learning process as a final-time-free optimal control problem and employs the calculus of variations to derive the learning algorithm of NODEs. In contrast to existing NODEs methods, the new approach empowers the NODEs models to choose their suitable final time, thus being more flexible in adjusting the model depth for given tasks. Additionally, we analyze the gradient estimation errors caused by numerical ordinary differential equations (ODEs) solvers and employ checkpoint-based methods to obtain accurate gradients. We demonstrate the effectiveness of the proposed method with experimental results on continuous normalizing flows (CNFs) and feedforward models.

Capacitated Clustering via Majorization-Minimization and Collaborative Neurodynamic Optimization

This paper addresses capacitated clustering based on majorization-minimization and collaborative neurodynamic optimization (CNO). Capacitated clustering is formulated as a combinatorial optimization problem. Its objective function consists of fractional terms with intra-cluster similarities in their numerators and cluster cardinalities in their denominators as normalized cluster compactness measures. To obviate the difficulty in optimizing the objective function with factional terms, the combinatorial optimization problem is reformulated as an iteratively reweighted quadratic unconstrained binary optimization problem with a surrogate function and a penalty function in a majorization-minimization framework. A clustering algorithm is developed based on CNO for solving the reformulated problem. It employs multiple Boltzmann machines operating concurrently for local searches and a particle swarm optimization rule for repositioning neuronal states upon their local convergence. Experimental results on ten benchmark datasets are elaborated to demonstrate the superior clustering performance of the proposed approaches against seven baseline algorithms in terms of 21 internal cluster validity criteria.

Supervised Feature Selection via Collaborative Neurodynamic Optimization

As a crucial part of machine learning and pattern recognition, feature selection aims at selecting a subset of the most informative features from the set of all available features. In this article, supervised feature selection is at first formulated as a mixed-integer optimization problem with an objective function of weighted feature redundancy and relevancy subject to a cardinality constraint on the number of selected features. It is equivalently reformulated as a bound-constrained mixed-integer optimization problem by augmenting the objective function with a penalty function for realizing the cardinality constraint. With additional bilinear and linear equality constraints for realizing the integrality constraints, it is further reformulated as a bound-constrained biconvex optimization problem with two more penalty terms. Two collaborative neurodynamic optimization (CNO) approaches are proposed for solving the formulated and reformulated feature selection problems. One of the proposed CNO approaches uses a population of discrete-time recurrent neural networks (RNNs), and the other use a pair of continuous-time projection networks operating concurrently on two timescales. Experimental results on 13 benchmark datasets are elaborated to substantiate the superiority of the CNO approaches to several mainstream methods in terms of average classification accuracy with three commonly used classifiers.

Toward coordinated planning and hierarchical optimization control for highly redundant mobile manipulator

This paper represents a constraint planning and optimization control scheme for a highly redundant mobile manipulator considering a complex indoor environment. Compared with the traditional optimization solution of a redundant manipulator, infinity norm and slack variable are additionally introduced and leveraged by the optimization algorithm. The former takes into account the joint limits effectively by considering individual joint velocities and the latter relaxes the equality constraint by decreasing the infeasible solution area. By using derived kinematic equations, the tracking control problem is expressed as an optimization problem and converted into a new quadratic programming (QP) problem. To address the optimization problem, the two-timescale recurrent neural networks optimization scheme is proposed and tested with a 9 DOFs nonholonomic mobile-based manipulator. Additionally, the BI2RRT∗ path-planning algorithm incorporates path planning in the complex environment where different obstacles are positioned. To test and evaluate the proposed optimization scheme, both predefined and generated paths are tested in the Neurorobotics Platform (NRP) 2which is open access and open source integrative simulation framework powered by Gazebo and developed by our team.

Two-timescale projection neural networks in collaborative neurodynamic approaches to global optimization and distributed optimization

In this paper, we propose a two-timescale projection neural network (PNN) for solving optimization problems with nonconvex functions. We prove the convergence of the PNN with sufficiently different timescales to a local optimal solution. We develop a collaborative neurodynamic approach with multiple such PNNs to search for global optimal solutions. In addition, we develop a collaborative neurodynamic approach with multiple PNNs connected via a directed graph for distributed global optimization. We elaborate on four numerical examples to illustrate the characteristics of the approaches.

Event-Triggered Cardinality-Constrained Cooling and Electrical Load Dispatch Based on Collaborative Neurodynamic Optimization

This article addresses event-triggered optimal load dispatching based on collaborative neurodynamic optimization. Two cardinality-constrained global optimization problems are formulated and two event-triggering functions are defined for event-triggered load dispatching in thermal energy and electric power systems. An event-triggered dispatching method is developed in the collaborative neurodynamic optimization framework with multiple projection neural networks and a meta-heuristic updating rule. Experimental results are elaborated to demonstrate the efficacy and superiority of the approach against many existing methods for optimal load dispatching in air conditioning systems and electric power generation systems.

Two-timescale recurrent neural networks for distributed minimax optimization

In this paper, we present two-timescale neurodynamic optimization approaches to distributed minimax optimization. We propose four multilayer recurrent neural networks for solving four different types of generally nonlinear convex-concave minimax problems subject to linear equality and nonlinear inequality constraints. We derive sufficient conditions to guarantee the stability and optimality of the neural networks. We demonstrate the viability and efficiency of the proposed neural networks in two specific paradigms for Nash-equilibrium seeking in a zero-sum game and distributed constrained nonlinear optimization.

Robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization

Non-negative matrix factorization (NMF) has been widely used in machine learning and data mining fields. As an extension of NMF, non-negative matrix tri-factorization (NMTF) provides more degrees of freedom than NMF. However, standard NMTF algorithm utilizes Frobenius norm to calculate residual error, which can be dramatically affected by noise and outliers. Moreover, the hidden geometric information in feature manifold and sample manifold is rarely learned. Hence, a novel robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization (RCHNMTF) is proposed. First, a robust capped norm is adopted to handle extreme outliers. Second, dual hyper-graph regularization is considered to exploit intrinsic geometric information in feature manifold and sample manifold. Third, orthogonality constraints are added to learn unique data presentation and improve clustering performance. The experiments on seven datasets testify the robustness and superiority of RCHNMTF.

Centralized and Collective Neurodynamic Optimization Approaches for Sparse Signal Reconstruction via L₁-Minimization

This article develops several centralized and collective neurodynamic approaches for sparse signal reconstruction by solving the L₁ -minimization problem. First, two centralized neurodynamic approaches are designed based on the augmented Lagrange method and the Lagrange method with derivative feedback and projection operator. Then, the optimality and global convergence of them are derived. In addition, considering that the collective neurodynamic approaches have the function of information protection and distributed information processing, first, under mild conditions, we transform the L₁ -minimization problem into two network optimization problems. Later, two collective neurodynamic approaches based on the above centralized neurodynamic approaches and multiagent consensus theory are proposed to address the obtained network optimization problems. As far as we know, this is the first attempt to use the collective neurodynamic approaches to deal with the L₁ -minimization problem in a distributed manner. Finally, several comparative experiments on sparse signal and image reconstruction demonstrate that our proposed centralized and collective neurodynamic approaches are efficient and effective.

Sparse Bayesian Learning Based on Collaborative Neurodynamic Optimization

Regression in a sparse Bayesian learning (SBL) framework is usually formulated as a global optimization problem with a nonconvex objective function and solved in a majorization-minimization framework where the solution quality and consistency depend heavily on the initial values of the used algorithm. In view of the shortcomings, this article presents an SBL algorithm based on collaborative neurodynamic optimization (CNO) for searching global optimal solutions to the global optimization problem. The CNO system consists of a population of recurrent neural networks (RNNs) where each RNN is convergent to a local optimum to the global optimization problem. Reinitialized repetitively via particle swarm optimization with exchanged local optima information, the RNNs iteratively improve their searching performance until reaching global convergence. The proposed CNO-based SBL algorithm is almost surely convergent to a global optimal solution to the formulated global optimization problem. Two applications with experimental results on sparse signal reconstruction and partial differential equation identification are elaborated to substantiate the superiority and efficacy of the proposed method in terms of solution optimality and consistency.

Hash Bit Selection via Collaborative Neurodynamic Optimization With Discrete Hopfield Networks

Hash bit selection (HBS) aims to find the most discriminative and informative hash bits from a hash pool generated by using different hashing algorithms. It is usually formulated as a binary quadratic programming problem with an information-theoretic objective function and a string-length constraint. In this article, it is equivalently reformulated in the form of a quadratic unconstrained binary optimization problem by augmenting the objective function with a penalty function. The reformulated problem is solved via collaborative neurodynamic optimization (CNO) with a population of classic discrete Hopfield networks. The two most important hyperparameters of the CNO approach are determined based on Monte Carlo test results. Experimental results on three benchmark data sets are elaborated to substantiate the superiority of the collaborative neurodynamic approach to several existing methods for HBS.

Hash Bit Selection Based on Collaborative Neurodynamic Optimization

Hash bit selection determines an optimal subset of hash bits from a candidate bit pool. It is formulated as a zero-one quadratic programming problem subject to binary and cardinality constraints. In this article, the problem is equivalently reformulated as a global optimization problem. A collaborative neurodynamic optimization (CNO) approach is applied to solve the problem by using a group of neurodynamic models initialized with particle swarm optimization iteratively in the CNO. Lévy mutation is used in the CNO to avoid premature convergence by ensuring initial state diversity. A theoretical proof is given to show that the CNO with the Lévy mutation operator is almost surely convergent to global optima. Experimental results are discussed to substantiate the efficacy and superiority of the CNO-based hash bit selection method to the existing methods on three benchmarks.

Deep Learning of Subject Context in Ideological and Political Class Based on Recursive Neural Network

Ideological and political education is the most important way to cultivate students' humanistic qualities, which can directly determine the development of other qualities. However, at present, the direction of ideological and political innovation in higher vocational colleges is vague. In response to this problem, this study proposes a model based on HS-EEMD-RNN. First, the ensemble empirical mode decomposition (EEMD) method is used to decompose the measured values, and then the recurrent neural network (RNN) is used to train each component and the remaining items. Finally, through the mapping relationship obtained by the model, the response prediction value of each component and the remaining items can be obtained. In the RNN training process, the harmony search (HS) algorithm is introduced to optimize it, and the noise is systematically denoised. Perturbation is used to obtain the optimal solution, thereby optimizing the weight and threshold of the RNN and improving the robustness of the model. The study found that, compared with EEMD-RNN, HS-EEMD-RNN has a better effect, because HS can effectively improve the training and fitting accuracy. The fitting accuracy of the HS-EEMD-RNN model after HS optimization is 0.9918. From this conclusion, the fitting accuracy of the HS-EEMD-RNN model is significantly higher than that of the EEMD-RNN model. In addition, four factors, career development, curriculum construction, community activities, and government support, have obvious influences on ideological and political classrooms in technical colleges. The use of recurrent neural networks in the research direction of deep and innovative research on the subject context of ideological and political classrooms can significantly improve the prediction accuracy of its development direction.

The Application of Computer Intelligence in the Cyber-Physical Business System Integration in Network Security

In order to address the false alarm detection problem caused by the inability to identify the transgression scene pages in the process of horizontal transgression detection, this study proposes a deep learning-based LSTM-AutoEncoder unsupervised prediction model. The model uses long short-term memory network to build AutoEncoder, extracts text features of page response data of horizontal transgression scenario, and reconstructs text features to restore. Meanwhile, it counts the error between the restored result and the original page response, judges whether the detection result of horizontal transgression is false alarm according to the error threshold of unknown page, and tests the effectiveness of the model effect under real business data by comparing it with other two algorithms, one-class SVM and AutoEncoder, which provides security for enterprise network business. The results show that the LSTM-AutoEncoder model achieves a more balanced index in terms of accuracy, precision, recall, and F1-score in the case of MAE, which is 0.3% more and 0.2% more than the case of MSE in terms of recall and accuracy. It is concluded that the LSTM-AutoEncoder model is more in line with the real business requirements, and the simple model architecture selected for this study can reduce the complexity of the model, speed up the prediction time of the model in the application phase, and improve the performance of the detection software. This indicates that this study has some application prospects in network security.

Visual Monitoring Technology for Substation Vulnerable High-Voltage Electrical Equipment Based on ISSA-LSTM Deep Learning Model Coupling Video Overlay Algorithm

To enhance the visualization effect of substation high-voltage electrical equipment vulnerability, this study proposes an ISSA-LSTM coupled video overlay algorithm-based substation high-voltage electrical equipment vulnerability visualization and monitoring model. Using the improved $\alpha$ blending algorithm combined with the inverse sampling of video background color, overlaying visible video as well as infrared video, using the improved adaptive weighted two-dimensional principal component analysis (W2DPCA) to fuse the base layer, selecting the detail layer as the final detail layer, obtaining the final fusion frame, and realizing the visualization and monitoring of substation high-voltage electrical equipment vulnerability, and introducing the improved sparrow search algorithm (ISSA) to establish long and short-term memory network prediction model to reduce the prediction error and improve the monitoring accuracy rate. The experimental results show that the monitoring frames obtained by this method can reflect rich details of substation high-voltage electrical equipment, and the texture color and equipment edge contrast are enhanced to facilitate accurate determination of substation high-voltage electrical equipment vulnerability, and the prediction accuracy of ISSA-LSTM model is as high as 99.85%.

Sparse signal reconstruction via collaborative neurodynamic optimization

In this paper, we formulate a mixed-integer problem for sparse signal reconstruction and reformulate it as a global optimization problem with a surrogate objective function subject to underdetermined linear equations. We propose a sparse signal reconstruction method based on collaborative neurodynamic optimization with multiple recurrent neural networks for scattered searches and a particle swarm optimization rule for repeated repositioning. We elaborate on experimental results to demonstrate the outperformance of the proposed approach against ten state-of-the-art algorithms for sparse signal reconstruction.

A Comparative Study of Cultural and Traditional Education in Primary and Secondary Schools in Developed Countries Based on the MOPSO-CD-DNN Model

In today's globalization, cultural and traditional education in primary and secondary schools has become the core of a country's future development, and how to improve the educational effect of cultural and traditional education in primary and secondary schools and find the development direction of cultural and traditional education has become the top priority. In response to this problem, this study proposes a MOPSO-CD-DNN hybrid prediction model, which introduces an optimization algorithm to optimize the parameters of the deep learning model. In this study, multiple benchmark models and evaluation methods are used for comparative research. The results show that the MOPSO-CD-DNN model has significant advantages in both prediction accuracy and prediction stability. Compared with other models, the prediction accuracy G value (average) is improved by 4.66%, 7.43%, and 9.25%, and the standard deviation (G value) is decreased by 0.001, 0.0502, and 0.0413, indicating its effectiveness and applicability to cultural tradition education. In addition, the introduction of the multiobjective optimization algorithm significantly improves the generalization ability of the model, and the prediction effect is significantly better than the single-objective optimization algorithm.

Boolean matrix factorization based on collaborative neurodynamic optimization with Boltzmann machines

This paper presents a collaborative neurodynamic approach to Boolean matrix factorization. Based on a binary optimization formulation to minimize the Hamming distance between a given data matrix and its low-rank reconstruction, the proposed approach employs a population of Boltzmann machines operating concurrently for scatter search of factorization solutions. In addition, a particle swarm optimization rule is used to re-initialize the neuronal states of Boltzmann machines upon their local convergence to escape from local minima toward global solutions. Experimental results demonstrate the superior convergence and performance of the proposed approach against six baseline methods on ten benchmark datasets.

A Study on the Impact of Digital Finance on Regional Productivity Growth Based on Artificial Neural Networks

The relationship between financial development and economic growth has become a hot topic in recent years and for China, which is undergoing financial liberalisation and policy reform, the efficiency of the use of digital finance and the deepening of the balance between quality and quantity in financial development are particularly important for economic growth. This paper investigates the utility of digital finance and financial development on total factor productivity in China using interprovincial panel data decomposing financial development into financial scale and financial efficiency; an interprovincial panel data model is used to explore the utility of digital finance on total factor productivity. This involves the collection and preprocessing of financial data, including feature engineering, and the development of an optimised predictive model. We preprocess the original dataset to remove anomalous information and improve data quality. This work uses feature engineering to select relevant features for fitting and training the model. In this process, the random forest algorithm is used to effectively avoid overfitting problems and to facilitate the dimensionality reduction of the relevant features. In determining the model to be used, the random forest regression model was chosen for training. The empirical results show that digital finance has contributed to productivity growth but is not efficiently utilised; China should give high priority to improving financial efficiency while promoting financial expansion; rapid expansion of finance without a focus on financial efficiency will not be conducive to productivity growth.

Analysis and Prediction of Subway Tunnel Surface Subsidence Based on Internet of Things Monitoring and BP Neural Network

With the acceleration of the urban development process and the rapid growth of China's population, the subway has become the first choice for people to travel, and the urban underground space has been continuously improved. The subway construction has become the focus of urban underground space development in the 21st century. During the construction of subway tunnels, the problem of surface settlement will inevitably be caused, and the problem of surface settlement will have a certain safety impact on the safe use of surface buildings. The impact of surface construction is predicted, so as to select the best construction technology and avoid the problem of surface subsidence to the greatest extent. On the basis of analyzing the principle of surface subsidence, this paper studies the optimal control strategy and process of subsidence in subway tunnel engineering. The research results of the article show the following. (1) The two sections of the pebble soil layer have basically the same subsidence trend. Among them, the first section has a larger settlement amplitude and both sides are steeper. The second section is mainly cobble clay soil. The pebble layer has good mechanical properties. If it can be well filled, its stability will be improved. The comparative analysis of the two sections shows that with the increase of the soil cover thickness, the maximum subsidence at the surface gradually decreases. The reason is that when the stratum loss is the same, the greater the soil cover thickness, the greater the settlement width. Sections 2 and 3 of a single silty clay have relatively close settlement laws, and the settlement changes on both sides of the tunnel are similar. (2) The surface subsidence caused by the excavation of the side hole accounts for more than 50% of the total surface subsidence, and the width of the settlement tank after the excavation of the side hole is increased by 8–10 meters compared with the excavation of the middle hole. (3) The prediction error of the BP neural network model proposed in this paper is the lowest among the four models, whether it is the prediction of the cumulative maximum surface subsidence or the location of the cumulative maximum surface subsidence, and the average relative error of the cumulative maximum surface subsidence is 3.27%, the root mean square error is 3.87, the average relative error of the location of the cumulative maximum surface subsidence is 7.96%, and the root mean square error is 21.06. In the prediction process of the cumulative maximum surface subsidence, the prediction error value of the Elman neural network is relatively large, and the GRNN generalized neural network and RBF neural network have no significant changes; in the process of predicting the position where the cumulative maximum surface subsidence occurs, the prediction error value of RBF neural network is maximum.

Central Nervous System: Overall Considerations Based on Hardware Realization of Digital Spiking Silicon Neurons (DSSNs) and Synaptic Coupling

The Central Nervous System (CNS) is the part of the nervous system including the brain and spinal cord. The CNS is so named because the brain integrates the received information and influences the activity of different sections of the bodies. The basic elements of this important organ are: neurons, synapses, and glias. Neuronal modeling approach and hardware realization design for the nervous system of the brain is an important issue in the case of reproducing the same biological neuronal behaviors. This work applies a quadratic-based modeling called Digital Spiking Silicon Neuron (DSSN) to propose a modified version of the neuronal model which is capable of imitating the basic behaviors of the original model. The proposed neuron is modeled based on the primary hyperbolic functions, which can be realized in high correlation state with the main model (original one). Really, if the high-cost terms of the original model, and its functions were removed, a low-error and high-performance (in case of frequency and speed-up) new model will be extracted compared to the original model. For testing and validating the new model in hardware state, Xilinx Spartan-3 FPGA board has been considered and used. Hardware results show the high-degree of similarity between the original and proposed models (in terms of neuronal behaviors) and also higher frequency and low-cost condition have been achieved. The implementation results show that the overall saving is more than other papers and also the original model. Moreover, frequency of the proposed neuronal model is about 168 MHz, which is significantly higher than the original model frequency, 63 MHz.

Investigating drug delivery of 5-fluorouracil by assistance of an iron-modified graphene scaffold: Computational studies

This computational work was performed to investigate drug delivery of 5-fluorouracil (FU) anti-cancer by assistance of an iron(Fe)-modified graphene (G) scaffold. The models were optimized to reach the minimized energy structures in both of singular and bimolecular models. Two models of FU@G complex were obtained including O2@G and O4@G by relaxation of FU through O2 and O4 atoms towards the Fe-atom region of G surface. The obtained results of energies indicated a higher stability and strength for the O2@G model in comparison with the O4@G model. The quantitative and qualitative features of electronic molecular orbitals indicated the investigated G surface could work as a carrier of FU by reducing the unwanted side effects and also playing the sensor role. As a final remark of this work, the investigated G model could be proposed for employing in the targeted drug delivery of FU in both of carrier and sensor agents.

A metaheuristic-based framework for index tracking with practical constraints

Recently, numerous investors have shifted from active strategies to passive strategies because the passive strategy approach affords stable returns over the long term. Index tracking is a popular passive strategy. Over the preceding year, most researchers handled this problem via a two-step procedure. However, such a method is a suboptimal global-local optimization technique that frequently results in uncertainty and poor performance. This paper introduces a framework to address the comprehensive index tracking problem (IPT) with a joint approach based on metaheuristics. The purpose of this approach is to globally optimize this problem, where optimization is measured by the tracking error and excess return. Sparsity, weights, assets under management, transaction fees, the full share restriction, and investment risk diversification are considered in this problem. However, these restrictions increase the complexity of the problem and make it a nondeterministic polynomial-time-hard problem. Metaheuristics compose the principal process of the proposed framework, as they balance a desirable tradeoff between the computational resource utilization and the quality of the obtained solution. This framework enables the constructed model to fit future data and facilitates the application of various metaheuristics. Competitive results are achieved by the proposed metaheuristic-based framework in the presented simulation.

Multivehicle Task Assignment Based on Collaborative Neurodynamic Optimization With Discrete Hopfield Networks

This article presents a collaborative neurodynamic optimization (CNO) approach to multivehicle task assignments (TAs). The original combinatorial quadratic optimization problem for TA is reformulated as a quadratic unconstrained binary optimization (QUBO) problem with a quadratic utility function and a penalty function for handling load capacity and cooperation constraints. In the framework of CNO with a population of discrete Hopfield networks (DHNs), a TA algorithm is proposed for solving the formulated QUBO problem. Superior experimental results in four typical multivehicle operation scenarios are reported to substantiate the efficacy of the proposed neurodynamics-based TA approach.

Cardinality-constrained portfolio selection based on collaborative neurodynamic optimization

Portfolio optimization is one of the most important investment strategies in financial markets. It is practically desirable for investors, especially high-frequency traders, to consider cardinality constraints in portfolio selection, to avoid odd lots and excessive costs such as transaction fees. In this paper, a collaborative neurodynamic optimization approach is presented for cardinality-constrained portfolio selection. The expected return and investment risk in the Markowitz framework are scalarized as a weighted Chebyshev function and the cardinality constraints are equivalently represented using introduced binary variables as an upper bound. Then cardinality-constrained portfolio selection is formulated as a mixed-integer optimization problem and solved by means of collaborative neurodynamic optimization with multiple recurrent neural networks repeatedly repositioned using a particle swarm optimization rule. The distribution of resulting Pareto-optimal solutions is also iteratively perfected by optimizing the weights in the scalarized objective functions based on particle swarm optimization. Experimental results with stock data from four major world markets are discussed to substantiate the superior performance of the collaborative neurodynamic approach to several exact and metaheuristic methods.

Two-timescale neurodynamic approaches to supervised feature selection based on alternative problem formulations

Feature selection is a crucial step in data processing and machine learning. While many greedy and sequential feature selection approaches are available, a holistic neurodynamics approach to supervised feature selection is recently developed via fractional programming by minimizing feature redundancy and maximizing relevance simultaneously. In view that the gradient of the fractional objective function is also fractional, alternative problem formulations are desirable to obviate the fractional complexity. In this paper, the fractional programming problem formulation is equivalently reformulated as bilevel and bilinear programming problems without using any fractional function. Two two-timescale projection neural networks are adapted for solving the reformulated problems. Experimental results on six benchmark datasets are elaborated to demonstrate the global convergence and high classification performance of the proposed neurodynamic approaches in comparison with six mainstream feature selection approaches.

A neurodynamic optimization approach to supervised feature selection via fractional programming

Feature selection is an important issue in machine learning and data mining. Most existing feature selection methods are greedy in nature thus are prone to sub-optimality. Though some global feature selection methods based on unsupervised redundancy minimization can potentiate clustering performance improvements, their efficacy for classification may be limited. In this paper, a neurodynamics-based holistic feature selection approach is proposed via feature redundancy minimization and relevance maximization. An information-theoretic similarity coefficient matrix is defined based on multi-information and entropy to measure feature redundancy with respect to class labels. Supervised feature selection is formulated as a fractional programming problem based on the similarity coefficients. A neurodynamic approach based on two one-layer recurrent neural networks is developed for solving the formulated feature selection problem. Experimental results with eight benchmark datasets are discussed to demonstrate the global convergence of the neural networks and superiority of the proposed neurodynamic approach to several existing feature selection methods in terms of classification accuracy, precision, recall, and F-measure.