Continuous Hopfield Neural Network Research Articles

Neural network to solve fuzzy constraint satisfaction problems

<p>It has been proven that solving the constraint satisfaction problem (CSP) is an No Polynomial hard combinatorial optimization problem. This holds true even in cases where the constraints are fuzzy, known as fuzzy constraint satisfaction problems (FCSP). Therefore, the continuous Hopfield neural network model can be utilized to resolve it. The original algorithm was developed by Talaavan in 2005. Many practical problems can be represented as a FCSP. In this paper, we expand on a neural network technique that was initially developed for solving CSP and adapt it to tackle problems that involve at least one fuzzy constraint. To validate the enhanced effectiveness and rapid convergence of our proposed approach, a series of numerical experiments are carried out. The results of these experiments demonstrate the superior performance of the new method. Additionally, the experiments confirm its fast convergence. Specifically, our study focuses on binary instances with ordinary constraints to test the proposed resolution model. The results confirm that both the proposed approaches and the original continuous Hopfield neural network approach exhibit similar performance and robustness in solving ordinary constraint satisfaction problems.</p>

Exploration of a neural-network-based joint method of mapping and wavelength assignment in optical network-on-chip

Optical network-on-chip (ONoC) is promising to provide higher bandwidth and lower latency, compared with the traditional electrical interconnects at either chip-scale or wafer-scale. There is research on the impact of mapping or wavelength assignment on reliability in ONoC. However, mapping and wavelength assignment have an interactive influence on each other, pushing a necessity of research on the joint method. In addition, there are various ways to realize the joint method, which have an influence on the reliability and thus the power efficiency. In this paper, we propose a neural-network-based iterative joint method of mapping and wavelength assignment. Compared to the methods without considering the interactive influence, the proposed iterative joint method based on the continuous Hopfield neural network provides a worst-case optical signal-to-noise ratio (OSNRWC) improvement of at least 61% under the considered applications. Compared to the simultaneous joint method and two-step joint method, the proposed iterative joint method obtains an OSNRWC improvement of at least 17.9% and 64.6%, respectively, under the considered applications. Thanks to the improvement of OSNR, the laser power is reduced by 87.9% by using our method of wavelength assignment, compared to the random method of wavelength assignment.

A collaborative neurodynamic optimization algorithm to traveling salesman problem

This paper proposed a collaborative neurodynamic optimization (CNO) method to solve traveling salesman problem (TSP). First, we construct a Hopfield neural network (HNN) with n times n neurons for the n cities. Second, to ensure the convergence of continuous HNN (CHNN), we reformulate TSP to satisfy the convergence condition of CHNN and solve TSP by CHNN. Finally, a population of CHNNs is used to search for local optimal solutions of TSP and the globally optimal solution is obtained using particle swarm optimization. Experimental results show the effectiveness of the CNO approach for solving TSP.

An Application of the Associate Hopfield Network for Pattern Matching in Chart Analysis

Chart patterns are significant for financial market behavior analysis. Lots of approaches have been proposed to detect specific patterns in financial time series data, most of them can be categorized as distance-based or training-based. In this paper, we applied a trainable continuous Hopfield Neural Network for financial time series pattern matching. The Perceptually Important Points (PIP) segmentation method is used as the data preprocessing procedure to reduce the fluctuation. We conducted a synthetic data experiment on both high-level noisy data and low-level noisy data. The result shows that our proposed method outperforms the Template Based (TB) and Euclidean Distance (ED) and has an advantage over Dynamic Time Warping (DTW) in terms of the processing time. That indicates the Hopfield network has a potential advantage over other distance-based matching methods.

Maritime Buoyage Inspection System Based on an Unmanned Aerial Vehicle and Active Disturbance Rejection Control

The unmanned aerial vehicle (UAV) is inexpensive and offers a fast response speed and robust flexibility; thus, it is a promising tool in the maritime buoyage inspection scenario, which involves monitoring and accessing a lateral mark system far away from the coast. However, two main problems can occur during inspection. The first is extreme weather conditions, resulting in a deviation between the inspection route and the design route. The second is that the buoyage beacons are visited only once. Therefore, this article proposes a buoyage inspection system consisting of a single UAV and random coastal buoys. The UAV automatically takes off from the depot, performs a self-check on the buoy beacons, and then returns to the depot. A cascade active disturbance rejection controller (ADRC) is designed to adjust the real-time trajectory of the UAV system. A feasible trajectory planning method is also designed based on the continuous Hopfield neural network (CHNN) and genetic algorithm (GA) to minimize the inspection distance. Extensive simulations are conducted to demonstrate the effectiveness of the proposed method.

An ad-hoc network routing algorithm based on improved neural network under the influence of COVID-19

Under the influence of COVID-19, an efficient Ad-hoc network routing algorithm is required in the process of epidemic prevention and control. Artificial neural network has become an effective method to solve large-scale optimization problems. It has been proved that the appropriate neural network can get the exact solution of the problem in real time. Based on the continuous Hopfield neural network (CHNN), this paper focuses on the study of the best algorithm path for QoS routing in Ad-hoc networks. In this paper, a new Hopfield neural network model is proposed to solve the minimum cost problem in Ad-hoc networks with time delay. In the improved version of the path algorithm, the relationship between the parameters of the energy function is provided, and it is proved that the feasible solution of the network belongs to the category of progressive stability by properly selecting the parameters. The calculation example shows that the solution is not affected by the initial value, and the global optimal solution can always be obtained. The algorithm is very effective in the prevention and control in COVID-19 epidemic.

Memristive continuous Hopfield neural network circuit for image restoration

Image restoration (IR) methods based on neural network algorithms have shown great success. However, the hardware circuits that can perform real-time IR task with high-effective analog computation are few in the literature. To address such problem, we propose a memristor-based continuous Hopfield neural network (HNN) circuit for processing the IR task in this work. In our circuit, a single memristor crossbar array is used to represent synaptic weights and perform matrix operations. Current feedback operation amplifiers are utilized to achieve integral operation and output function. Given these designs, the proposed circuit can perform continuous recursive operations in parallel and process different optimization problems with the programmability of the memristor array. On the basis of the proposed circuit, binary and greyscale image restorations are conducted through self-organizing network operations, providing a hardware implementation platform for IR tasks. Comparative simulations show the designed HNN circuit provides effective improvements in terms of speed and accuracy compared with software simulation. Moreover, the hardware circuit shows good robustness to memristive variation and input noise.

An optimization routing protocol for FANETs

With the wide-ranging application of mobile ad hoc networks, flying ad hoc networks (FANETs) have received more and more attention from the industry. Routing technology is a key technology of ad hoc networks. The high-speed mobility of nodes poses a greater challenge to FANET routing technology. Based on the Dynamic Source Routing (DSR) protocol, the continuous Hopfield neural network is used to optimize the route to be adapted to the high-speed movement of the FANET node. In a simulation using NS3, the result shows that the optimized DSR protocol has greatly improved key indicators such as end-to-end average delay, throughput, and packet delivery ratio.

Using continuous Hopfield neural network for solving a new optimization architecture model of probabilistic self organizing map

Probabilistic models have proven their strength to model many natural phenomena as close as possible to reality, in particular, the probabilistic self organizing map (PRSOM) that belongs to the unsupervised learning models. It allows to provide an estimation of the probability density function through the likelihood maximization. This latter function depends on several parameters given by the model architecture. In this context, the aim of this paper is to deal with the architecture choice problem that consists in determining the optimal number of components needed for a better performance. In this paper, we propose a new optimization model that describes the problem above. We present the architecture of PRSOM in a mathematical system of a non linear objective function with mixed variables under linear and quadratic constraints. Due to the complexity of the resolution, we suggest the continuous Hopfield neural network (CHN) that we support by a deep stability analysis. Performance of the proposed model is demonstrated through the dataset clustering.

A Polarity Optimization Algorithm Taking Into Account Polarity Conversion Sequence

The polarity conversion sequence directly determines polarity conversion efficiency and then affects polarity optimization efficiency. However, few studies have focused on the polarity conversion sequence problem of Reed-Muller (RM) circuits. In this paper, we propose a continuous Hopfield neural network (CHNN)-based polarity conversion algorithm (CHNNPCA) for Mixed Polarity RM (MPRM) circuits, which uses the CHNN to solve the best polarity conversion sequence of polarity set waiting for evaluation before converting the polarity set. Moreover, based on the CHNNPCA, a polarity optimization algorithm (POA) is proposed to improve the polarity optimization efficiency of MPRM circuits. The experimental results on MCNC benchmark circuits show that for the large-scale polarity set, the CHNNPCA is superior to the mixed polarity conversion algorithm based on the tabular technique in terms of polarity conversion efficiency. Furthermore, compared to the traditional polarity optimization algorithm neglecting polarity conversion sequence, the POA has a considerable advantage in improving polarity optimization efficiency, especially for large-scale circuits. The POA can be extended to improve the polarity optimization efficiency of fixed polarity RM circuits.

Mathematical mixed-integer programming for solving a new optimization model of selective image restoration: modelling and resolution by CHN and GA

In grey-level image restoration, a prior knowledge of degraded areas allows, thanks to the selective filtering, to achieve a good protection of the image features. In this paper, we propose a quadratic programming-based technique that deals with the issue of details preservation during the restoration process. Based on the classical model of image restoration, we build a modified model by introducing a set of binary variables that indicate the pixel categories. We combine each pixel with the median of its neighbours in a decision rule so that one of them generates the optimal solution. The obtained model is a nonlinear mixed-integer problem where resolution by exact methods is not feasible. In this regard, we use both of the continuous Hopfield neural network and the genetic algorithm to solve the suggested model. Performance of our method is demonstrated numerically and visually by several computational tests.

Neural Network and Local Search to Solve Binary CSP

<p>Continuous Hopfield neural Network (CHN) is one of the effective approaches to solve Constrain Satisfaction Problems (CSPs). However, the main problem with CHN is that it can reach stabilisation with outputs in real values, which means an inconsistent solution or an incomplete assignment of CSP variables. In this paper, we propose a new hybrid approach combining CHN and min-conflict heuristic to mitigate these problems. The obtained results show an improvement in terms of solution quality, either our approach achieves feasible soluion with a high rate of convergence, furthermore, this approach can also enhance theperformance more than conventional CHN in some cases, particularly, when the network crashes.</p>

Neural networks for MANET AODV: an optimization approach

To find a route with good stability and less cost is a hot issue because of MANET's mobility. AODV is one of the most widely used routing protocols in MANET because of its wide application, good performance and expansion. However, AODV is only an optional route instead of an optimized one. In this paper, continuous Hopfield Neural Networks is used to optimize the route to seek an optimal or nearly-optimal route, which can improve the usability and survivability of MANET. The simulation results show that CHNN-AODV is more effective and advantageous than AODV in the measurement of packet receiving rate, end-to-end average delay and routing recovery frequency.

Multi-factors based sentence ordering for cross-document fusion from multimodal content

Organizing a coherent structure of the sentences extracted from multiple documents, guarantees the fluency and readability of the fused document. In this paper, sentence ordering problem is treated as a combinatorial optimization problem and solved with continuous Hopfield neural network (CHNN). We unify the existing factors by considering the most frequent orders temporal information, and topical relevance between local themes during overall ordering process. Specifically, ordering algorithm traverses all the local themes and locates a shortest path as the final sentence ordering. We show the results with data from Document Understanding Conferences (DUC) 2002–2005, and demonstrate the effectiveness of the developed approach compared with Random Ordering (RO), Chronological Ordering (CO), Majority Ordering (MO), and Precedence Relation Ordering (PRO).

Constrained parameterized optimal control of switched systems based on continuous Hopfield neural networks

This paper studies the problem of optimal control of switched systems under state constraints. It suggests a hybrid approach based on Continuous Hopfield Neural Network (CHNN). To deal with this issue, we need first to determine the optimal switching instants as well as the optimal control input, which guarantees the minimization of a performance criterion while respecting the constraints imposed on the system. Hence, this paper divides the issue under study into two stages. In the first, it starts with the transformation of the problem into an equivalent problem based on parameterization of the switching instants. This step would allow us to calculate the optimal control law and to determine the optimal cost’s derivatives’ expressions at the same time. These expressions are used in the second stage by the CHNN to define the optimal switching instants. In order to respect the state inequalities constraints of the system, the Karush-Kuhn-Tucker conditions and the Lagrange multipliers method associated with the Pontryagin Maximum Principle are used, which we apply on the equivalent problem. The results of this approach have been illustrated through a hydraulic system under state constraints.

Hopfield Lagrange Network Based Method for Economic Emission Dispatch Problem of Fixed-Head Hydro Thermal Systems

This paper proposes a Hopfield Lagrange Network (HLN) based method (HLNM) for economic emission dispatch of fixed head hydrothermal systems. HLN is a combination of Lagrange function and continuous Hopfield neural network where the Lagrange function is directly used as the energy function for the continuous Hopfield neural network. In the proposed method, HLN is used to find a set of non-dominated solutions and a fuzzy based mechanism is then exploited to determine the best compromise solution among the obtained ones. The proposed method has been tested on four hydrothermal systems and the obtained results in terms of total fuel cost, emission, and computational time have been compared to those other methods in the literature. The result comparisons have indicated that the proposed method is favorable for solving the economic emission dispatch problem of fixed-head hydrothermal systems.

An Improved Job Scheduling in Cloud Environment using Auto-Associative-Memory Network

Cloud computing plays a vital role in the field of information sharing through the internet. In this current scenario, some of the major problems in cloud computing are job scheduling, resource clustering, storage allocation, VM migration etc. In this paper, problems such as job scheduling and resource clustering are concentrated. Arrival time, waiting time, response time, makespan time, communication time, utilization time, throughput time of a job are considered while scheduling the jobs in a cloud environment. A good scheduling policy should achieve minimum makespan time. Efficiency of the storage and computation nodes is considered during the process of resource clustering. In this regard, a near optimal approach is proposed to perform job scheduling and resource clustering. Hopfield neural network (Auto-Associative-Memory network) is used along with equivalence partitioning recurrent node weight (EPRNW) algorithm to schedule the jobs in an excellent manner. The comparative study and performance evaluation is done between the existing approaches and proposed approach. The proposed approach minimizes the makespan time by using continuous Hopfield neural network to achieve the near optimal scheduling and equivalence partitioning recurrent node weight algorithm is used to identify the corresponding computation nodes instead of random selection of computation nodes for resource clustering. Efficiency of scheduling process is maximized and resource clustering is performed rapidly by using the proposed algorithm.

Multi-Objective Short-Term Fixed Head Hydrothermal Scheduling Using Augmented Lagrange Hopfield Network

This paper proposes an augmented Lagrange Hopfield network (ALHN) based method for solving multi-objective short term fixed head hydrothermal scheduling problem. The main objective of the problem is to minimize both total power generation cost and emissions of NOx, SO₂, and CO₂ over a scheduling period of one day while satisfying power balance, hydraulic, and generator operating limits constraints. The ALHN method is a combination of augmented Lagrange relaxation and continuous Hopfield neural network where the augmented Lagrange function is directly used as the energy function of the network. For implementation of the ALHN based method for solving the problem, ALHN is implemented for obtaining non-dominated solutions and fuzzy set theory is applied for obtaining the best compromise solution. The proposed method has been tested on different systems with different analyses and the obtained results have been compared to those from other methods available in the literature. The result comparisons have indicated that the proposed method is very efficient for solving the problem with good optimal solution and fast computational time. Therefore, the proposed ALHN can be a very favorable method for solving the multi-objective short term fixed head hydrothermal scheduling problems.

Optimal Control of Switched Systems Based on Continuous Hopfield Neural Network

In this paper, a new approach is proposed for the optimal control problem of switched systems. This approach, based on Continuous Hopfield Neural Network (CHNN), has been used to find the optimal switching instants to minimize a performance index that is defined over a finite time horizon and transformed into the energy function of CHNN. The switching instants present the output vector of the neurons of CHNN. As a result, solving a dynamic optimization problem is equivalent to operating associated CHNN from its initial state to the terminal state. Based on the stable output vector of CHNN, which represents the optimal switching instants, we can find the optimal control sequence. As CHNN works in parallel and as it is of real-time characteristic, the present method is easier to satisfy the requirement of real-time control and is promising in application. We demonstrate via numerical examples the effectiveness of the proposed approach where the results are compared to those obtained by conventional methods, such as simple gradient and Quasi-Newton methods, and other non-conventional methods such as the Particle Swarm Optimization (PSO). By applying the proposed algorithm on a hydraulic system, it seems a general solution for the optimal control problem of switching instants, for a number of reasons; first, no regularity in the performance function is required; second, it is valid for many dynamics, and finally, it provides a global optimum.

Augmented Lagrange Hopfield network initialized by quadratic programming for economic dispatch with piecewise quadratic cost functions and prohibited zones

This paper proposes a method based on quadratic programming (QP) and augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problem with piecewise quadratic cost functions and prohibited zones. The ALHN method is a continuous Hopfield neural network with its energy function based on augmented Lagrange function which can properly deal with constrained optimization problems. In the proposed method, the QP method is firstly used to determine the fuel cost curve for each unit and initialize for the ALHN method, then a heuristic search is used for repairing prohibited zone violations, and the ALHN method is finally applied for solving the problem if any violations found. The proposed method has been tested on different systems and the obtained results are compared to those from many other methods in the literature. The result comparison has indicated that the proposed method has obtained better solution quality than many other methods. Therefore, the proposed QP-ALHN method could be a favorable method for solving the ED problem with piecewise quadratic cost functions and prohibited zones.