A unified framework for chaotic neural-network approaches to combinatorial optimization

Aperiodically intermittent quantized control-based exponential synchronization of quaternion-valued inertial neural networks

Inertial neural networks are proposed via introducing an inertia term into the Hopfield models, which make their dynamic behavior more complex compared to the traditional first-order models. Besides, the aperiodically intermittent quantized control over conventional feedback control has its potential advantages on reducing communication blocking and saving control cost. Based on these facts, we are mainly devoted to exploring of exponential synchronization of quaternion-valued inertial neural networks under aperiodically intermittent quantized control. Firstly, a compact quaternion-valued aperiodically intermittent quantized control protocol is developed, which can mitigate significantly the complexity of theoretical derivation. Subsequently, several concise criteria involving matrix inequalities are formulated through constructing a type of Lyapunov functional and employing a direct analysis approach. The correctness of the obtained results eventually is verified by a typical example.

Adaptive control-based synchronization of discrete-time fractional-order fuzzy neural networks with time-varying delays

This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ-difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a novel discrete-time adaptive controller with time-varying delay is designed, by virtue of 1-norm Lyapunov function and newly established lemmas herein as well as inequality techniques and contradiction method, some judgement conditions are derived to guarantee complete synchronization for the explored DFFNNs. Benefitting from discrete-time adaptive control strategy and our analysis method, the conservatism of the derived synchronization criteria is reduced. Ultimately, the effectiveness of our theoretical results and secure communication scheme are demonstrated through two numerical examples.

Remote Wind Farm Path Planning for Patrol Robot Based on the Hybrid Optimization Algorithm

Globally, wind power plays a leading role in the renewable energy industry. In order to ensure the normal operation of a wind farm, the staff will regularly check the equipment of the wind farm. However, manual inspection has some disadvantages, such as heavy workload, low efficiency and easy misjudgment. In order to realize automation, intelligence and high efficiency of inspection work, inspection robots are introduced into wind farms to replace manual inspections. Path planning is the prerequisite for an intelligent inspection robot to complete inspection tasks. In order to ensure that the robot can take the shortest path in the inspection process and avoid the detected obstacles at the same time, a new path-planning algorithm is proposed. The path-planning algorithm is based on the chaotic neural network and genetic algorithm. First, the chaotic neural network is used for the first step of path planning. The planning results are encoded into chromosomes to replace the individuals with the worst fitness in the genetic algorithm population. Then, according to the principle of survival of the fittest, the population is selected, hybridized, varied and guided to cyclic evolution to obtain the new path. The shortest path obtained by the algorithm can be used for the robot inspection of the wind farms in remote areas. The results show that the proposed new algorithm can generate a shorter inspection path than other algorithms.

Chaotic Image Encryption: State-of-the-Art, Ecosystem, and Future Roadmap

Recently, many researchers have been interested in the application of chaos in cryptography. Specifically, numerous research works have been focusing on chaotic image encryption. A comprehensive survey can highlight existing trends and shed light on less-studied topics in the area of chaotic image encryption. In addition to such a survey, this paper studies the main challenges in this field, establishes an ecosystem for chaotic image encryption, and develops a future roadmap for further research in this area.

A GCM Neural Network with Piecewise Logistic Chaotic Map

In order to explore dynamic mechanisms and chaos control of globally coupled map (GCM) chaotic neural networks, a new GCM model, called the PL-GCM model is proposed, of which a piecewise logistic chaotic map is used instead of a logistic map. As a result of the strong chaotic features of the map, the neurons’ period and chaotic characteristics over a wide range of parameters are discussed, the dynamic mechanism is demonstrated in detail, and the numerical simulations such as state evolution, the largest Lyapunov exponent (LLE), contour map, and so on are exhibited. Furthermore, chaos control of the proposed PL-GCM model is investigated by adopting two chaos control methods. It is shown that the network with conventional coupling or delay coupling can be precisely controlled to any specified periodic orbit by feedback control, and its dynamic associative memory is realized by the variable threshold parameter control method with external information. The results of simulations and experiments suggest that the network is controlled successfully and can output period patterns with a specified period that contains the stored pattern closest to the initial pattern. All features suggest that the network is fit for pattern recognition and information processing.

Finite- and Fixed-Time Cluster Synchronization of Nonlinearly Coupled Delayed Neural Networks via Pinning Control

In this article, the cluster synchronization problem for a class of the nonlinearly coupled delayed neural networks (NNs) in both finite- and fixed-time cases are investigated. Based on the Lyapunov stability theory and pinning control strategy, some criteria are provided to ensure the cluster synchronization of the nonlinearly coupled delayed NNs in both finite-and fixed-time aspects. Then, the settling time for stabilization that is dependent on the initial value and independent of the initial value is estimated, respectively. Finally, we illustrate the feasibility and practicality of the results via a numerical example.

Nonseparation Method-Based Finite/Fixed-Time Synchronization of Fully Complex-Valued Discontinuous Neural Networks

This article mainly focuses on the problem of synchronization in finite and fixed time for fully complex-variable delayed neural networks involving discontinuous activations and time-varying delays without dividing the original complex-variable neural networks into two subsystems in the real domain. To avoid the separation method, a complex-valued sign function is proposed and its properties are established. By means of the introduced sign function, two discontinuous control strategies are developed under the quadratic norm and a new norm based on absolute values of real and imaginary parts. By applying nonsmooth analysis and some novel inequality techniques in the complex field, several synchronization criteria and the estimates of the settling time are derived. In particular, under the new norm framework, a unified control strategy is designed and it is revealed that a parameter value in the controller completely decides the networks are synchronized whether in finite time or in fixed time. Finally, some numerical results for an example are provided to support the established theoretical results.

Exponential and adaptive synchronization of inertial complex-valued neural networks: A non-reduced order and non-separation approach

This paper mainly deals with the problem of exponential and adaptive synchronization for a type of inertial complex-valued neural networks via directly constructing Lyapunov functionals without utilizing standard reduced-order transformation for inertial neural systems and common separation approach for complex-valued systems. At first, a complex-valued feedback control scheme is designed and a nontrivial Lyapunov functional, composed of the complex-valued state variables and their derivatives, is proposed to analyze exponential synchronization. Some criteria involving multi-parameters are derived and a feasible method is provided to determine these parameters so as to clearly show how to choose control gains in practice. In addition, an adaptive control strategy in complex domain is developed to adjust control gains and asymptotic synchronization is ensured by applying the method of undeterminated coefficients in the construction of Lyapunov functional and utilizing Barbalat Lemma. Lastly, a numerical example along with simulation results is provided to support the theoretical work.

Finite-Time Synchronization of Discontinuous Neural Networks With Delays and Mismatched Parameters

This paper investigates the problem of finite-time drive-response synchronization for a class of neural networks with discontinuous activations, time-varying discrete and infinite-time distributed delays, and mismatched parameters. In order to cope with the difficulties induced by discontinuous activations, time delays, as well as mismatched parameters simultaneously, new 1-norm-based analytical techniques are developed. Both state feedback and adaptive controllers with and without the sign function are designed. Based on differential inclusion theory and Lyapunov functional method, several sufficient conditions on the finite-time synchronization are obtained. Our results show that the controllers with a sign function can reduce the conservativeness of control gains and the controllers without a sign function can overcome the chattering phenomenon. Numerical examples are given to show the effectiveness of the theoretical analysis.

Exponential synchronization for neural networks with mixed time-varying delays via periodically intermittent control

This paper deals with exponential synchronization for a class of neural networks with mixed time-varying delays via periodically intermittent control. Some novel and effective exponential synchronization criteria are derived by constructing Lyapunov functional and applying some analysis techniques. These results presented in this paper generalize and improve many known results. Finally, this paper presents an illustrative example and uses the simulated results to show the feasibility and effectiveness of the proposed scheme.

Asymmetric continuous-time neural networks without local traps for solving constraint satisfaction problems

There has been a long history of using neural networks for combinatorial optimization and constraint satisfaction problems. Symmetric Hopfield networks and similar approaches use steepest descent dynamics, and they always converge to the closest local minimum of the energy landscape. For finding global minima additional parameter-sensitive techniques are used, such as classical simulated annealing or the so-called chaotic simulated annealing, which induces chaotic dynamics by addition of extra terms to the energy landscape. Here we show that asymmetric continuous-time neural networks can solve constraint satisfaction problems without getting trapped in non-solution attractors. We concentrate on a model solving Boolean satisfiability (k-SAT), which is a quintessential NP-complete problem. There is a one-to-one correspondence between the stable fixed points of the neural network and the k-SAT solutions and we present numerical evidence that limit cycles may also be avoided by appropriately choosing the parameters of the model. This optimal parameter region is fairly independent of the size and hardness of instances, this way parameters can be chosen independently of the properties of problems and no tuning is required during the dynamical process. The model is similar to cellular neural networks already used in CNN computers. On an analog device solving a SAT problem would take a single operation: the connection weights are determined by the k-SAT instance and starting from any initial condition the system searches until finding a solution. In this new approach transient chaotic behavior appears as a natural consequence of optimization hardness and not as an externally induced effect.

Novel hysteretic noisy chaotic neural network for broadcast scheduling problems in packet radio networks

Noisy chaotic neural network (NCNN), which can exhibit stochastic chaotic simulated annealing (SCSA), has been proven to be a powerful tool in solving combinatorial optimization problems. In order to retain the excellent optimization property of SCSA and improve the optimization performance of the NCNN using hysteretic dynamics without increasing network parameters, we first construct an equivalent model of the NCNN and then control noises in the equivalent model to propose a novel hysteretic noisy chaotic neural network (HNCNN). Compared with the NCNN, the proposed HNCNN can exhibit both SCSA and hysteretic dynamics without introducing extra system parameters, and can increase the effective convergence toward optimal or near-optimal solutions at higher noise levels. Broadcast scheduling problem (BSP) in packet radio networks (PRNs) is to design an optimal time-division multiple-access (TDMA) frame structure with minimal frame length, maximal channel utilization, and minimal average time delay. In this paper, the proposed HNCNN is applied to solve BSP in PRNs to demonstrate its performance. Simulation results show that the proposed HNCNN with higher noise amplitudes is more likely to find an optimal or near-optimal TDMA frame structure with a minimal average time delay than previous algorithms.

A novel chaotic neural network with the ability to characterize local features and its application

To provide an ability to characterize local features for the chaotic neural network (CNN), Gauss wavelet is used for the self-feedback of the CNN with the dilation parameter acting as the bifurcation parameter. The exponentially decaying dilation parameter and the chaotically varying translation parameter not only govern the wavelet self-feedback transform but also enable the CNN to generate complex dynamics behavior preventing the network from being trapped in the local minima. Analysis of the energy function of the CNN indicates that the local characterization ability of the proposed CNN is effectively provided by the wavelet self-feedback in the manner of inverse wavelet transform and that the proposed CNN can achieve asymptotical stability. The experimental results on traveling salesman problem (TSP) suggest that the proposed CNN has a higher average success rate for obtaining globally optimal or near-optimal solutions.

A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.

Comparison of simulated annealing and mean field annealing as applied to the generation of block designs

This paper describes an experimental comparison between a discrete stochastic optimization procedure (Simulated Annealing, SA) and a continuous deterministic one (Mean Field Annealing), as applied to the generation of Balanced Incomplete Block Designs (BIBDs). A neural cost function for BIBD generation is proposed with connections of arity four, and its continuous counterpart is derived, as required by the mean field formulation. Both strategies are optimized with regard to the critical temperature, and the expected cost to the first solution is used as a performance measure for the comparison. The results show that SA performs slightly better, but the most important observation is that the pattern of difficulty across the 25 problem instances tried is very similar for both strategies, implying that the main factor to success is the energy landscape, rather than the exploration procedure used.

An approach to improve Wang-Smith chaotic simulated annealing

Previous research shows that Wang-Smith chaotic simulated annealing, which employs a gradually decreasing time-step, has only a scaling effect to computational energy of the Hopfield model without changing its shape. This makes the net has sensitive dependence on the value of damping factor. Considering Chen-Aihara chaotic simulated annealing with decaying self-coupling has a shape effect to computational energy of the Hopfield model, a novel approach to improve Wang-Smith chaotic simulated annealing, which reaps the benefits of Wang-Smith model and Chen-Aihara model, is proposed in this paper. With the aid of this method the improved model can affect on computational energy of the Hopfield model from scaling and shape. By adjusting the time-step, the improved neural network can also pass from a chaotic to a non-chaotic state. From numerical simulation experiments, we know that the improved model can escape from local minima more efficiently than original Wang-Smith model.

Experimental analysis of chaotic neural network models for combinatorial optimization under a unifying framework

The aim of this paper is to study both the theoretical and experimental properties of chaotic neural network (CNN) models for solving combinatorial optimization problems. Previously we have proposed a unifying framework which encompasses the three main model types, namely, Chen and Aihara's chaotic simulated annealing (CSA) with decaying self-coupling, Wang and Smith's CSA with decaying timestep, and the Hopfield network with chaotic noise. Each of these models can be represented as a special case under the framework for certain conditions. This paper combines the framework with experimental results to provide new insights into the effect of the chaotic neurodynamics of each model. By solving the N-queen problem of various sizes with computer simulations, the CNN models are compared in different parameter spaces, with optimization performance measured in terms of feasibility, efficiency, robustness and scalability. Furthermore, characteristic chaotic neurodynamics crucial to effective optimization are identified, together with a guide to choosing the corresponding model parameters.