A Class of Chaotic Neural Network with Morlet Wavelet Function Self-feedback

Chaotic neural networks have been proved to be strong tools to solve the optimization problems. In order to escape the local minima, a new function is introduced into the self-feedback item of the transiently chaotic neural network, this paper proposes chaotic neural network with nonlinear function self-feedback by improving the self-feedback item of Chen and Aihara's network making that the network has new character which is different from linear self-feedback network. The figures of the reversed bifurcation and the maximal Lyapunov exponents of single neural unit were given, We constructed the energy function of chaotic neural network, and analyzed the sufficient condition for the networks to reach asymptotical stability and set the parameters of the networks for solving traveling salesman problem (TSP). The simulation results in solving 10-city TSP show that the new model is valid in solving optimization problems.

A parallel immune algorithm for traveling salesman problem and its application on cold rolling scheduling

It is prone to get stuck in a local minimum when solving the Traveling Salesman Problem (TSP) by the traditional Hopfield neural network (HNN) and hard to converge to an efficient solution, resulting from the defect of the penalty method used by the HNN. In order to mend this defect, an accelerated augmented Lagrangian Hopfield neural network (AALHNN) algorithm was proposed in this paper. This algorithm gets out of the dilemma of penalty method by Lagrangian multiplier method, ensuring that the solution to the TSP is undoubtedly efficient. The second order factor added in the algorithm stabilizes the neural network dynamic model of the problem, thus improving the efficiency of solution. In this paper, when solving the TSP by AALHNN, some changes were made to the TSP models of Hopfield and Tank. Say, constraints of TSP are multiplied by Lagrange multipliers and augmented Lagrange multipliers respectively, The augmented Lagrange function composed of path length function can ensure robust convergence and escape from the local minimum trap. The Lagrange multipliers are updated by using nesterov acceleration technique. In addition, it was theoretically proved that the extremum obtained by this improved algorithm is the optimal solution of the initial problem and the approximate optimal solution of the TSP was successfully obtained several times in the simulation experiment. Compared with the traditional HNN, this method can ensure that it is effective for TSP solution and the solution to the TSP obtained is better.

In order to install a chaotic neural network to solve the traveling salesman problem (TSP) on an integrated circuit, a chaotic neuron circuit is designed by using a current mode circuit. First, the characteristics of the output function of the neuron circuit are determined by numerical simulation so that they have excellent capability to solve the TSP. Next, the network is designed such that the chaotic neural network consisting of the designed neuron circuits can seek the optimum solution efficiently. Further, a circuit is proposed which realizes chaotic annealing in order to improve the convergence of the chaotic neural network. The ability of the proposed network using the annealing circuit to derive an optimum solution of the TSP is studied. From the simulation results, it is confirmed that the proposed chaotic neuron circuit is suitable for integration of the chaotic neural network to solve the TSP. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(9): 52–62, 1999

Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.

In this paper, a new chaotic neural network model is proposed, we introduce a Bessel function as self-feedback term in this model, Compared with other chaotic neural network model, owing to the Bessel function is a nonlinear function with good nature, and it has stronger function approximation ability, so that the novel chaotic network model has stronger traversal search ability.When it is applied to solve combinatorial optimization problems, the simulation results show that the network has better ability to avoid network convergence to local minima if the appropriate coefficient of expansion and the network has been taken, so the efficiency of network optimization capability is improved.

We review our model of chaotic neural networks with chaotic dynamics and apply it to associative memory. We demonstrate that dynamical assocative memory can be realized with the chaotic neural network.

The Seventh International Symposium on Neural Networks (ISNN 2010) was held on June 6–9, 2010 in Shanghai, China. The ISNN 2010 was a great success and provided a high-level international forum for scientists and engineers to present the latest research in neural networks, computational intelligence, cognitive systems, and related fields. To highlight the success of this conference, we edited this special issue for Cognitive Computation. We chose nine papers from over 591 papers submitted to ISNN 2010, which reflect the high quality of the presentations at the conference while capturing the spirit of our theme, ‘‘Advances in Computational Intelligence and Applications,’’ for this special issue. Our goal for this special issue is to present the latest research developments in computational intelligence with a focus on cognitive computation and their applications across a wide range of domains. Over the past decades, we have witnessed tremendous interest and developments in all aspects of computational intelligence research, ranging from both theoretical foundations, principles, to practical applications in different domains. To reflect a flavor of recent research activities in the community, we carefully selected these nine papers for this special issue. The selected papers can be organized into the following four coherent sections. The first section is directly related to neural network models and applications. The paper by Deng presents a new control strategy for the chaotic neural network, in which the refractoriness is tuned by using feedback control based on online averaging of network states. Simulation results demonstrate that the proposed model can achieve favorable performance in handling noisy, incomplete, and composite patterns, while also achieving either enhanced or comparable memory capacity compared with the classic Hopfield net and other chaotic neural network models. In the other paper, Gluge et al. discuss recurrent networks for implicit learning of temporal sequences, a very important area to understand high-level cognitive intelligence. The authors propose a recurrent network with backpropagation training algorithm that is adapted to the reinforcement learning scheme. The simulation results fit quantitatively as well as qualitatively to the behavioral results, suggesting the role of temporal context in associative learning scenarios. The second section is related to language processing and understanding, an important topic in cognitive science and computational intelligence. The paper by Murata et al. investigates the maximum entropy (ME) approach for natural language processing (NLP) problems including machine translation and information extraction. Comparative studies of the proposed approach with the existing techniques are illustrated in this paper. In related work to this field, the paper by Kaznatcheev investigates connectionist models on the interplay of nouns and pronouns in personal pronoun acquisition, a very interesting and important problem in psychology. For instance, the author discusses the learning in the shifting reference situation for children. It is reported that learning of two different noun-and-pronoun addressee patterns is consistent with Z. Zeng (&) Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P. R. China e-mail: zgzeng@gmail.com

Effects of correlation among stored patterns on associative dynamics of chaotic neural network

A new transient chaotic neuron model which introduces Legendre function into the self-feedback term is constructed. The dynamic characteristics of the single neuron are analyzed by the time evolution graph and the inverted bifurcation graph of the largest Lyapunov exponent. The network parameters are set for settling the combinatorial optimization problem. The effectiveness of this model has been verified by the simulation results in nonlinear function optimization, traveling salesman problem (TSP).KeywordsChaotic neural networkLegendre function self-feedbackLyapunov exponentsCombinatorial optimization problem

Construction of blind restoration model for super-resolution image based on chaotic neural network

Using the new method and roulette wheel, the traditional Ant Colony Algorithm is improved in the aspect of searching process and pheromone modification. The defects of low searching efficiency and easy to fall into local minimum in traditional Ant Colony Algorithm are remedied. the validity of the improved algorithm has been verified using a testing function.Moreover,a satisfactory optimum solution for a Power Distribution Network Planning has been obtained. And the effective design method for permanent-magnet synchronous Ant colony algorithm is a simulation based on the species evolution to solve complex optimization problem for heuristic. The idea of ant colony algorithm are simulated ants foraging behavior,That is, the use of a large number of ants in the search space in the random search,And use of information has always been to strengthen the search route, and guide other artificial ants search,At the same time, the introduction of the volatile pheromone mechanism(1). Ant colony algorithm proposed by the Italian scholars Dorigo in the twentieth century nineties. The algorithm in the traveling salesman problem (TSP), quadratic assignment problem (QAP) and shop scheduling problem (JSP) solution to achieve good results. Now ant colony algorithm has been optimized in the motor design, network distribution, function optimization and integrated circuit wiring in areas such as applied. Forestry waste from electricity distribution network from the power station involved in each location, size to meet future demand for electricity in rural areas since, at the same time for each subject since the power station capacity, radial network structure, as well as reliability requirements, such as binding. Because of lot of variables and constraints involved, spontaneous power distribution network planning is a very complex combinatorial optimization problem. In this paper, these issues of improved ant colony algorithm and proposes a multi-modal adaptive ant colony pheromone search mechanisms, and their use for the electricity distribution network optimization, and achieved good results. I. THE MATHEMATICAL MODEL OF ACA The ant optimization algorithm is mainly composed of the switching rules and the renewaling information element rule. As an example,We present the ACO algorithm applied to the TSP(Traveling Salesman Problem) for illustrating the principle of ant colony algorithm. there is the assumption N cities, traveling salesman problem are looking for an optimal travel path of the shortest route. The TSP models the situation of a travelling sales man who is required to pass through a number of cities(2). The goal of the travelling sales man is to traverse these cities(visiting each city exactly once)so that the total travelling distance is minimal. Feasible solution of the traveling salesman problem is a non-repeat sequences of all the citis. Assumeing that only m ants Add to the given n cities: dij(i,j=1,2,…,n) where dij is distance between city i with city j. bi(t) where bi(t) is the number of ants is located in city i when it's t. m= ∑ = n

This paper presents an adaptation of the flying ant colony optimization (FACO) algorithm to solve the traveling salesman problem (TSP). This new modification is called dynamic flying ant colony optimization (DFACO). FACO was originally proposed to solve the quality of service (QoS)-aware web service selection problem. Many researchers have addressed the TSP, but most solutions could not avoid the stagnation problem. In FACO, a flying ant deposits a pheromone by injecting it from a distance; therefore, not only the nodes on the path but also the neighboring nodes receive the pheromone. The amount of pheromone a neighboring node receives is inversely proportional to the distance between it and the node on the path. In this work, we modified the FACO algorithm to make it suitable for TSP in several ways. For example, the number of neighboring nodes that received pheromones varied depending on the quality of the solution compared to the rest of the solutions. This helped to balance the exploration and exploitation strategies. We also embedded the 3-Opt algorithm to improve the solution by mitigating the effect of the stagnation problem. Moreover, the colony contained a combination of regular and flying ants. These modifications aim to help the DFACO algorithm obtain better solutions in less processing time and avoid getting stuck in local minima. This work compared DFACO with (1) ACO and five different methods using 24 TSP datasets and (2) parallel ACO (PACO)-3Opt using 22 TSP datasets. The empirical results showed that DFACO achieved the best results compared with ACO and the five different methods for most of the datasets (23 out of 24) in terms of the quality of the solutions. Further, it achieved better results compared with PACO-3Opt for most of the datasets (20 out of 21) in terms of solution quality and execution time.

Sliced Neighborhood Search

A new state space representation of a class of combinatorial optimization problems is introduced. The representation enables efficient implementation of exhaustive search for an optimal solution in bounded NP complete problems such as the traveling salesman problem (TSP) with a relatively small number of cities. Furthermore, it facilitates effective heuristic search for sub optimal solutions for problems with large number of cities. This paper surveys structures for representing solutions to the TSP and the use of these structures in iterative hill climbing (ITHC) and genetic algorithms (GA). The mapping of these structures along with respective operators to a newly proposed electro-optical vector by matrix multiplication (VMM) architecture is detailed. In addition, time space tradeoffs related to using a record keeping mechanism for storing intermediate solutions are presented and the effect of record keeping on the performance of these heuristics in the new architecture is evaluated. Results of running these algorithms on sequential architecture as well as a simulation-based estimation of the speedup obtained are supplied. The results show that the VMM architecture can speedup various variants of the TSP algorithm by a factor of 30x to 50x.