This paper proposes a simple enhanced augmented Hopfield Lagrange neural network (EALH) for solving economic dispatch (ED) problem with piecewise quadratic cost functions. The EALH is an augmented Lagrange Hopfield neural network (ALH), which is a combination of continuous Hopfield neural network and augmented Lagrangian relaxation function as its energy function, enhanced by a heuristic search...

Hopfield [1, 2] took as a starting point physical systems like the magnetic Ising model �formalism resulting from statistical physics describing a system composed of units with two possible states named spins) to build a Neural Network �NN) with abilities of learning and recovery of patterns. The capacities and limitations of this Network, called associative memory, were well established in a t...

The state space of a conventional Hopfield network typically exhibits many different attractors of which only a small subset satisfies constraints between neurons in a globally optimal fashion. It has recently been demonstrated that combining Hebbian learning with occasional alterations of normal neural states avoids this problem by means of self-organized enlargement of the best basins of attr...

Many neural network architectures operate only on real data and simple complex inputs. But there are applications where considerations of complex and quaternion inputs are quite desirable. Prior complex neural network models have generalized the Hopfield model, backpropagation and the perceptron learning rule to handle complex inputs. The Hopfield model for inputs and outputs falling on the uni...

In this letter we unveil the existence of transient hidden coexisting chaotic attractors, in a simplified Hopfield neural network with three neurons. keyword Hopfield neural network; Transient hidden chaotic attractor; Limit cycle

Electric power system is a highly complex and non linear system. Its analysis and control in real time environment requires highly sophisticated computational skills. Computations are reaching a limit as far as conventional computer based algorithms are concerned. It is therefore required to find out newer methods which can be easily implemented on dedicated hardware. It is a very difficult tas...

We study a “two-pattern” Hopfield model with Gaussian disorder. We find that there are infinitely many pure states at low temperatures in this model, and we find that the metastate is supported on an infinity of symmetric pairs of pure states. The origin of this phenomenon is the random breaking of a rotation symmetry of the distribution of the disorder variables.

The remarkable collective computational properties of the Hopfield model for neural networks [Proc. Nat. Acad. Sci. USA 79, 2554 (1982)] are reviewed. These include recognition from partial input, robustness, and error-correction capability. Features of the model that make its optical implementation attractive are discussed, and specific optical implementation schemes are given.

Abstract. For the Traveling Salesman Problem ( ), a combinatorial optimization problem, a feedforward artificial neural network model, the Continuous Hopfield Network ( ) model, is used to solve it. This neural network approach is based on the solution of a differential equation. An appropriate parameter setting of this differential equation can assure that the solution is associated with a tou...

Continuous-time Hopfield network has been an important focus of research area since 1980s whose applications vary from image restoration to combinatorial optimization from control engineering to associative memory systems. On the other hand, in wireless communications systems literature, power control has been intensively studied as an essential mechanism for increasing the system performance. ...