Hiroshi Ninomiya

Neural network approach to traveling salesman problem based on hierarchical city adjacency

A neural network approach based on city adjacency has been proposed in order to solve the traveling salesman problems. This method, in which a novel energy function is used for TSPs, produces frequently several traveling closed subtours. To cope with this problem, the authors propose a method to make a traveling tour without any closed subtours, where hierarchical city adjacency is considered. It is easy to apply this technique recursively. Therefore, this approach is applicable to larger scale problems.

A study of Hopfield neural networks with external noises

This paper describes the influence of the external noise with the autocorrelation on the Hopfield neural network approach to optimization problems. In order to investigate the noise effects, several types of external noises, namely chaotic noises and uniformly random noises, are injected into the network and the improvement of the ability to trace the optimal solution is examined for the travelling salesman problem (TSP). As a result, it is confirmed that the autocorrelation has a large influence on the frequency of transitions among the network states, and the noises generated from the logistic map and the double scroll attractor are useful for tracing solutions.

Tiling algorithm with fitting violation function for analog neural array

This paper describes a neuro-based optimization algorithm for tiling with polyominoes. First, we review the previous neuro-based parallel algorithm for the tiling problem where the maximum neural array is used. Next, we propose a robust neuro-based tiling algorithm using the modified energy function which includes the fitting violation function of the polyominoes and the analog neural array. Finally, we compare our algorithm with the previous one and show that our method is much more vigorous and practical for larger tiling problems.

Application of neuro-based optimization algorithm to three dimensional cylindric puzzles

This paper describes an application of the neuro-based optimization algorithm to 3D cylindric puzzles which are problems to arrange the irregular-shaped slices so that they perfectly fit into a fixed 3D cylindric shape. First, the 2D tiling algorithm is expanded for 3D puzzles. Next, the energy function with the fitting function is introduced, which is available for 3D cylindric puzzles. Furthermore our algorithm is applied to several examples using the analog neural array. Finally, it is shown that our algorithm is useful for solving 3D cylindric puzzles.

Design and implementation of neuro-based discrete Walsh transform processor

The discrete Walsh transform (DWT) is one of the most important techniques as well as the discrete Fourier transform (DFT) in the field of signal processing. We have proposed the theoretical design of a DWT processor based on Hopfield linear programming neural networks, and then we have also proved the rapid convergence and high accuracy of the DWT processor both analytically and by simulation. We show the experimental design and the hardware implementation of the neuro-based DWT processor. Finally, it is confirmed both by experiments and SPICE simulations that our processor is useful and practical.

Analog neuro‐based approach to tiling problem using fitting function of polyominoes

The tiling problem is a typical NP-complete problem, where the polyominoes are to be arranged without a gap on a finite checkerboard. In this study, the arrangement of l polyominoes on an m ×n checkerboard is considered. As the first step, the conventional parallel algorithm using the maximum neural network is verified. Then, the authors propose a solution procedure for the tiling problem, where the analog neural network is used in addition to the fitting function. Lastly, the proposed method and the conventional method are compared, and it is shown that the proposed method is also effective for more complex tiling problems.

Application of neuro-based optimization to 3-D rectangular puzzles

This paper describes a neuro-based optimization algorithm for 3D rectangular puzzles which are the problems to arrange the irregular-shaped blocks so that they perfectly fit into a fixed cuboid. First, the energy function with fitting function of each block is introduced which is available for 3D rectangular puzzles. Next, our algorithm is applied to several examples using the analog neural array. Finally, it is shown that our algorithm is useful for solving 3D rectangular puzzles.

Convergence of Hopfield neural network for orthogonal transformation

In this paper, we describe the convergence of the discrete Walsh transform (DWT) processor based on Hopfield neural networks. First, the influence of the orthonormal matrix on solving linear equations by the steepest descent (SD) method is investigated and this theory is applied to the convergence of Hopfield neural networks. Finally, it is shown both analytically and by simulation that this type of network is suitable for orthogonal transforms.

Neural network simulator for spatiotemporal pattern analysis

This paper describes a fast simulator for spatiotemporal pattern analysis of multivalued continuous-time neural networks, where the multivalued transfer function of a neuron is regarded as a stepwise constant function. Use of stepwise constant method enables one to analyse the state transition of the network without solving explicitly the differential equations. Furthermore, this method also enables one to select the optimal timestep in numerical integration. We have constructed a neural network simulator for the spatiotemporal pattern analysis and compared it with conventional simulators. Finally, it is shown that our simulator is faster and more practical than conventional simulators.

Neuro-based tiling algorithm using fitting violation function of polyominoes

This paper describes a neuro-based optimization algorithm for tiling with polyominoes. First, we review the previous neuro-based parallel algorithm for the tiling problem where l/spl times/m/spl times/n maximum neural array is required for an m/spl times/n checkerboard. Next, we propose a robust neuro-based tiling algorithm using the modified energy function which includes the fitting violation function of the polyominoes and the analog neural array. Finally, we compare our algorithm with the previous one and show that our method is much more vigorous and practical for larger tiling problems.