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2 Control and Cybernetics

2 2002

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Neural networks for the N-Queens Problem : a review

Mańdziuk J.

Control and Cybernetics

2002

Vol. 31, no 2

217-248

Neural networks can be successfully applied to solving certain types of combinatorial optimization problems. In this paper several neural approaches to solving constrained optimization problems are presented and their properties discussed. The main goal of the paper is to present various improvements to the wellknown Hopfield models which are intensively used in combinatorial optimization domain. These improvements include deterministic modifications (binary Hopfield model with negative self-feedback connections and Maximum Neural Network model), stochastic modifications (Gaussian Machine), chaotic Hopfield-based models (Chaotic Neural Network and Transiently Chaotic Neural Network), hybrid approaches (Dual-mode Dynamic Neural Network and Harmony Theory approach) and finally modifications motivated by digital implementation feasibility (Strictly Digital Neural Network). All these models are compared based on a commonly used benchmark prohlem - the N-Queens Problem (NQP). Numerical results indicate that each of modified Hopfield models can be effectively used to solving the NQP. Coonvergence to solutions rate of these methods is very high - usually close to 100%. Experimental time requirements are generally low - polynomial in most casos. Some discussion of non-neural, heuristic approaches to solving the NQP is also presented in the paper.

Binary neural networks for N-queens problems and their VLSI implementations

Funabiki N., Kurokawa T., Ohta M.

Control and Cybernetics

2002

Vol. 31, no 2

271-296

Combinatorial optimization problems compose an important class of matliematical problems that include a variety of practical applications, such as VLSI design automation, communication network design and control, job scheduling, games, and genome informatics. These problems usually have a large number of variables to be solved. For example, problems for VLSI design automation require several million variables. Besides, thieir computational complexity is often intractable due to NP-hardness. Neural networks have provided elegant solutions as approximation algorithms to these hard problems due to their natural parallelism and their affinity to hardware realization. Particularly, binary neural networks have great potential to conform to current digital VLSI design technology, because any state and parameter in binary neural networks are expressed in a discrete fashion. This paper presents our studies on binary neural networks to the N-queens problem, and the three different approaches to VLSI implementations focusing on the efficient realization of the synaptic connection networks. Reconfigurable devices such as CPLDs and FPGAs contribute the realization of a scalable architecture with the ultra high speed of computation. Based on the proposed architecture, more than several thousands of binary neurons can be realized on one FPGA chip.