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The N queens problem - new variants of the Wirth algorithm

Łajtar M.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

2013

Vol. 13, no. 1

53--61

The paper presents new ways of n-queens problem solving . Briefly,this is a problem on a nxn chessboard of a set n-queens, so that any two of the mare not in check. At the beginning, currently used algorithm to find solutions is discussed. Then sequentially 4 new algorithms, along with the interpretation of changes are given. The research results, including comparison, of calculation times of all algorithms together with their interpretation are discussed. Finally, conclusions are given. The results were obtained thanks to the pre-created application.Chapters except for By filtering ver. 2 were based on the previous studies carried out during the Bachelor course [1].

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.