A Preliminary Study on Solving Knight’s Tour Problem Using Binary Magnetic Optimization Algorithm

Suzanna, Ridzuan Aw and Mohd Muzafar, Ismail and Amar Faiz, Zainal Abidin and Nur Anis, Nordin and Seri Mastura, Mustaza and Ezreen Farina, Shair and Asrani, Lit and Arfah Syahida, Mohd Noor and Nur Latif Azyze, Mohd Shaari Azyze and Ahmad Rijal, Abdul Rahman and Ili Najaa, Aimi and Safirin, Mohd Karis and Amira Sarayati, Ahmad Dahlan (2013) A Preliminary Study on Solving Knight’s Tour Problem Using Binary Magnetic Optimization Algorithm. In: IGCESH 2013 (4th International Graduate Conference on Engineering, Science and Humanities), 16th to 17th April 2013, Johor Bahru, Johor, Malaysia.

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Abstract

The knight’s tour problem is a sub chess puzzle where the objective of the puzzle is to find combination moves made by a knight so that it visits every square of the chessboard exactly once. This paper proposes a model using Binary Magnetic Optimization Algorithm to solve the problem. Each particle represents a possible solution of the problem. A pair of 3 binary bits is used to represent a move made by the knight for each move. The numerical value for each move can be in the range of 0 to 7 according to the 8 possible moves that can be taken by the knight. The fitness of a particle is then calculated based on the number of legal moves it has taken starting from the first move. The proposed model has been tested using the standard 8x8 chessboard setup. A comparative performance study is done based on two updating rules of Binary Magnetic Optimization Algorithm: sigmoid & tanh functions. Results obtained show that the proposed model has a potential for further improvement.

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