Optimal Dartboard Design with Simulated Annealing
DOI:
https://doi.org/10.5281/zenodo.8071687Keywords:
Dartboard design, Meta-heuristic, Simulated Annealing, Penalty function methodAbstract
Darts game is a popular game where people compete in competition while having fun. Although most people do not know, the dartboard design used while playing the game is an optimization problem studied by different researchers. A dartboard design that will increase the competition in the game and make the game more complex can be set up as a combinatorial optimization problem. This study used the Simulated Annealing algorithm to obtain an optimal dartboard design. Contrary to the algorithm's classical structure, it aims to achieve better results by using more than one neighborhood structure. By running the designed algorithm with four different objective functions, the best designs were tried to be obtained. As a result, in addition to the existing designs in the literature, two new designs are proposed that provide good solutions for all objective functions.
References
D. McFarlan, “The Guinness Book of Records”, Guinness Publishing, Enfield, Middlesex, 1990, p. 242. Ed. 1989.
H.A. Eiselt, G. Laporte, “A combinatorial optimization problem arising in dartboard design”, 1.0per. Res. Soc., vol. 42, pp. l13-118, 1991.
P. W. A. Donkers, “Dartbord arrangement” Delft University of Technology Faculty of Electrical Engineering, Mathematics and Computer Science Delft Institute of Applied Mathematics, 2010.
A. Bellos, “Optimal dartboard hits the bullseye”, The Guardian. UK, 2020, June 5. https:// www.theguardian.com/ science/ alexs-adventures-in numberland/2013/jan/09/optimal-dartboard-hits-bullseye.
K. Selkirk, “Re-designing the dartboard”, Math. Gazette, vol. 60, pp. 171-178, 1976.
D. Kohler, “Optimal strategies for the game of darts”, Journal of the Operational Research Society, Vol 33, pp. 871-884, 1982.
S.A. Curtis, “Darts and hoopla board design”, Information Processing Letters, 92 (2004) 53–56.
Y. J. Liao, “On the Design of Generalized Dartboard”. October 19, 2006.
Y. J. Liao, M. Z. Shieh, S. C. Tsai, “Arranging numbers on circles to reach maximum total variations”, The Electronic Journal of Combinatorics, 14 2007, #R47.
D. F. Percy, “Winning darts!”, Mathematics Today, vol. 35, pp. 54–57, 1999.
D. F. Percy, “The Optimal Dartboard?” Mathematics Today, vol. 35, pp. 268–270, 2012.
A. Eleni, V. Aristidis, “A meta-heuristic algorithm is used for dartboard design”, International Journal of Management Science and Engineering Management. Vol. 4 (2009) No.3, pp. 198-204.
C. Drosos, G. Trichas, A. Vlachos, “A comparative study of meta heuristic algorithms for Dartboard Design” Conference: Fifth International Conference on Information, Intelligence, Systems and Applications IISA, Chania, Greece. 2014. DOI: 10.1109/IISA.2014.6878759.
R. Eastaway, and J. Haigh, “The Hidden Mathematics of Sport”, London. Portico, 2011.
D. Singmaster, “Arranging a dartboard”, IMA Bulletin, vol. 16, pp. 93-97, 1980.
A. Homaifar, S.H.Y. Lai, and X. Qi, “Constrained optimization via genetic algorithms”, Simulation, 62, 242-254, 1994.
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