论文信息 - The construction of subsquare free Latin squares by simulated annealing

The construction of subsquare free Latin squares by simulated annealing

The Construction of Subsquare Free Latin Squares by Simulated Annealing J.R. Elliott and P.B. Gibbons Department of Computer Science University of Auckland New Zealand A simulated annealing algorithm is used in the construction of subsquare free Latin squares. The algorithm is described and experience from its application is reported. Results obtained include the construction of subsquare free Latin squares of orders 16 and 18, the smallest orders for which existence of such squares was previously in doubt.

Peter B. Gibbons | J. R. Elliott

[2] J. Dénes,et al. Latin squares and their applications , 1974 .

[3] C. D. Gelatt,et al. Optimization by Simulated Annealing , 1983, Science.

[4] Anton Kotzig,et al. On certain constructions for latin squares with no latin subsquares of order two , 1976, Discret. Math..

[5] KATHERINE HEINRICH. Latin Squares with No Proper Subsquares , 1980, J. Comb. Theory, Ser. A.

[6] Emile H. L. Aarts,et al. Simulated annealing and Boltzmann machines - a stochastic approach to combinatorial optimization and neural computing , 1990, Wiley-Interscience series in discrete mathematics and optimization.

[7] N. Metropolis,et al. Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[8] Douglas R. Stinson. Hill-Climbing Algerithms for the Construction of Combinatorial Designs , 1985 .

[9] Alexander Rosa,et al. One-factorizations of the complete graph - A survey , 1985, J. Graph Theory.

[10] D. Balmer. Theoretical and Computational Aspects of Simulated Annealing , 1991 .