Harmony search (HS) algorithm was applied to solving Sudoku puzzle. The HS is an evolutionary algorithm which mimics musicians’ behaviors such as random play, memory-based play, and pitch-adjusted play when they perform improvisation. Sudoku puzzles in this study were formulated as an optimization problem with number-uniqueness penalties. HS could successfully solve the optimization problem after 285 function evaluations, taking 9 seconds. Also, sensitivity analysis of HS parameters was performed to obtain a better idea of algorithm parameter values.


Sudoku puzzle harmony search combinatorial optimization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Zong Woo Geem
    • 1
  1. 1.Johns Hopkins University, Environmental Planning and Management Program, 729 Fallsgrove Drive #6133, Rockville, Maryland 20850USA

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