Knowledge-Based Intelligent Information and Engineering Systems

Volume 4692 of the series Lecture Notes in Computer Science pp 371-378

Harmony Search Algorithm for Solving Sudoku

  • Zong Woo GeemAffiliated withJohns Hopkins University, Environmental Planning and Management Program, 729 Fallsgrove Drive #6133, Rockville, Maryland 20850


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