Harmony Search Algorithm with Two Problem-Specific Operators for Solving Nonogram Puzzle

The nonogram is a logic puzzle where each cell should be colored or left blank according to row and column clues to reveal a hidden picture. This puzzle is known as an NP-complete combinatorial problem characterized by an exponential increase in the number of candidate solutions with increasing puzzle size. So far, some methods have been investigated to address these challenges, including conventional line-solving techniques, integer programming, and neural networks. This study introduces a novel Harmony Search (HS)-based approach for solving nonogram puzzles, incorporating problem-specific operators designed to effectively reduce the solution search space and accelerate convergence. Experimental results obtained from benchmark puzzles demonstrate that the proposed HS model utilizing a clue-constrained random-generation operator significantly reduces the average number of iterations and enhances the solution-finding success rate. Additionally, the HS model integrating an initially confirmed cell-scanning operator exhibited promising performance on specific benchmark problems. The authors think that the nonogram puzzle can be a good benchmark problem for quantum computing-based optimization in the future, and the proposed HS algorithm can also be combined with quantum computing mechanisms.