Simulated Annealing Approach to Solve Nonogram Puzzles with Multiple Solutions

Abstract

Nonogram, a popular Japanese puzzle game, is a well-known NP-complete problem. A number of approaches have been proposed and some algorithms are efficient in solving puzzles with one single solution. However, many puzzles are not limited to one ideal single solution. If there are multiple solutions to a puzzle, even the puzzle that is small in size may sometimes take a very long time to conquer. This type of problem is often observed to have sparse distribution of its colored cells. The existing efficient algorithms often gain no advantages, because the search space can stay huge and not reducible. For this reason, incorporating learning algorithms can be beneficial to support the deficiency. The objective of this study is to develop a heuristic means by the concept of simulated annealing (SA) to learn to explore different types of search spaces. Experiments are conducted to solve a number of multi-solution puzzles and the effectiveness of this approach is discussed.