Nonogram

Abstract: Discrete Tomography (DT) is concerned with the reconstruction of binary images from their horizontal and vertical projections. In this paper we consider an evolutionary algorithm for computing such reconstructions.We show that the famous Japanese puzzles are a special case of a more general DT problem and successfully apply our algorithm to such puzzles.

Abstract: Nonogram is one of logical games popular in Japan and Netherlands. Solving nonogram is a NP-complete problem. There are some related papers proposed. Some use genetic algorithm (GA), but the solution may get stuck in local optima. Some use depth first search (DFS) algorithm, the execution speed is very slow. In this paper, we propose a puzzle solving algorithm to treat these problems. Based on the fact that most of nonograms are compact and contiguous, some logical rules are deduced to paint some cells. Then, we use the chronological backtracking algorithm to solve those undetermined cells and logical rules to improve the search efficiently. Experimental results show that our algorithm can solve nonograms successfully, and the processing speed is significantly faster than that of DFS. Moreover, our method can determine that a nonogram has no solution.

Abstract: A Taguchi-based genetic algorithm (TBGA) is proposed to solve Japanese nonogram puzzles. The TBGA exploits the power of global exploration inherent in the traditional genetic algorithm (GA) and the abilities of the Taguchi method in efficiently generating offspring. In past researches, the GA with binary encoding and inappropriate fitness functions makes a huge search space size and inaccurate direction for searching the solution of a nonogram. Consequently, the GA does not easily converge to the solution. The proposed TBGA includes the effective condensed encoding, the improved fitness function, the modified crossover, the modified mutation, and the Taguchi method for solving Japanese nonograms. The systematic reasoning ability of the Taguchi method is incorporated in the modified crossover operation to select the better genes to achieve crossover, and eventually enhance the GA. In this study, the condensed encoding can make sure that the chromosome is a feasible solution in all rows for Japanese nonograms. In the reconstruction process of a Japanese nonogram, the numbers in the left column are used as encoding conditions, and the numbers in the top row with the improved fitness function are employed to evaluate the reconstruction result. From the computational experiments, the proposed TBGA approach is effectively applied to solve nonograms and better than a GA does.