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A genetic algorithm for the picture maze generation problem. (English) Zbl 1458.68144
Summary: A picture maze is a maze puzzle that reveals a hidden picture when the solution path is filled. The picture maze generation problem (PMGP) consists in generating a picture maze whose solution path draws the shape most similar to a given raster image. The PMGP can be formulated as the longest path problem (LPP) on grid graphs, and we propose a genetic algorithm (GA) for this problem. In our formulation, we optimize the start and exit positions simultaneously as well as the solution path. To construct an effective GA, we employ edge assembly crossover (EAX), which is known as a very effective crossover operator for the traveling salesman problem (TSP). However, because of the difference between the two problems, we adapt EAX to the PMGP in a novel manner. The proposed GA can generate satisfactory picture mazes in 17s for complicated raster images with sizes up to $$55 \times 105$$.
##### MSC:
 68R10 Graph theory (including graph drawing) in computer science 05C38 Paths and cycles 05C85 Graph algorithms (graph-theoretic aspects) 68W50 Evolutionary algorithms, genetic algorithms (computational aspects) 90C59 Approximation methods and heuristics in mathematical programming
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