Solving nurikabe with ant colony optimization

Abstract

We present the first nature-inspired algorithm for the NP-complete Nurikabe pencil puzzle. Our method, based on Ant Colony Optimization (ACO), offers competitive performance with a direct logic-based solver, with improved run-time performance on smaller instances, but poorer performance on large instances. Importantly, our algorithm is "problem agnostic", and requires no heuristic information. This suggests the possibility of a generic ACO-based framework for the efficient solution of a wide range of similar logic puzzles and games. We further suggest that Nurikabe may provide a challenging benchmark for nature-inspired optimization.

J-POP: Japanese Puzzles as Optimization Problems

“…We adapt our description of Nurikabe from [35]. The name of the puzzle is taken from that of a spirit in Japanese folklore, which manifests itself as an invisible barrier that impedes travellers.…”

“…Early experimental work on solving Nurikabe used both Answer Set Programming and Constraint Programming [38], [39]. Another Nurikabe solution based on Constraint Programming [40] supplied the baseline for comparisons with a recent solution using Ant Colony Optimization [35].…”

“…A solution to the puzzle therefore has C hashi = 0. 4) Nurikabe: The Nurikabe simulator uses the construction process described in [35]. The grid is initally filled with black cells, apart from the numbered cells.…”

“…We include this addition since it was found to improve the performance of the algorithm in the case of Sudoku. The algorithm is the same as that described in [16] and [35] with the exception of the pheromone data structure, which is adapted to work with the simulator platform. We store pheromone values in an associative array which maps simulator choices onto floating point pheromone values.…”

“…The parameters for our ACS implementation are ρ 0 , the minimum pheromone value, which we set to 1/N , where N is the number of cells in the puzzle instance, q 0 , the probability of making a 'greedy' choice in the random proportional rule, ξ = 0.1 (the standard ACS value), the local pheromone update parameter, ρ, the pheromone evaporation parameter, ρ BVE , which controls best-value evaporation, and m, the number of ants. A full description can be found in [16] and [35].…”