Solving Sudoku With Ant Colony Optimization

Abstract

In this paper we present a new Ant Colony Optimisation-based algorithm for Sudoku, which out-performs existing methods on large instances. Our method includes a novel anti-stagnation operator, which we call Best Value Evaporation.

Solving nurikabe with ant colony optimization

“…It is worth noting that the runtime for the Copris solver is always of order a second or longer, whereas ACS runs on the small instances often complete in milliseconds. These results contrast with the results on Sudoku [7], in which ACS significantly outperformed the best direct solvers on harder instances. This may suggest that Nurikabe offers a far more challenging benchmark for ACO algorithms than Sudoku.…”

“…In all runs we set a timeout of one minute of wall-clock time. For all ACS runs, we used the following parameters: m = 10, ρ = 0.2, ξ = 0.1, q 0 = 0.9, and f BVE = 0.001 (see [7] for the meanings of parameters). We ran the Copris solver [8] on each of the instances, using the same machine (and Java Virtual Machine) as for the ACS solver.…”

“…Once this island is completely filled, the ant moves to the next island, and the process repeats until all ants have completed their moves. The bestperforming ant is then selected (according to a cost function which counts how many constraints are broken), the global pheromone matrix is updated, and the "best value evaporation" [7] operator is applied.…”

J-POP: Japanese Puzzles as Optimization Problems

“…We adapt our description of Sudoku from [16]. The simplest variant of Sudoku uses a 9×9 grid of cells divided into nine 3×3 subgrids (Figure 1 (left)).…”

“…Notable approaches to solving Sudoku include formal logic [18], constraint programming [19], [20], evolutionary algorithms [21], particle swarm optimisation [22], [23], simulated annealing [24], tabu search [25], and entropy minimization [26]. Lloyd & Amos [16] describe an algorithm for Sudoku, based on Ant Colony Optimisation [27], and compare its performance to an iterated local search algorithm with constraint programming [28] and the deterministic algorithms of Knuth [29] and Norvig [30].…”