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.
In this paper, we focus on the application of ACO to the solution of Sudoku. ACO is a population-based search method inspired by the foraging behaviour of ants @cite_4 @cite_9 , and it has been successfully applied to a wide range of computational problems (see @cite_13 @cite_20 for overviews of both the algorithm and its applications).
@cite_13 @cite_9 @cite_4 @cite_20
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Recently, a number of algorithms inspired by the foraging behavior of ant colonies have been applied to the solution of difficult discrete optimization problems. We put these algorithms in a common framework by defining the Ant Colony Optimization (ACO) meta-heuristic. A couple of paradigmatic examples of applications of these novel meta-heuristic are given, as well as a brief overview of existing applications. Sudoku puzzle is a popular logic game since 2005. This puzzle is an NP-Complete problem which means that a very hard problem that is required deep and efficient algorithm to be solved. So it also draws attention of the scientists to develop methods and algorithm in order to solve Sudoku puzzles. In this study I tried to develop a hybrid algorithm which consist both analytical and heuristic steps to solve the Sudoku puzzle. The developed hybrid algorithm includes two analytical steps and one heuristically step. In the first analytical step, basic manual Sudoku solving methods are used to solve the puzzle. If puzzle is not solved completely than improvement analytical step is applied to solve the puzzle. If still puzzle is not solved completely then heuristic step applied to solve the puzzle completely. In the heuristic step ant colony optimization algorithm (ACO) will be applied to the puzzle. Experiments show that this hybrid ACO algorithm can solve the hardest Sudoku puzzles less than one second. As a result, this study shows that ACO is an effective method that can be applied to solve Sudoku puzzles. Ant colony optimization (ACO) is a metaheuristic approach to tackle hard combinatorial optimization problems. The basic component of ACO is a probabilistic solution construction mechanism. Due to its constructive nature, ACO can be regarded as a tree search method. Based on this observation, we hybridize the solution construction mechanism of ACO with beam search, which is a well-known tree search method. We call this approach Beam-ACO. The usefulness of Beam-ACO is demonstrated by its application to open shop scheduling (OSS). We experimentally show that Beam-ACO is a state-of-the-art method for OSS by comparing the obtained results to the best available methods on a wide range of benchmark instances. Ant Colony Optimization (ACO) is a new population oriented search metaphor that has been successfully applied to NP-hard combinatorial optimization problems. In this paper we discuss parallelization strategies for Ant Colony Optimization algorithms. We empirically test the most simple strategy, that of executing parallel independent runs of an algorithm. The empirical tests are performed applying MAX-MIN Ant System, one of the most efficient ACO algorithms, to the Traveling Salesman Problem and show that using parallel independent runs is very effective.