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 @cite_28 , Mantere presents a hybrid ACO genetic algorithm approach to Sudoku, which combines global (evolutionary) search with greedy local (ACO-based) search. Schiff @cite_5 and Sabuncu @cite_2 also present relatively recent work on applying ACO to Sudoku, but, in both cases, the performance of the algorithm is relatively poor.
@cite_28 @cite_5 @cite_2
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In this paper we introduce our new improved version of ant colony optimization genetic algorithm hybrid for Sudoku puzzle solving. Sudoku is combinatorial number puzzle that had become worldwide phenomenon in the last decade. It has also become popular mathematical test problem in order to test new optimization ideas and algorithms for combinatorial problems. In this paper we present our new ideas for populations sorting and elitism rules in order to improve our earlier evolutionary algorithm based Sudoku solvers. Experimental results show that the new ideas significantly improved the speed of Sudoku solving. 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. A recent and very promising approach for combinatorial optimization is to embed local search into the framework of evolutionary algorithms. In this paper, we present such hybrid algorithms for the graph coloring problem. These algorithms combine a new class of highly specialized crossover operators and a well-known tabu search algorithm. Experiments of such a hybrid algorithm are carried out on large DIMACS Challenge benchmark graphs. Results prove very competitive with and even better than those of state-of-the-art algorithms. Analysis of the behavior of the algorithm sheds light on ways to further improvement. Minimum dominating set, which is an NP-hard problem, finds many practical uses in diverse domains. A greedy algorithm to compute the minimum dominating set is proven to be the optimal approximate algorithm unless P=NP. Meta-heuristics, generally, find solutions better than simple greedy approximate algorithms as they explore the search space better without incurring the cost of an exponential algorithm. However, there are hardly any studies of application of meta-heuristic techniques for this problem. In some applications it is important to minimize the dominating set as much as possible to reduce cost and or time to perform other operations based on the dominating set. In this paper, we propose a hybrid genetic algorithm and an ant-colony optimization (ACO) algorithm enhanced with local search. We compare the performance of these two hybrid algorithms against the solutions obtained using the greedy heuristic and another hybrid genetic algorithm proposed in literature. We find that the ACO algorithm enhanced with a minimization heuristic performs better than all other algorithms in almost all instances.