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The Sudoku problem is a well-known logic-based puzzle of combinatorial number-placement. It consists in filling a n(2) × n(2) grid, composed of n columns, n rows, and n subgrids, each one containing distinct integers from 1 to n(2). Such a puzzle belongs to the NP-complete collection of problems, to which there exist diverse exact and approximate methods able to solve it. In this paper, we propose a new hybrid algorithm that smartly combines a classic tabu search procedure with the alldifferent global constraint from the constraint programming world. The alldifferent constraint is known to be efficient for domain filtering in the presence of constraints that must be pairwise different, which are exactly the kind of constraints that Sudokus own. This ability clearly alleviates the work of the tabu search, resulting in a faster and more robust approach for solving Sudokus. We illustrate interesting experimental results where our proposed algorithm outperforms the best results previously reported by hybrids and approximate methods.

The Sudoku is a famous logic-placement game, originally popularized in Japan and today widely employed as pastime and as testbed for search algorithms. The classic Sudoku consists in filling a 9 × 9 grid, divided into nine 3 × 3 regions, so that each column, row, and region contains different digits from 1 to 9. This game is known to be NP-complete, with existing various complete and incomplete search algorithms able to solve different instances of it. In this paper, we present a new cuckoo search algorithm for solving Sudoku puzzles combining prefiltering phases and geometric operations. The geometric operators allow one to correctly move toward promising regions of the combinatorial space, while the prefiltering phases are able to previously delete from domains the values that do not conduct to any feasible solution. This integration leads to a more efficient domain filtering and as a consequence to a faster solving process. We illustrate encouraging experimental results where our approach noticeably competes with the best approximate methods reported in the literature.

Metaheuristics are multi-purpose problem solvers devoted to particularly tackle large instances of complex optimization problems. However, in spite of the relevance of metaheuristics in the optimization world, their proper design and implementation to reach optimal solutions is not a simple task. Metaheuristics require an initial parameter configuration, which is dramatically relevant for the efficient exploration and exploitation of the search space, and therefore to the effective finding of high-quality solutions. In this paper, the authors propose a variation of the water cycle inspired metaheuristic capable of automatically adjusting its parameter by using the autonomous search paradigm. The goal of our proposal is to explore and to exploit promising regions of the search space to rapidly converge to optimal solutions. To validate the proposal, we tested 160 instances of the manufacturing cell design problem, which is a relevant problem for the industry, whose objective is to minimize the number of movements and exchanges of parts between organizational elements called cells. As a result of the experimental analysis, the authors checked that the proposal performs similarly to the default approach, but without being specifically configured for solving the problem. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms have been widely used to solve large and complex optimisation problems. Cultural algorithms (CAs) are evolutionary algorithms that have been used to solve both single and, to a less extent, multiobjective optimisation problems. In order to solve these optimisation problems, CAs make use of different strategies such as normative knowledge, historical knowledge, circumstantial knowledge, and among others. In this paper we present a comparison among CAs that make use of different evolutionary strategies; the first one implements a historical knowledge, the second one considers a circumstantial knowledge, and the third one implements a normative knowledge. These CAs are applied on a biobjective uncapacitated facility location problem (BOUFLP), the biobjective version of the well-known uncapacitated facility location problem. To the best of our knowledge, only few articles have applied evolutionary multiobjective algorithms on the BOUFLP and none of those has focused on the impact of the evolutionary strategy on the algorithm performance. Our biobjective cultural algorithm, called BOCA, obtains important improvements when compared to other well-known evolutionary biobjective optimisation algorithms such as PAES and NSGA-II. The conflicting objective functions considered in this study are cost minimisation and coverage maximisation. Solutions obtained by each algorithm are compared using a hypervolume S metric. [ABSTRACT FROM AUTHOR]

The Sudoku is a famous logic-placement game, originally popularized in Japan and today widely employed as pastime and as testbed for search algorithms.The classic Sudoku consists in filling a 9 × 9 grid, divided into nine 3 × 3 regions, so that each column, row, and region contains different digits from 1 to 9. This game is known to be NP-complete, with existing various complete and incomplete search algorithms able to solve different instances of it. In this paper, we present a new cuckoo search algorithmfor solving Sudoku puzzles combining prefiltering phases and geometric operations. The geometric operators allow one to correctly move toward promising regions of the combinatorial space, while the prefiltering phases are able to previously delete from domains the values that do not conduct to any feasible solution. This integration leads to a more efficient domain filtering and as a consequence to a faster solving process. We illustrate encouraging experimental results where our approach noticeably competes with the best approximate methods reported in the literature. [ABSTRACT FROM AUTHOR]

The set covering problem is a formal model for many practical optimization problems. In the set covering problem the goal is to choose a subset of the columns of minimal cost that covers every row. Here, we present a novel application of the artificial bee colony algorithm to solve the non-unicost set covering problem. The artificial bee colony algorithm is a recent swarm metaheuristic technique based on the intelligent foraging behavior of honey bees. Experimental results show that our artificial bee colony algorithm is competitive in terms of solution quality with other recent metaheuristic approaches for the set covering problem. [ABSTRACT FROM AUTHOR]

The balanced academic curriculum problem consists in the assignation of courses to academic periods satisfying all the load limits and prerequisite constraints. In this paper, we present the design of a solution to the balanced academic curriculum problem based on the ACO metaheuristic, in particular via the Best-Worst Ant System. We provide an experimental evaluation which illustrates the effectiveness of the proposed approach on a set of classic benchmarks as well as on real instances. [ABSTRACT FROM AUTHOR]

Subset problems (set partitioning, packing, and covering) are formal models for many practical optimization problems. A set partitioning problem determines how the items in one set (S) can be partitioned into smaller subsets. All items in S must be contained in one and only one partition. Related problems are set packing (all itemsmust be contained in zero or one partitions) and set covering (all itemsmust be contained in at least one partition).Here, we present a hybrid solver based on ant colony optimization (ACO) combined with arc consistency for solving this kind of problems. ACO is a swarm intelligence metaheuristic inspired on ants behavior when they search for food. It allows to solve complex combinatorial problems for which traditional mathematical techniques may fail. By other side, in constraint programming, the solving process of Constraint Satisfaction Problems can dramatically reduce the search space by means of arc consistency enforcing constraint consistencies either prior to or during search. Our hybrid approach was tested with set covering and set partitioning dataset benchmarks. It was observed that the performance of ACO had been improved embedding this filtering technique in its constructive phase. [ABSTRACT FROM AUTHOR]

Metaheuristics are solution methods which combine local improvement procedures and higher level strategies for solving combinatorial and nonlinear optimization problems. In general, metaheuristics require an important amount of effort focused on parameter setting to improve its performance. In this work a 2-level metaheuristic approach is proposed so that Scatter Search and Ant Colony Optimization act as "low level" metaheuristics, whose parameters are set by a "higher level" Genetic Algorithm during execution, seeking to improve the performance and to reduce the maintenance. The Set Covering Problem is taken as reference since is one of the most important optimization problems, serving as basis for facility location problems, airline crew scheduling, nurse scheduling, and resource allocation [ABSTRACT FROM AUTHOR]

The Software Project Scheduling Problem is a specific Project Scheduling Problem present in many industrial and academic areas. This problem consists in making the appropriate worker-task assignment in a software project so the cost and duration of the project are minimized. We present the design of a Max–Min Ant System algorithm using the Hyper-Cube framework to solve it. This framework improves the performance of the algorithm. We illustrate experimental results and compare with other techniques demonstrating the feasibility and robustness of the approach, while reaching competitive solutions. [ABSTRACT FROM AUTHOR]

Highlights: [•] We propose a new hybrid AC3-tabu search algorithm for Sudoku problems. [•] We perform experiments considering easy, medium, and hard Sudokus. [•] The approach generally outperforms the best results reached by incomplete search. [ABSTRACT FROM AUTHOR]

Abstract: A Constraint Satisfaction Problem is defined by a set of variables and a set of constraints, each variable has a nonempty domain of possible values. Each constraint involves some subset of the variables and specifies the allowable combinations of values for that subset. A solution of the problem is defined by an assignment of values to some or all of the variables that does not violate any constraints. To solve an instance, a search tree is created and each node in the tree represents a variable of the instance. The order in which the variables are selected for instantiation changes the form of the search tree and affects the cost of finding a solution. In this paper we explore the use of a Choice Function to dynamically select from a set of variable ordering heuristics the one that best matches the current problem state in order to show an acceptable performance over a wide range of instances. The Choice Function is defined as a weighted sum of process indicators expressing the recent improvement produced by the heuristic recently used. The weights are determined by a Particle Swarm Optimization algorithm in a multilevel approach. We report results where our combination of strategies outperforms the use of individual strategies. [Copyright &y& Elsevier]

Abstract: Cell formation consists in organizing a plant as a set of cells, each of them containing machines that process similar types or families of parts. The idea is to minimize the part flow among cells in order to reduce costs and increase productivity. The literature presents different approaches devoted to solve this problem, which are mainly based on mathematical programming and on evolutionary computing. Mathematical programming can guarantee a global optimal solution, however at a higher computational cost than an evolutionary algorithm, which can assure a good enough optimum in a fixed amount of time. In this paper, we model and solve this problem by using state-of-the-art constraint programming (CP) techniques and Boolean satisfiability (SAT) technology. We present different experimental results that demonstrate the efficiency of the proposed optimization models. Indeed, CP and SAT implementations are able to reach the global optima in all tested instances and in competitive runtime. [Copyright &y& Elsevier]