The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

Stochastic local search algorithms based on the WalkSAT architecture are among the best known methods for solving hard and large instances of the propositional satisfiability problem (SAT). The performance and behaviour of these algorithms critically depends on the setting of the noise parameter, which controls the greediness of the search process. The optimal setting for the noise parameter varies considerably between different types and sizes of problem instances; consequently, considerable manual tuning is typically required to obtain peak performance. In this paper, we characterise the impact of the noise setting on the behaviour of WalkSAT and introduce a simple adaptive noise mechanism for WalkSAT that does not require manual adjustment for different problem instances. We present experimental results indicating that by using this selftuning noise mechanism, various WalkSAT variants (including WalkSAT/SKC and Novelty ) achieve performance levels close to their peak performance for instance-specific, manually tuned noise settings.

The determination of appropriate values for free algorithm parameters is a challenging and tedious task in the design of effective algorithms for hard problems. Such parameters include categorical choices (e.g., neighborhood structure in local search or variable/value ordering heuristics in tree search), as well as numerical parameters (e.g., noise or restart timing). In practice, tuning of these parameters is largely carried out manually by applying rules of thumb and crude heuristics, while more principled approaches are only rarely used. In this paper, we present a local search approach for algorithm configuration and prove its convergence to the globally optimal parameter configuration. Our approach is very versatile: it can, e.g., be used for minimising run-time in decision problems or for maximising solution quality in optimisation problems. It further applies to arbitrary algorithms, including heuristic tree search and local search algorithms, with no limitation on the number of parameters. Experiments in four algorithm configuration scenarios demonstrate that our automatically determined parameter settings always outperform the algorithm defaults, sometimes by several orders of magnitude. Our approach also shows better performance and greater flexibility than the recent CALIBRA system. Our ParamILS code, along with instructions on how to use it for tuning your own algorithms, is available on-line at

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In this paper we describe a new incomplete approach for solving constraint satisfaction problems (CSPs) based on the ant colony optimization (ACO) metaheuristic. The idea is to use artificial ants to keep track of promising areas of the search space by laying trails of pheromone. This pheromone information is used to guide the search, as a heuristic for choosing values to be assigned to variables.

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MAX-SAT, the optimisation variant of the satisfiability problem in propositional logic, is an important and widely studied combinatorial optimisation problem with applications in AI and other areas of computing science. In this paper, we present a new stochastic local search (SLS) algorithm for MAXSAT that combines Iterated Local Search and Tabu Search, two well-known SLS methods that have been successfully applied to many other combinatorial optimisation problems. The performance of our new algorithm exceeds that of current state-of-the-art MAX-SAT algorithms on various widely studied classes of unweighted and weighted MAX-SAT instances, particularly for Random-3-SAT instances with high variance clause weight distributions. We also report promising results for various classes of structured MAX-SAT instances.

Over the last decade many metaheuristics have been applied to the flowshop scheduling problem, ranging from Simulated Annealing or Tabu Search to complex hybrid techniques. Some of these methods provide excellent effectiveness and efficiency at the expense of being utterly complicated. In fact, several published methods require substantial implemen-tation efforts, exploit problem specific speed-up techniques that cannot be applied to slight variations of the original problem, and often re-implementations of these methods by other researchers produce results that are quite different from the original ones. In this work we present a new iterated greedy algorithm that applies two phases iteratively, named destruc-tion, were some jobs are eliminated from the incumbent solution, and construction, where the eliminated jobs are reinserted into the sequence using the well known NEH construction £Corresponding author 1 heuristic. Optionally, a local search can be applied after the construction phase. Our iterated greedy algorithm is both very simple to implement and, as shown by experimental results, highly effective when compared to state-of-the-art methods.

Graph coloring is a well known problem from graph theory that, when solving it with local search algorithms, is typically treated as a series of constraint satisfaction problems: for a given number of colors k, one has to find a feasible coloring; once such a coloring is found, the number of colors is decreased and the local search starts again. Here we explore the application of Iterated Local Search to the graph coloring problem. Iterated Local Search is a simple and powerful metaheuristic that has shown very good results for a variety of optimization problems. In our research we investigate different perturbation schemes and present computational results on some hard instances from the DIMACS benchmark suite.

lpaquete,tom¡ Abstract. This article proposes the Two-Phase Local Search for finding a good approximate set of non-dominated solutions. The two phases of this procedure are to (i) generate an initial solution by optimizing only one single objective, and then (ii) to start from this solution a search for non-dominated solutions exploiting a sequence of different formulations of the problem based on aggregations of the objectives. This second phase is a single chain, using the local optimum obtained in the previous formulation as a starting solution to solve the next formulation. Based on this basic idea, we propose some further improvements and report computational results on several instances of the biobjective TSP that show competitive results with state-of-the-art algorithms for this problem. 1