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...set of solutions examined here are taken from the union of a large set of solutions returned by many runs of several high-performing stochastic local search algorithms for these problems described in =-=[11]-=-.2 Luís Paquete and Thomas Stützle 2 Clusters of Non-dominated Solutions For this analysis, we extend the notion of efficient graph given in [5] by introducing a distance δ that corresponds to the mi...

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...se, in subsection 4.1, a Stochastic Local Search algorithm CoStar to solve it. This algorithm searches for a near optimal solution given a local knowledge provided by the definition of a neighborhood =-=[25]-=-. We demonstrate, in subsection 4.2, that CoStar outputs a Pareto local optimum solution of the problem. In subsection 4.3, we propose a way to evaluate a neighbor solution incrementally. Finally subs...

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... MOSA [11] as the best performing algorithm. 2.3 Two-Phase Local Search and Pareto Local Search In this paper, we study SLS algorithms that represent two main classes of multiobjective SLS algorithms =-=[12]-=-: algorithms that follow a component-wise acceptance criterion (CWAC), and those that follow a scalarized acceptance criterion (SAC). As two paradigmatic examples of each of these classes, we use two-...

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...oblems (linear, nonlinear, combinatorial) [11], [9], [10], [8]. In particular, there is a huge effort in developing efficient meta-heuristics such as evolutionary algorithms [2], [3] and local search =-=[6]-=- to handle complex engineering problems. Recently we proposed an alternative methodology which approximates the Pareto front of a multi-criteria optimization problem using queries to a constraint solv...

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...euristics for 7 ha l-0 05 22 62 2,sv er sio ns1s- 4sO cts2 01 0 solving real-world applications [26, 27]. Several multi-objective neighborhood search methods have been proposed in the literature, see =-=[10, 28]-=- for a survey. Most of them are based on a set of aggregations of the objective functions. Dominance-based local search algorithms are more rare. However, an Indicator-Based Multi-Objective Local Sear...

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...applied to hard combinatorial optimization problems such as the traveling salesman, scheduling or assignment problems. Many state-of-the-art local search algorithms have their multi-objective version =-=[PS06]-=-. For instance, there exists multi-objective extensions of simulated annealing [CJ98], [BSMD08] and tabu search [GMF97]. A typical way of treating several objectives in that context is to optimize a p...

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...n the literature are scalar approaches. Among these methods one can find the aggregation methods, the weighted metrics, the -constraint methods . . . A review of these methods is given in [9]. The second class consists in defining the acceptance of the LS according to a dominance relationship such as the Pareto dominance. The idea of Pareto approaches is to maintain an archive of non-dominated solutions, to explore the neighborhood of the solutions contained in the archive and to update the archive with the visited solutions. A complete description of the different algorithms can be found in [10]. 2.2 Parallel Models of Local Search Algorithms For non-trivial problems, executing the iterative process of a MLS on large neighborhoods requires a large amount of computational resources. In general, evaluating a fitness function for each solution is frequently the most costly operation of the MLS. Consequently, a variety of algorithmic issues are being studied to design efficient MLS heuristics. Parallelism arises naturally when dealing with a neighborhood, since each of the solutions belonging to it is an independent unit. Parallel design and implementation of metaheuristics have been stu...

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...olutions, to explore the neighborhood of the solutions contained in the archiveand to update the archive with the visited solutions. A complete description of the different algorithms can be found in =-=[10]-=-. 2.2 Parallel Models of Local Search Algorithms Fornon-trivialproblems,executingthe iterativeprocessofaMLSonlargeneighborhoods requires a large amount of computational resources. In general, evaluati...