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Multiobjective optimization, combinatorial optimization, heuristics, metaheuristics, approximation, 90C29, 90C27, 90C59,

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International audienceIn this paper, we present two versions of an algorithm for the computation of all nondominated extreme points in the outcome set of a multiobjective integer programme. We define adjacency of these points based on weight space decomposition. Thus, our algorithms generalise the well-known dichotomic scheme to compute the set of nondominated extreme points in the outcome set of a biobjective programme. Both algorithms are illustrated with and numerically tested on instances of the assignment and knapsack problems with three objectives

International audienceIn this article, we develop a heuristic two-phase solution procedure for the dial-a-ride problem with two objectives. Besides the minimum cost objective a client centered objective has been defined. Phase one consists of an iterated variable neighborhood search-based heuristic, generating approximate weighted sum solutions; phase two is a path relinking module, computing additional efficient solutions. Results for two sets of benchmark instances are reported. For the smaller instances, exact efficient sets are generated by means of the e-constraint method. Comparison shows that the proposed two-phase method is able to generate high-quality approximations of the true Pareto frontier

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The principles of the Greedy Randomized Adaptative Search Procedure (GRASP) metaheuristic are instantiated for the set packing problem. We investigated several construction phases, and evaluated improvements based on advanced strategies. These improvements include a self-tuning procedure (using reactive GRASP), an intensification procedure (using path relinking) and a procedure involving the diversification of the selection (using a learning process). Two sets of various numerical instances were used to perform the computational experiments. The first set contains randomly generated instances, while the second includes instances relating to real problems in railway planning. No metaheuristic has previously been applied to this combinatorial problem. Consequently, we have discussed GRASPÕs performances both in relation to lower/upper bounds and to the results obtained with Cplex when such results are available. Our analysis, based on the average performances observed, shows the impact of the suggested strategies, and indicates the configuration that produces the best results.

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