Abstract. Today, a variety of heuristic approaches are available to the operations research practitioner. One methodology that has a strong intuitive appeal, a prominent empirical track record, and is trivial to efficiently implement on parallel processors is GRASP (Greedy Randomized Adaptive Search Procedures). GRASP is an iterative randomized sampling technique in which each iteration provides a solution to the problem at hand. The incumbent solution over all GRASP iterations is kept as the final result. There are two phases within each GRASP iteration: the first intelligently constructs an initial solution via an adaptive randomized greedy function; the second applies a local search procedure to the constructed solution in hope of finding an improvement. In this paper, we define the various components comprising a GRASP and demonstrate, step by step, how to develop such heuristics for combinatorial optimization problems. Intuitive justifications for the observed empirical behavior of the methodology are discussed. The paper concludes with a brief literature review of GRASP implementations and mentions two industrial applications.

. The bin packing problem consists in finding the minimum number of bins of given capacity which are necessary to pack a certain number of itens. In this work, we propose an improvement procedure for the bin packing problem, based on the progressive reduction of the number of bins used by a previously constructed solution. Since bin eliminations often lead to unfeasible solutions, a local search feasibility operator based on the differencing method for number partition is used. Encouraging computational results on benchmark instances are reported. Key words. Combinatorial optimization, bin packing, local search, differencing method 1. Introduction. Given a set of n items with weights w i ; i = 1; : : : ; n associated with each of them, the classical bin packing problem consists in finding the minimum number of bins of capacity b necessary to pack the items. Alternatively, the problem may also be seen as that of partitioning the items into a minimum number of subsets, such that the sum ...

We propose in this work a hybrid improvement procedure for the bin packing problem, based on the progressive increase of the number of bins used by a possibly feasible solution. This heuristic has several features: the incorporation of lower bounding

The Number Partitioning Problem (MNP) remains as one of the simplest-to-describe yet hardest-to-solve combinatorial optimization problems. In this work we use the MNP as a surrogate for several related real-world problems, in order to test new heuristics ideas. To be precise, we study the use of weight-matching techniques in order to devise smart memetic operators. Several options are considered and evaluated for that purpose. The positive computational results indicate that —despite the MNP may be not the best scenario for exploiting these ideas — the proposed operators can be really promising tools for dealing with more complex problems of the same family.

Abstract. GRASP (Greedy Randomized Adaptive Search Procedures) is a multistart metaheuristic for producing good-quality solutions of combinatorial optimization problems. Each GRASP iteration is usually made up of a construction phase, where a feasible solution is constructed, and a local search phase which starts at the constructed solution and applies iterative improvement until a locally optimal solution is found. While, in general, the construction phase of GRASP is a randomized greedy algorithm, other types of construction procedures have been proposed. Repeated applications of a construction procedure yields diverse starting solutions for the local search. This chapter gives an overview of GRASP describing its basic components and enhancements to the basic procedure, including reactive GRASP and intensification strategies. 1.

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A greedy randomized adaptive search procedure (GRASP) is an iterative multistart metaheuristic for difficult combinatorial optimization. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Since 1989, GRASP has been applied to a wide range of combinatorial optimization problems, ranging from scheduling and routing to drawing and turbine balancing. In this paper, we cover the literature where GRASP is applied to scheduling,