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.

Many realistic planning problems (such as those in manufacturing) place a high premium on plan efficiency. However, classical planning theory does not offer much insight into ways of obtaining efficient plans. The objective of this paper is to present a model of planning for plan efficiency that has been drawn from a case study in the machining domain. Some of the important features of this domain are that problems are stated as sets of conjunctive goals, and operators that achieve those goals have a high degree of overlap. Operators can be said to overlap when they can share work. Because of this overlap, the cost of the operators is dependent on their order in the plan, (for example, it is less time consuming to

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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,