GRASP: BASIC COMPONENTS AND ENHANCEMENTS PAOLA FESTA AND MAURICIO G.C. RESENDE Abstract. GRASP (Greedy Randomized Adaptive Search Procedures) is a multistart metaheuristic for producing good-quality solutions of combinato- rial 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 im- provement 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 in- tensification strategies. 1. Introduction Combinatorial optimization problems involve a finite number of alternatives: given a finite solution set X and a real-valued objective function f : X → R, one seeks a solution x ∗ ∈ X with f (x ∗ ) ≤ f (x), ∀ x ∈ X . Several combinatorial optimization problems can be solved in polynomial time, but many of them are com- putationally intractable since exact polynomial-time algorithms are unknown [59]. To find an optimal solution it is theoretically possible to enumerate all solutions and evaluate each with respect to the stated objective function f . Optimal seek- ing methods that do not explicitly require an examination of each alternative have been developed in the last decades, such as Branch & Bound, Cutting Planes, and Dynamic Programming. Nevertheless, most real-world problems found in industry and government are either computationally intractable by their nature, or suffi- ciently large so as to preclude the use of exact algorithms. In such cases, heuristic methods are usually employed to find good, but not necessarily guaranteed optimal solutions. The effectiveness of these methods depends upon their ability to adapt to a particular realization, avoid entrapment at local optima, and exploit the basic structure of the problem. Building on these notions, various heuristic search tech- niques have been developed that have demonstrably improved our ability to obtain good solutions to difficult combinatorial optimization problems. The most promis- ing of such techniques include simulated annealing [79], tabu search [61, 62, 65], genetic algorithms [70], variable neighborhood search [72], and GRASP (Greedy Randomized Adaptive Search Procedures) [46, 47]. Date : July 1, 2008. Key words and phrases. GRASP, hybrid heuristics, metaheuristics, path-relinking, variable neighborhood descent, tabu search, simulated annealing, iterated local search. AT&T Labs Research Technical Report. 1