GRASP: Greedy Randomized Adaptive Search Procedures

Abstract

others. The method described in this chapter represents another example of such a technique. Metaheuristics are based on distinct paradigms and offer different mechanisms to escape from locally optimal solutions. They are among the most effective solution strategies for solving combinatorial optimization problems in practice and have been applied to a wide array of academic and real-world problems. The customization (or instantiation) of a metaheuristic to a given problem yields a heuristic for that problem.In this chapter, we consider the combinatorial optimization problem of minimizing f (S) over all solutions S ∈ X, which is defined by a finite set E = {e 1 ,..., e n } (called the ground set), by a set of feasible solutions X ⊆ 2 E and by an objective function f : 2 E → R. The ground set E, the objective function f , and the constraints defining the set of feasible solutions X are specific for each problem. We seek an optimal solution S * ∈ X such that f (S * ) ≤ f (S), ∀S ∈ X.GRASP, which stands for greedy randomized adaptive search procedures Resende 1989, 1995), is a multistart, or iterative, metaheuristic in which

A Differential Evolution Algorithm Developed for a Nurse Scheduling Problem

“…GRASP is a meta-heuristic that is characterised by multiple initialisations [27,42]. In this algorithm, a feasible solution is initially obtained, and then is improved by a local search technique.…”

“…DE is a mathematical global optimisation method, based on population generation, which tries to minimise the non-linear and non-differentiable continuous space functions as much as possible. In order to examine the performance of the proposed DE algorithm, the problem is also solved by another meta-heuristic -the greedy randomised adaptive search procedure (GRASP) -that was introduced by Feo & Resende [27] and Resende [42]. The results are subsequently compared.…”

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“…Later on, Martí et al [31] developed a modified Greedy Randomized Adaptive Search Procedure (GRASP) (See Resende and Ribeiro [34]) heuristic for a bi-objective path dissimilarity problem by making the trade-off between the two conflicting objectives: minimizing the average length of the paths while maximizing the dissimilarity among the paths.…”

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“…The solutions created by the Construction function are not guaranteed to be locally optimal [51]. A solution is locally optimal if there is no better solution in its neighborhood.…”