One of a number of successful metaheuristics appearing in the late years of the last century is GRASP, a multi-start method designed to solve hard combinatorial optimization problems. In its basic version, each iteration consists of two phases: a constructive phase whose product is a good but not necessarily locally optimal solution, and a local search procedure, during which, neighborhoods of the solution are examined until a local optimum is attained. The iterations proceed, keeping the best found solution, until a stopping criterion is reached. In this chapter, the basic components of GRASP are reviewed, along with some parameter setting strategies like reactive GRASP. A discussion of the use of path relinking as a method to introduce memory features in the local search phase follows. The chapter concludes with a description of parallel GRASP, with extensive experimentation to compare independent and cooperative implementation.
In this paper the Path Dissimilarity Problem is considered. The problem has been previously studied in several contexts, the most popular motivated by the need of selecting routes for transportation of hazardous materials. The aim of this paper is to formally introduce the problem as a bi-objective optimization problem, in which a single solution consists of a set of p different paths, and two conflicting objectives arise, on one side the average length of the paths that must be kept low, and on the other side the dissimilarity among the paths in the set, that should be kept high. Previous methods are reviewed and adapted to our bi-objective problem, in this way we are able to compare the methods using the standard measures in multi-objective optimization. A new GRASP procedure is proposed and tested among the revised methods, and we show that it is able of creating better approximations of the efficient frontiers than existing methods.
In recent years the Just-in-Time (JIT) production philosophy as been adopted by many companies around the world. This has motivated the study of scheduling models that embrace the essential components of JIT systems. In this paper, we present a search heurustic for the weighted earliness penalty problem with deadlines in parallel identical machines. Our approach combines elements of the solution methods known as greedy randomized adaptive search procedure (GRASP) and tabu search. It also uses a branch-and-bound post-processor to optimize individually the sequence of the jobs assigned to each machine.
Abstract. The problem of determining optimal tolls established on a subset of arcs in a multicommodity capacitated transportation network is presented. The problem is formulated as a bilevel optimization problem where the upper level consists of an administrator who establishes tolls in some arcs of a network, while the lower level is represented by a group of users who travel along the shortest paths with respect to the travel cost. The objective is not only to increase the tolls, but also to maintain an optimal flow on the arcs of the network in order to maximize the leader's profit. If the leader sets very high toll values, the followers will be discouraged from using the tolled arcs, so the profit obtained from that decision is not going to be convenient for the leader. A methodology to solve this problem using optimization software at the lower level and the metaheuristic Scatter Search at the upper level is proposed.
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