In the job shop scheduling problem (JSP), a finite set of jobs is processed on a finite set of machines. Each job is required to complete a set of operations in a fixed order. Each operation is processed on a specific machine for a fixed duration. A machine can process no more than one job at a time and once a job initiates processing on a given machine it must complete processing without interruption. A schedule is an assignment of operations to time slots on the machines. The objective of the JSP is to find a schedule that minimizes the maximum completion time, or makespan, of the jobs. In this paper, we describe a parallel greedy randomized adaptive search procedure (GRASP) with path-relinking for the JSP. A GRASP is a metaheuristic for combinatorial optimization. It usually consists of a construction procedure based on a greedy randomized algorithm and of a local search. Path-relinking is an intensification strategy that explores trajectories that connect high quality solutions. Independent and cooperative parallelization strategies are described and implemented. Computational experience on a large set of standard test problems indicates that the parallel GRASP with path-relinking finds goodquality approximate solutions of the job shop scheduling problem.

Given n customers and a set F of m potential facilities, the p-median problem consists in finding a subset of F with p facilities such that the cost of serving all customers is minimized.

Given an undirected graph with edge weights, the MAX-CUT problem consists in finding a partition of the nodes into two subsets, such that the sum of the weights of the edges having endpoints in different subsets is maximized.

. GRASP (greedy randomized adaptive search procedure) is a metaheuristic for combinatorial optimization. GRASP usually is implemented as a multistart procedure, where each iteration is made up of a construction phase, where a randomized greedy 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. This chapter gives an overview of GRASP. Besides describing the basic building blocks of a GRASP, the chapter covers enhancements to the basic procedure, including reactive GRASP, hybrid GRASP, and intensification strategies. 1. Introduction Consider a combinatorial optimization problem, where one is given a discrete set X of solutions and an objective function f(x) : x # X # to be minimized and seeks a solution x # # X such that f(x # ) # f(x), for all x # X . Problems of this type are sometimes easy to solve, i.e. they can be solved in polynomial time, but mor...

Abstract. Parallel implementationsof metaheuristicsappear quite naturally asan effective alternative to speed up the search for approximate solutions of combinatorial optimization problems. They not only allow solving larger problems or finding improved solutions with respect to their sequential counterparts, but they also lead to more robust algorithms. We review some trends in parallel computing and report recent results about linear speedups that can be obtained with parallel implementations using multiple independent processors. Parallel implementations of tabu search, GRASP, genetic algorithms, simulated annealing, and ant colonies are reviewed and discussed to illustrate the main strategies used in the parallelization of different metaheuristics and their hybrids. 1. Introduction. Although

A GRASP with path relinking for finding good-quality solutions of the weighted maximum satisfiability problem (MAX-SAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multistart metaheuristic, where, at each iteration, locally optimal solutions are constructed, each independent of the others. Previous experimental results indicate its effectiveness for solving weighted MAX-SAT instances. Path relinking is a procedure used to intensify the search around good-quality isolated solutions that have been produced by the GRASP heuristic. Experimental comparison of the pure GRASP (without path relinking) and the GRASP with path relinking illustrates the effectiveness of path relinking in decreasing the average time needed to find a good-quality solution for the weighted maximum satisfiability problem.

this paper we present a new search procedure that combines GRASP concepts and those of Path Relinking. Summarizing, original Path Relinking finds a path between two "good" solutions in order to discover new ones, potentially better than the older solutions. GRASP's basic mechanisms are the greedy randomized construction phase, where a feasible solution is built, and the local search procedure, where the neighborhood of the solution obtained is explored. Greedy randomized adaptive path relinking (GRAPR) constructs a GRASP to build di#erent paths in a Path Relinking phase

Network migration scheduling is the problem where inter-nodal traffic from an outdated telecommunications network is to be migrated to a new network. Nodes are migrated, one at each time period, from the old to the new network. All traffic originating or terminating at given node in the old network is moved to a specific node in the new network. Routing is predetermined on both networks and therefore arc capacities are known. Traffic between nodes in the same network is routed in that network. When a node is migrated, one or more temporary arcs may need to be set up since the node migrated may be adjacent to more than one still active node in the old network. A temporary arc remains active until both nodes connected by the arc are migrated to the new network. In one version of the problem, one seeks an ordering of the migration of the nodes that minimizes the maximum sum of capacities of the temporary arcs. In another version, the objective is to minimize the sum of the total capacities of the temporary arcs over each period in the planning horizon. In this paper, we propose a hybrid heuristic which combines GRASP with path-relinking to find cost-efficient solutions to both versions of the network migration problem.

A GRASP (Greedy Randomized Adaptive Search Procedure) is a metaheuristic for producing good-quality solutions of combinatorial optimization problems. It is usually implemented with a construction procedure based on a greedy randomized algorithm followed by local search. In this Chapter, we survey parallel implementations of GRASP. We describe simple strategies to implement independent parallel GRASP heuristics and more complex cooperative schemes using a pool of elite solutions to intensify the search process. Some applications of independent and cooperative parallelizations are presented in detail.

Abstract. The generalized quadratic assignment problem (GQAP) is a generalization of the NP-hard quadratic assignment problem (QAP) that allows multiple facilities to be assigned to a single location as long as the capacity of the location allows. In this paper, we propose several GRASP with pathrelinking heuristics for the GQAP using different construction, local search, and path-relinking procedures. Experimental results using time-to-target plots illustrate the relative effectiveness of these variants on instances found in the literature. 1.