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.

. Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment problem. We focus our attention on recent developments. 1. Introduction Given a set N = f1; 2; : : : ; ng and n \Theta n matrices F = (f ij ) and D = (d kl ), the quadratic assignment problem (QAP) can be stated as follows: min p2\Pi N n X i=1 n X j=1 f ij d p(i)p(j) + n X i=1 c ip(i) ; where \Pi N is the set of all permutations of N . One of the major applications of the QAP is in location theory where the matrix F = (f ij ) is the flow matrix, i.e. f ij is the flow of materials from facility i to facility j, and D = (d kl ) is the distance matrix, i.e. d kl represents the distance from location k to location l [62, 67, 137]. The cost of simultaneously assigning facility i to locat...

. A greedy randomized adaptive search procedure (Grasp) is a randomized heuristic that has been shown to quickly produce good quality solutions for a wide variety of combinatorial optimization problems. In this paper, we describe a Grasp for the satisfiability (SAT) problem. This algorithm can be also directly applied to both the weighted and unweighted versions of the maximum satisfiability (MAX-SAT) problem. We review basic concepts of Grasp: construction and local search algorithms. The implementation of Grasp for the SAT problem is described in detail. Computational experience on a large set of test problems is presented. Key words. Combinatorial optimization, logic, satisfiability, artificial intelligence, local search, Grasp, computer implementation AMS(MOS) subject classifications. 90B80, 90C20, 90C35, 90C27, 65H20, 65K05 1. Introduction. Let x be a Boolean variable, i.e. a variable that takes on only the values true or false, and let a literal be a variable x or its negation...

. 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...

Scheduling is concerned with allocating limited resources to tasks to optimize certain objective functions. Due to the popularity of the Total Quality Management concept, ontime delivery of jobs has become one of the crucial factors for customer satisfaction. Scheduling plays an important role in achieving this goal. Recent developments in scheduling theory have focused on extending the models to include more practical constraints. Furthermore, due to the complexity studies conducted during the last two decades, it is now widely understood that most practical problems are NP-hard. This is one of the reasons why local search methods have been studied so extensively during the last decade. In this paper, we review briefly some of the recent extensions of scheduling theory, the recent developments in local search techniques and the new developments of scheduling in practice. Particularly, we survey two recent extensions of theory: scheduling with a 1-job-on-r-machine pattern and machine scheduling with availability constraints. We also review several local search techniques, including simulated annealing, tabu search, genetic algorithms and constraint guided heuristic search. Finally, we study the robotic cell scheduling problem, the automated guided vehicles scheduling problem, and the hoist scheduling problem.

Abstract. In the job shop scheduling problem (JSP), a finite set of jobs is processed on a finite set of machines. Each job is characterized by a fixed order of operations, each of which is to be processed on a specific machine for a specified duration. Each machine can process at most one job at a time and once a job initiates processing on a given machine it must complete processing uninterrupted. 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 greedy randomized adaptive search procedure (GRASP) for the JSP. A GRASP is a metaheuristic for combinatorial optimization. Although GRASP is a general procedure, its basic concepts are customized for the problem being solved. We describe in detail our implementation of GRASP for job shop scheduling. Further, we incorporate to the conventional GRASP two new concepts: an intensification strategy and POP (Proximate Optimality Principle) in the construction phase. These two concepts were first proposed by Fleurent & Glover (1999) in the context of the quadratic assignment problem. Computational experience on a large set of standard test problems indicates that GRASP is a competitive algorithm for finding approximate solutions of the job shop scheduling problem. 1.

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This paper presents an enhanced heuristic for minimizing the makespan of the flow shop scheduling problem with sequence-dependent setup times. The procedure transforms an instance of the problem into an instance of the traveling salesman problem by introducing a cost function that penalizes for both large setup times and bad fitness of schedule. This hybrid cost function is an improvement over earlier approaches that penalized for setup times only, ignoring the flow shop aspect of the problem. To establish good parameter values, each component of the heuristic was evaluated computationally over a wide range of problem instances. In the testing stage, an experimental comparison with a greedy randomized adaptive search procedure revealed the conditions and data attributes where the proposed procedure works best.

In this work we present two heuristics for the owshop machine scheduling problem with setup costs and makespan minimization criteria. One of the proposed procedures is an extension of an algorithm that has been very successful for the general owshop scheduling problem. The other is a greedy randomized adaptive search procedure (GRASP) which is a technique that has successfully addressed many kinds of combinatorial optimization problems. Both procedures are compared to a previously developed algorithm. In addition, a postprocessing phase for improving the quality of the solutions is developed and adapted to each of the heuristics. All procedures are compared for two di erent classes of randomly generated instances. It is observed that for the case where both processing times and setup times are identically distributed, the existing heuristic proves superior to the proposed approaches; for the case where setup times are an order of magnitude smaller than the processing times, the proposed procedures outperform the existing heuristic. 1

The point-feature cartographic label placement problem (PFCLP) is an NP-hard problem which appears during the production of maps. The labels must be placed in predefined places avoiding overlaps and considering cartographic preferences. Due to its high complexity several heuristics have been presented searching for approximated solutions. This paper proposes a greedy randomized adaptive search procedure (GRASP) for the PFCLP that is based on its associated conflict graph. The computational results show that this metaheuristic is a good strategy for PFCLP, generating better solutions than all those reported in the literature in reasonable computational times.