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29
A greedy randomized adaptive search procedure for the 2partition problem
 Operations Research
, 1994
"... 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 ..."
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Cited by 526 (79 self)
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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.
A Grasp For Satisfiability
 CLIQUES, COLORING, AND SATISFIABILITY: THE SECOND DIMACS IMPLEMENTATION CHALLENGE, VOLUME 26 OF DIMACS SERIES ON DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1996
"... 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 ..."
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Cited by 31 (6 self)
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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 (MAXSAT) 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.
A GRASP for aircraft routing in response to groundings and delays
 Journal of Combinatorial Optimization
, 1997
"... Abstract. This paper presents a greedy randomized adaptive search procedure (GRASP) to reconstruct aircraft routings in response to groundings and delays experienced over the course of the day. Whenever the schedule is disrupted, the immediate objective of the airlines is to minimize the cost of rea ..."
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Cited by 24 (6 self)
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Abstract. This paper presents a greedy randomized adaptive search procedure (GRASP) to reconstruct aircraft routings in response to groundings and delays experienced over the course of the day. Whenever the schedule is disrupted, the immediate objective of the airlines is to minimize the cost of reassigning aircraft to flights taking into account available resources and other system constraints. Associated costs are measured by flight delays and cancellations. In the procedure, the neighbors of an incumbent solution are generated and evaluated, and the most desirable are placed on a restricted candidate list. One is selected randomly and becomes the incumbent. The heuristic is polynomial with respect to the number of flights and aircraft. This is reflected in our computational experience with data provided by Continental Airlines. Empirical results demonstrate the ability of the GRASP to quickly explore a wide range of scenarios and, in most cases, to produce an optimal or nearoptimal solution.
A greedy randomized adaptive search procedure for job shop scheduling
 IEEE Trans. on Power Systems
, 2001
"... 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 ..."
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Cited by 21 (3 self)
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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.
A reactive GRASP and path relinking for a combined productiondistribution problem.Computers and Operations Research,34
, 2007
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Heuristics for the flow line problem with setup costs
 European Journal of Operational Research
, 1998
"... 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 randomiz ..."
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Cited by 6 (0 self)
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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 Locomotive Routing Problem
 TRANSPORTATION SCIENCE
, 2008
"... Given a schedule of trains, the locomotive planning (or scheduling) problem (LPP) is to determine the minimum cost assignment of locomotive types to trains that satisfies a number of business and operational constraints. Once this is done, the railroad has to determine the sequence of trains to whic ..."
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Cited by 2 (0 self)
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Given a schedule of trains, the locomotive planning (or scheduling) problem (LPP) is to determine the minimum cost assignment of locomotive types to trains that satisfies a number of business and operational constraints. Once this is done, the railroad has to determine the sequence of trains to which each locomotive is assigned by unit number so that it can be fueled and serviced as necessary. We refer to this problem as the locomotive routing problem (LRP). The LRP is a very large scale combinatorial optimization problem, and the general version that we consider has previously been unstudied and unsolved in the research literature. In this paper, we develop robust optimization methods to solve the LRP. There are two major constraints that need to be satisfied by each locomotive route: (1) locomotive fueling constraints, which require that every unit visits a fueling station at least once for every F miles of travel, and (2) locomotive servicing constraints, which require that every unit visits a service station at least once for every S miles of travel. The output of the LPP is not directly implementable because the LPP does not consider these fueling and servicing constraints. The LRP considers these constraints and its output is therefore implementable. We model the LRP by considering alternative fueling and servicingfriendly train paths (or strings) between servicing stations on the network. We formulate the LRP as an
An annotated bibliography of GRASP
 AT&T Labs Research, Florham Park, NJ 07932
, 2004
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Solving the robust and integrated aircraft routing and crew pairing problem in practice  a discussion of heuristic and optimization methods
, 2008
"... We formulate an integrated aircraft routing and crew pairing model that yields solutions for both problems that incur small costs and are robust to typical stochastic variability in airline operations, i.e. effects of delays occurring in operations are minimised. We propose two new solution methods ..."
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Cited by 1 (0 self)
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We formulate an integrated aircraft routing and crew pairing model that yields solutions for both problems that incur small costs and are robust to typical stochastic variability in airline operations, i.e. effects of delays occurring in operations are minimised. We propose two new solution methods to solve the integrated model. The first approach is an optimisation based heuristic that is capable of generating good quality solutions quickly, the second approach utilises DantzigWolfe decomposition to solve the integrated model to optimality. Using data from domestic Air New Zealand schedules, we evaluate the benefits of solving the integrated model on real world problem instances. Our solutions satisfy all rules imposed on aircraft routings and crew pairings and are ready to be implemented in practice. We obtain solutions that dramatically improve costs and robustness of solutions obtained by traditional methods. We also compare our approaches with an existing Benders decomposition approach. 1