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24
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 478 (75 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 twophase exact algorithm for MAXSAT and weighted MAXSAT problems
 Journal of Combinatorial Optimization
, 1997
"... We describe a two phase algorithm for MAXSAT and weighted MAX SAT problems. In the first phase, we use the GSAT heuristic to find a good solution to the problem. In the second phase, we use an enumeration procedure based on the DavisPutnamLoveland algorithm, to find a provably optimal soluti ..."
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Cited by 80 (4 self)
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We describe a two phase algorithm for MAXSAT and weighted MAX SAT problems. In the first phase, we use the GSAT heuristic to find a good solution to the problem. In the second phase, we use an enumeration procedure based on the DavisPutnamLoveland algorithm, to find a provably optimal solution. The first heuristic stage improves the performance of the algorithm by obtaining an upper bound on the minimum number of unsatisfied clauses that can be used in pruning branches of the search tree. We compare our algorithm with an integer programming branch and cut algorithm. Our implementation of the two phase algorithm is faster Research partially supported by ONR Grant number N000149410391. y Mathematics Department, New Mexico Tech, Socorro, NM 87801. z Department of Mathematical Sciences, Clemson University, Clemson, SC 29634 than the integer programming approach on many problems. However, the integer programming approach is more effective than the two phase algorithm o...
Local search algorithms for SAT: An empirical evaluation
 JOURNAL OF AUTOMATED REASONING
, 2000
"... Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large num ..."
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Cited by 62 (18 self)
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Local search algorithms are among the standard methods for solving hard combinatorial problems from various areas of Artificial Intelligence and Operations Research. For SAT, some of the most successful and powerful algorithms are based on stochastic local search and in the past 10 years a large number of such algorithms have been proposed and investigated. In this article, we focus on two particularly wellknown families of local search algorithms for SAT, the GSAT and WalkSAT architectures. We present a detailed comparative analysis of these algorithms' performance using a benchmark set which contains instances from randomised distributions as well as SATencoded problems from various domains. We also investigate the robustness of the observed performance characteristics as algorithmdependent and problemdependent parameters are changed. Our empirical analysis gives a very detailed picture of the algorithms' performance for various domains of SAT problems; it also reveals a fundamental weakness in some of the bestperforming algorithms and shows how this can be overcome.
A Discrete LagrangianBased GlobalSearch Method for Solving Satisfiability Problems
 Journal of Global Optimization
, 1998
"... Satisfiability is a class of NPcomplete problems that model a wide range of realworld applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a n ..."
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Cited by 60 (7 self)
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Satisfiability is a class of NPcomplete problems that model a wide range of realworld applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrangemultiplierbased globalsearch method for solving satisfiability problems. We derive new approaches for applying Lagrangian methods in discrete space, show that equilibrium is reached when a feasible assignment to the original problem is found, and present heuristic algorithms to look for equilibrium points. Instead of restarting from a new starting point when a search reaches a local trap, the Lagrange multipliers in our method provide a force to lead the search out of a local minimum and move it in the direction provided by the Lagrange multipliers. One of the major advantages of our method is that it has very few algorithmic parameters to be tuned by users, and the se...
The Exponentiated Subgradient Algorithm for Heuristic Boolean Programming
 IN PROC. IJCAI01
, 2001
"... Boolean linear programs (BLPs) are ubiquitous in AI. Satisfiability testing, planning with resource constraints, and winner determination in combinatorial auctions are all examples of this type of problem. Although increasingly wellinformed by work in OR, current AI research has tended to focu ..."
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Cited by 45 (2 self)
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Boolean linear programs (BLPs) are ubiquitous in AI. Satisfiability testing, planning with resource constraints, and winner determination in combinatorial auctions are all examples of this type of problem. Although increasingly wellinformed by work in OR, current AI research has tended to focus on specialized algorithms for each type of BLP task and has only loosely patterned new algorithms on effective methods from other tasks. In this paper we introduce a single generalpurpose local search procedure that can be simultaneously applied to the entire range of BLP problems, without modification. Although one might suspect that a generalpurpose algorithm might not perform as well as specialized algorithms, we find that this is not the case here. Our experiments show that our generic algorithm simultaneously achieves performance comparable with the state of the art in satisfiability search and winner determination in combinatorial auctions two very different BLP problems. Our algorithm is simple, and combines an old idea from OR with recent ideas from AI.
Probability distribution of solution time in GRASP: An experimental investigation
 J Heuristic
"... Abstract. A GRASP (greedy randomized adaptive search procedure) is a multistart metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a suboptimal target value in five GRASPs that have appeared in the literature and for which source code is availa ..."
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Cited by 42 (28 self)
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Abstract. A GRASP (greedy randomized adaptive search procedure) is a multistart metaheuristic for combinatorial optimization. We study the probability distributions of solution time to a suboptimal target value in five GRASPs that have appeared in the literature and for which source code is available. The distributions are estimated by running 12,000 independent runs of the heuristic. Standard methodology for graphical analysis is used to compare the empirical and theoretical distributions and estimate the parameters of the distributions. We conclude that the solution time to a suboptimal target value fits a twoparameter exponential distribution. Hence, it is possible to approximately achieve linear speedup by implementing GRASP in parallel. 1.
Approximate Solution Of Weighted MAXSAT Problems Using GRASP
, 1997
"... Computing the optimal solution to an instance of the weighted maximum satisfiability problem (MAXSAT) is difficult even when each clause contains at most two literals. In this paper, we describe a greedy randomized adaptive search procedure (GRASP) for computing approximate solutions of weighted MA ..."
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Cited by 33 (11 self)
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Computing the optimal solution to an instance of the weighted maximum satisfiability problem (MAXSAT) is difficult even when each clause contains at most two literals. In this paper, we describe a greedy randomized adaptive search procedure (GRASP) for computing approximate solutions of weighted MAXSAT problems. The heuristic is tested on a large set of test instances. Computational experience indicates the suitability of GRASP for this class of problems.
Greedy Randomized Adaptive Search Procedures
 Handbook of Applied Optimization
, 2001
"... . 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 wh ..."
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Cited by 27 (4 self)
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. 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...
Satisfiability Solvers
, 2008
"... The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and h ..."
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Cited by 24 (0 self)
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The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worstcase exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a generalpurpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern generation [138, 221], planning [129, 197], scheduling [103], and even challenging problems from algebra [238]. Annual SAT competitions have led to the development of dozens of clever implementations of such solvers [e.g. 13,