Results 1  10
of
69
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 ..."
Abstract

Cited by 478 (75 self)
 Add to MetaCart
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.
The Maximum Clique Problem
, 1999
"... Contents 1 Introduction 2 1.1 Notations and Definitions . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Problem Formulations 4 2.1 Integer Programming Formulations . . . . . . . . . . . . . . . . . . . 5 2.2 Continuous Formulations . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Computation ..."
Abstract

Cited by 140 (20 self)
 Add to MetaCart
Contents 1 Introduction 2 1.1 Notations and Definitions . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Problem Formulations 4 2.1 Integer Programming Formulations . . . . . . . . . . . . . . . . . . . 5 2.2 Continuous Formulations . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Computational Complexity 12 4 Bounds and Estimates 15 5 Exact Algorithms 19 5.1 Enumerative Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.2 Exact Algorithms for the Unweighted Case . . . . . . . . . . . . . . 21 5.3 Exact Algorithms for the Weighted Case . . . . . . . . . . . . . . . . 25 6 Heuristics 27 6.1 Sequential Greedy Heuristics . . . . . . . . . . . . . . . . . . . . . . 28 6.2 Local Search Heuristics . . . . . . . . . . . . . . . . . . . . . . . . . 29 6.3 Advanced Search Heuristics . . . . . . . . . . . . . . . . . . . . . . . 30 6.3.1 Simulated annealing . . . . . . . . . . . . . . . . . . . . . . . 30 6.3.2 Neural networks . . . . . . . . . . . . . . . . . . . . . . . .
Reactive Local Search for the Maximum Clique Problem
 Algorithmica
"... A new Reactive Local Search (RLS ) algorithm is proposed for the solution of the MaximumClique problem. RLS is based on local search complemented by a feedback (historysensitive) scheme to determine the amount of diversification. The reaction acts on the single parameter that decides the temporary ..."
Abstract

Cited by 77 (14 self)
 Add to MetaCart
A new Reactive Local Search (RLS ) algorithm is proposed for the solution of the MaximumClique problem. RLS is based on local search complemented by a feedback (historysensitive) scheme to determine the amount of diversification. The reaction acts on the single parameter that decides the temporary prohibition of selected moves in the neighborhood, in a manner inspired by Tabu Search. The performance obtained in computational tests appears to be significantly better with respect to all algorithms tested at the the second DIMACS implementation challenge. The worstcase complexity per iteration of the algorithm is O(max{n, m}) where n and m are the number of nodes and edges of the graph. In practice, when a vertex is moved, the number of operations tends to be proportional to its number of missing edges and therefore the iterations are particularly fast in dense graphs.
A Column Generation Approach For Graph Coloring
 INFORMS Journal on Computing
, 1995
"... We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph). We use a column generation method for implicit optimization of the linear program at each node of the branchandbound tree. This approac ..."
Abstract

Cited by 73 (2 self)
 Add to MetaCart
We present a method for solving the independent set formulation of the graph coloring problem (where there is one variable for each independent set in the graph). We use a column generation method for implicit optimization of the linear program at each node of the branchandbound tree. This approach, while requiring the solution of a difficult subproblem as well as needing sophisticated branching rules, solves small to moderate size problems quickly. We have also implemented an exact graph coloring algorithm based on DSATUR for comparison. Implementation details and computational experience are presented. 1 INTRODUCTION The graph coloring problem is one of the most useful models in graph theory. This problem has been used to solve problems in school timetabling [10], computer register allocation [7, 8], electronic bandwidth allocation [11], and many other areas. These applications suggest that effective algorithms for solving the graph coloring problem would be of great importance. D...
A Fast Algorithm for the Maximum Clique Problem
 DISCRETE APPL. MATH
"... Given a graph, in the maximum clique problem one wants to find ..."
Abstract

Cited by 70 (2 self)
 Add to MetaCart
Given a graph, in the maximum clique problem one wants to find
ThreeDimensional Orthogonal Graph Drawing
, 2000
"... vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . ..."
Abstract

Cited by 27 (10 self)
 Add to MetaCart
vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv I Orthogonal Graph Drawing 1 1
Relaxation Labeling Networks for the Maximum Clique Problem
 J. Artif. Neural Networks
, 1995
"... this paper, it is shown how to take advantage of the properties of these models to approximately solve the maximum clique problem, a wellknown intractable optimization problem which has practical applications in various fields. The approach is based on a result by Motzkin and Straus which naturally ..."
Abstract

Cited by 27 (16 self)
 Add to MetaCart
this paper, it is shown how to take advantage of the properties of these models to approximately solve the maximum clique problem, a wellknown intractable optimization problem which has practical applications in various fields. The approach is based on a result by Motzkin and Straus which naturally leads to formulate the problem in a manner that is readily mapped onto a relaxation labeling network. Extensive simulations have demonstrated the validity of the proposed model, both in terms of quality of solutions and speed. Maximum clique problem, relaxation labeling processes, neural networks, optimization. 1 INTRODUCTION
Experiments with Parallel Graph Coloring Heuristics
 In (Johnson & Trick
, 1994
"... We report on experiments with a new hybrid graph coloring algorithm, which combines a parallel version of Morgenstern's SImpasse algorithm [20], with exhaustive search. We contribute new test data arising in five different application domains, including register allocation and class scheduling. We ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
We report on experiments with a new hybrid graph coloring algorithm, which combines a parallel version of Morgenstern's SImpasse algorithm [20], with exhaustive search. We contribute new test data arising in five different application domains, including register allocation and class scheduling. We test our algorithms both on this test data and on several types of randomly generated graphs. We compare our parallel implementation, which is done on the CM5, with two simple heuristics, the Saturation algorithm of Br'elaz [4] and the Recursive Largest First (RLF) algorithm of Leighton [18]. We also compare our results with previous work reported by Morgenstern [20] and Johnson et al. [13]. Our main results are as follows. ffl On the randomly generated graphs, the performance of Hybrid is consistently better than the sequential algorithms, both in terms of speed and number of colorings produced. However, on large random graphs, our algorithms do not come close to the best colorings found ...
Clique relaxations in social network analysis: The maximum kplex problem
, 2006
"... This paper introduces and studies the maximum kplex problem, which arises in social network analysis, but can also be used in several other important application areas, including wireless networks, telecommunications, and graphbased data mining. We establish NPcompleteness of the decision version ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
This paper introduces and studies the maximum kplex problem, which arises in social network analysis, but can also be used in several other important application areas, including wireless networks, telecommunications, and graphbased data mining. We establish NPcompleteness of the decision version of the problem on arbitrary graphs. An integer programming formulation is presented and basic polyhedral study of the problem is carried out. A branchandcut implementation is discussed and computational test results on the proposed benchmark instances and reallife scalefree graphs are also provided.
An Algorithm for Finding a Maximum Clique in a Graph
, 1997
"... This paper introduces a branchandbound algorithm for the maximum clique problem which applies existing clique finding and vertex coloring heuristics to determine lower and upper bounds for the size of a maximum clique. Computational results on a variety of graphs indicate the proposed procedure in ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
This paper introduces a branchandbound algorithm for the maximum clique problem which applies existing clique finding and vertex coloring heuristics to determine lower and upper bounds for the size of a maximum clique. Computational results on a variety of graphs indicate the proposed procedure in most instances outperforms leading algorithms.