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Iterated local search
 Handbook of Metaheuristics, volume 57 of International Series in Operations Research and Management Science
, 2002
"... Iterated Local Search has many of the desirable features of a metaheuristic: it is simple, easy to implement, robust, and highly effective. The essential idea of Iterated Local Search lies in focusing the search not on the full space of solutions but on a smaller subspace defined by the solutions th ..."
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Cited by 121 (15 self)
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Iterated Local Search has many of the desirable features of a metaheuristic: it is simple, easy to implement, robust, and highly effective. The essential idea of Iterated Local Search lies in focusing the search not on the full space of solutions but on a smaller subspace defined by the solutions that are locally optimal for a given optimization engine. The success of Iterated Local Search lies in the biased sampling of this set of local optima. How effective this approach turns out to be depends mainly on the choice of the local search, the perturbations, and the acceptance criterion. So far, in spite of its conceptual simplicity, it has lead to a number of stateoftheart results without the use of too much problemspecific knowledge. But with further work so that the different modules are well adapted to the problem at hand, Iterated Local Search can often become a competitive or even state of the art algorithm. The purpose of this review is both to give a detailed description of this metaheuristic and to show where it stands in terms of performance. O.M. acknowledges support from the Institut Universitaire de France. This work was partially supported by the “Metaheuristics Network”, a Research Training Network funded by the Improving Human Potential programme of the CEC, grant HPRNCT199900106. The information provided is the sole responsibility of the authors and does not reflect the Community’s opinion. The Community is not responsible for any use that might be made of data appearing in this publication. 1 1
Combining Simulated Annealing with Local Search Heuristics
, 1993
"... We introduce a metaheuristic to combine simulated annealing with local search methods for CO problems. This new class of Markov chains leads to significantly more powerful optimization methods than either simulated annealing or local search. The main idea is to embed deterministic local search tech ..."
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Cited by 81 (7 self)
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We introduce a metaheuristic to combine simulated annealing with local search methods for CO problems. This new class of Markov chains leads to significantly more powerful optimization methods than either simulated annealing or local search. The main idea is to embed deterministic local search techniques into simulated annealing so that the chain explores only local optima. It makes large, global changes, even at low temperatures, thus overcoming large barriers in configuration space. We have tested this metaheuristic for the traveling salesman and graph partitioning problems. Tests on instances from public libraries and random ensembles quantify the power of the method. Our algorithm is able to solve large instances to optimality, improving upon state of the art local search methods very significantly. For the traveling salesman problem with randomly distributed cities in a square, the procedure improves on 3opt by 1.6%, and on LinKernighan local search by 1.3%. For the partitioni...
HypergraphPartitioning Based Decomposition for Parallel SparseMatrix Vector Multiplication
 IEEE Trans. on Parallel and Distributed Computing
"... In this work, we show that the standard graphpartitioning based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrixvector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph mo ..."
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Cited by 61 (34 self)
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In this work, we show that the standard graphpartitioning based decomposition of sparse matrices does not reflect the actual communication volume requirement for parallel matrixvector multiplication. We propose two computational hypergraph models which avoid this crucial deficiency of the graph model. The proposed models reduce the decomposition problem to the wellknown hypergraph partitioning problem. The recently proposed successful multilevel framework is exploited to develop a multilevel hypergraph partitioning tool PaToH for the experimental verification of our proposed hypergraph models. Experimental results on a wide range of realistic sparse test matrices confirm the validity of the proposed hypergraph models. In the decomposition of the test matrices, the hypergraph models using PaToH and hMeTiS result in up to 63% less communication volume (30%38% less on the average) than the graph model using MeTiS, while PaToH is only 1.32.3 times slower than MeTiS on the average. ...
Parallel Decomposition of Unstructured FEMMeshes
 Concurrency: Practice & Experience
, 1995
"... . We present a massively parallel algorithm for static and dynamic partitioning of unstructured FEMmeshes. The method consists of two parts. First a fast but inaccurate sequential clustering is determined which is used, together with a simple mapping heuristic, to map the mesh initially onto the pr ..."
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Cited by 41 (15 self)
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. We present a massively parallel algorithm for static and dynamic partitioning of unstructured FEMmeshes. The method consists of two parts. First a fast but inaccurate sequential clustering is determined which is used, together with a simple mapping heuristic, to map the mesh initially onto the processors of a massively parallel system. The second part of the method uses a massively parallel algorithm to remap and optimize the mesh decomposition taking several cost functions into account. It first calculates the amount of nodes that have to be migrated between pairs of clusters in order to obtain an optimal load balancing. In a second step, nodes to be migrated are chosen according to cost functions optimizing the amount and necessary communication and other measures which are important for the numerical solution method (like for example the aspect ratio of the resulting domains). The parallel parts of the method are implemented in C under Parix to run on the Parsytec GCel systems. R...
Greedy, Prohibition, and Reactive Heuristics for Graph Partitioning
 IEEE Transactions on Computers
, 1998
"... New heuristic algorithms are proposed for the Graph Partitioning problem. A greedy construction scheme with an appropriate tiebreaking rule (MINMAXGREEDY) produces initial assignments in a very fast time. For some classes of graphs, independent repetitions of MINMAXGREEDY are sufficient to rep ..."
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Cited by 29 (5 self)
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New heuristic algorithms are proposed for the Graph Partitioning problem. A greedy construction scheme with an appropriate tiebreaking rule (MINMAXGREEDY) produces initial assignments in a very fast time. For some classes of graphs, independent repetitions of MINMAXGREEDY are sufficient to reproduce solutions found by more complex techniques. When the method is not competitive, the initial assignments are used as starting points for a prohibitionbased scheme, where the prohibition is chosen in a randomized and reactive way, with a bias towards more successful choices in the previous part of the run. The relationship between prohibitionbased diversification (Tabu Search) and the variabledepth KernighanLin algorithm is discussed. Detailed experimental results are presented on benchmark suites used in the previous literature, consisting of graphs derived from parametric models (random graphs, geometric graphs, etc.) and of "realworld " graphs of large size. On the first series ...
A comparison of the performance of different metaheuristics on the timetabling problem
 IN: PROCEEDINGS OF THE 4TH INTERNATIONAL CONFERENCE ON PRACTICE AND THEORY OF AUTOMATED TIMETABLING (PATAT 2002
, 2002
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Applying iterated local search to the permutation flow shop problem
, 1998
"... Iterated local search (ILS) is a general and powerful metaheuristic which provides an easily implementable way of improving the performance of local search algorithms. In this article we consider the application of ILS to the permutation flow shop problem (FSP), a strongly studied problem in machi ..."
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Cited by 25 (9 self)
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Iterated local search (ILS) is a general and powerful metaheuristic which provides an easily implementable way of improving the performance of local search algorithms. In this article we consider the application of ILS to the permutation flow shop problem (FSP), a strongly studied problem in machine scheduling. We experimentally investigate the effect of specific implementation choices in our ILS algorithm and analyze its performance. Computational results show that our ILS approach compares very favorably to other approaches proposed for the FSP and is, despite its simplicity, even able to find new best solutions for some benchmark instances which have already been attacked by many other algorithms.
On twodimensional sparse matrix partitioning: Models, methods, and a recipe
 SIAM J. Sci. Comput
, 2010
"... Abstract. We consider twodimensional partitioning of general sparse matrices for parallel sparse matrixvector multiply operation. We present three hypergraphpartitioningbased methods, each having unique advantages. The first one treats the nonzeros of the matrix individually and hence produces f ..."
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Cited by 21 (15 self)
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Abstract. We consider twodimensional partitioning of general sparse matrices for parallel sparse matrixvector multiply operation. We present three hypergraphpartitioningbased methods, each having unique advantages. The first one treats the nonzeros of the matrix individually and hence produces finegrain partitions. The other two produce coarser partitions, where one of them imposes a limit on the number of messages sent and received by a single processor, and the other trades that limit for a lower communication volume. We also present a thorough experimental evaluation of the proposed twodimensional partitioning methods together with the hypergraphbased onedimensional partitioning methods, using an extensive set of public domain matrices. Furthermore, for the users of these partitioning methods, we present a partitioning recipe that chooses one of the partitioning methods according to some matrix characteristics.
Cut Size Statistics of Graph Bisection Heuristics
 SIAM JOURNAL ON OPTIMIZATION
, 1999
"... We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by “local” algorithms becomes peaked as the number ..."
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Cited by 20 (5 self)
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We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut sizes found by “local” algorithms becomes peaked as the number of vertices in the graphs becomes large. Evidence is given that this distribution tends towards a Gaussian whose mean and variance scales linearly with the number of vertices of the graphs. Given the distribution of cut sizes associated with each heuristic, we provide a ranking procedure which takes into account both the quality of the solutions and the speed of the algorithms. This procedure is demonstrated for a selection of local graph bisection heuristics.