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Simulated annealing for graph bisection
 in Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science
, 1993
"... We resolve in the affirmative a question of Boppana and Bui: whether simulated annealing can, with high probability and in polynomial time, find the optimal bisection of a random graph in Gnpr when p r = O(n*’) for A 5 2. (The random graph model Gnpr specifies a “planted ” bisection of density r, ..."
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Cited by 34 (1 self)
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We resolve in the affirmative a question of Boppana and Bui: whether simulated annealing can, with high probability and in polynomial time, find the optimal bisection of a random graph in Gnpr when p r = O(n*’) for A 5 2. (The random graph model Gnpr specifies a “planted ” bisection of density r, separating two n/2vertex subsets of slightly higher density p.) We show that simulated “annealing ” at an appropriate fixed temperature (i.e., the Metropolis algorithm) finds the unique smallest bisection in O(n2+‘) steps with very high probability, provided A> 1116. (By using a slightly modified neighborhood structure, the number of steps can be reduced to O(n’+‘).) We leave open the question of whether annealing is effective for A in the range 312 < A 5 1116, whose lower limit represents the threshold at which the planted bisection becomes lost amongst other random small bisections. It also remains open whether hillclimbing (i.e., annealing at temperature 0) solves the same problem. 1
Searching Randomly for Maximum Matchings
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 76 (2004)
, 2004
"... Many realworld optimization problems in, e. g., engineering or biology have the property that not much is known about the function to be optimized. This excludes the application of problemspecific algorithms. Simple randomized search heuristics are then used with surprisingly good results. In ord ..."
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Cited by 3 (0 self)
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Many realworld optimization problems in, e. g., engineering or biology have the property that not much is known about the function to be optimized. This excludes the application of problemspecific algorithms. Simple randomized search heuristics are then used with surprisingly good results. In order to understand the working principles behind such heuristics, they are analyzed on combinatorial optimization problems whose structure is wellstudied. The idea is to investigate when it is possible to “simulate randomly ” clever optimization techniques and when this random search fails. The main purpose is to develop methods for the analysis of general randomized search heuristics. The maximum matching problem is well suited for this approach since long augmenting paths do not allow local improvements and since our results on randomized local search and simple evolutionary algorithms can be compared with published results on the Metropolis algorithm and simulated annealing.
Heuristics for the MinLA Problem: An Empirical and Theoretical Analysis (Extended Abstract)
, 1998
"... ) Josep D'iaz Jordi Petit i Silvestre Mar'ia Jos'e Serna Departament de Llenguatges i Sistemes Inform`atics (LSI) Universitat Polit`ecnica de Catalunya (UPC) Campus Nord  M`odul C6 Jordi Girona Salgado, 13 08034 Barcelona, Catalonia (Spain) Fax: +34 934 017 014 fdiaz,jpetit,mjsernag@lsi.upc.es ..."
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Cited by 1 (1 self)
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) Josep D'iaz Jordi Petit i Silvestre Mar'ia Jos'e Serna Departament de Llenguatges i Sistemes Inform`atics (LSI) Universitat Polit`ecnica de Catalunya (UPC) Campus Nord  M`odul C6 Jordi Girona Salgado, 13 08034 Barcelona, Catalonia (Spain) Fax: +34 934 017 014 fdiaz,jpetit,mjsernag@lsi.upc.es Paul Spirakis Computer Technology Institute (CTI) Kolokotroni 3 GR 262 21 Patras (Greece) spirakis@cti.gr Supported by ESPRIT LTR Project no. 20244  ALCOMIT, CICYT Project TIC971475CE, DGES Project PB9J0787Koala and CIRIT 1997SGR00366. The implementation and evaluation of these heuristics has been done at the C 4 (Centre de Computaci'o i Comunicacions de Catalunya). 1 Introduction Several wellknown optimization problems on graphs can be formulated as Linear Arrangement Problems. Their goal is to find a layout (ordering) of the nodes of an input graph such that a certain function is minimized. Linear arrangement problems are an important class of problems with many differe...
the Deutsche Forschungsgemeinschaft. Simulated Annealing Beats Metropolis in Combinatorial Optimization
, 2004
"... The Metropolis algorithm is simulated annealing with a fixed temperature. Surprisingly enough, many problems cannot be solved more efficiently by simulated annealing than by the Metropolis algorithm with the best temperature. The problem of finding a natural example (artificial examples are known) w ..."
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The Metropolis algorithm is simulated annealing with a fixed temperature. Surprisingly enough, many problems cannot be solved more efficiently by simulated annealing than by the Metropolis algorithm with the best temperature. The problem of finding a natural example (artificial examples are known) where simulated annealing outperforms the Metropolis algorithm for all temperatures has been discussed by Jerrum and Sinclair (1996) as “an outstanding open problem”. This problem is solved here. The examples are simple instances of the wellknown minimum spanning tree problem. Moreover, it is investigated which instances of the minimum spanning tree problem can be solved efficiently by simulated annealing. This is motivated by the aim to develop further methods to analyze the simulated annealing process. 1
Nonnumerical Algorithms and Problems—Computations
"... To understand the working principles of randomized search heuristics like evolutionary algorithms they are analyzed on optimization problems whose structure is wellstudied. The idea is to investigate when it is possible to simulate clever optimization techniques for combinatorial optimization probl ..."
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To understand the working principles of randomized search heuristics like evolutionary algorithms they are analyzed on optimization problems whose structure is wellstudied. The idea is to investigate when it is possible to simulate clever optimization techniques for combinatorial optimization problems by random search. The maximum matching problem is well suited for this approach since long augmenting paths do not allow immediate improvements by local changes. It is known that randomized search heuristics like simulated annealing, the Metropolis algorithm, the (1+1) EA and randomized local search efficiently approximate maximum matchings for any graph; however, there are graphs where they fail to find maximum matchings in polynomial time. In this paper, we examine randomized local search (RLS) for graphs whose structure is simple. We show that RLS finds maximum matchings on trees in expected polynomial time. Categories and Subject Descriptors