E.H.L. Aarts, J. Korst and W. Michiels (2005). Simulated annealing. In: E.K. Burke and G. Kendall (eds.) (2005). Introductory Tutorials in Optimisation, Decision Support and Search Methodology. ISBN: 0387234608, Springer. Chapter 7, 187-211.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....pieces have to be cut, a lot of 2D placement problems arise. Because of their importance a couple of approaches for solving 2D placement problems are developed which are based on sequential allocation ( Art66, BDSW89, AS80, DD93, ABJ90, MDL92, HL98, SST97] meta heuristics (simulated annealing [AKL97, OF93, Dow93], tabu search [BHW93] etc. local improvement techniques (compaction, LM93, MDL92] or integer linear and or nonlinear programming ( SNK96, ST93] Moreover, a variety of approaches is addressed to containment problems too ( MD97, Mil97] In order to develop efficient solution approaches, the ....

E. Aarts, J. Korst and P. Van Laarhoven, Simulated annealing, in: E. Aarts and J.K. Lenstra (Eds.) Local Search in Combinatorial Optimization, John Wiley & Sons Ltd., 1997.

....problem structure. Numerical results on QAPLIB problems presented by Battiti and Tecchiolli show that in the majority of the cases the reactive TS converges to the best known solution faster than any other known tabu search scheme. 3. 2 SIMULATED ANNEALING (SA) The simulated annealing technique [Aarts, et al. 1997] belongs to a class of local search algorithms that are known as threshold algorithms. A new solution is generated and compared against the current solution. The new solution is accepted as the current solution if the difference in quality does not exceed a dynamically selected threshold. The ....

: Emile H. L. Aarts, Jan H.M. Korst and Peter J. M. van Laarhoven. "Simulated Annealing ". Local Search in Combinatorial Optimization. Edited by E.Aarts and K.Lenstra. Chapter 4, pp. 91 to 120. John Wiley and Sons Ltd.

....and cooling chains length (wL and c L ) are constant. The aim of each Metropolis chain is to restore equilibrium broken by temperature reduction. Since true thermal equilibrium cannot be reached in a finite time, the concept of quasi equilibrium can be successfully used to guide scheduling [2]. If the initial temperature is such that virtually any neighbour is accepted, quasi equilibrium is then obtained. The temperature decrement and the chain length must be chosen such that quasi equilibrium is restored at the end of each chain. This theoretical analysis led to the proposal of a new ....

....feedback, and especially the standard deviation of the energy, is an important component of an effective schedule. A third, more sophisticated, temperature schedule (SAEF) using a variable chain length was described in [7] It is considered as one the most efficient annealing schedules available [2]. Although the temperature reduction rule is different from the second schedule, it uses the same kind of feedback (previous temperature, standard deviation and a constant cooling factor #) An approximate criterion to detect equilibrium is used to determine the chain length: each chain ....

E.H.L. Aarts, J.H.M. Korst and P.J.M. van Laarhoven, Simulated Annealing, chapter 4, in: Aarts and Lenstra [3], 1997.

....ned mathematical context. II. Simple Simulated Annealing Simulated annealing is a probabilistic method proposed by Kirpatrick et al. KTV83] The origin and the choice of the algorithm lie in the physical annealing process. Here we just give a short synopsis. The interested reader is referred to [AKvL97] for a more detailed description. The basic elements of simulated annealing (SA) are the following: 1. A nite set S. 2. A real valued cost function c de ned on S. Let S S be the set of global minima of the function c. 3. For each x 2 S, a set S(x) S fxg, called the set of neighbors of ....

....A. Convergence Analysis Having de ned the algorithm, we now address its performance. The main questions are 1. Under which assumptions does x(t) converge to the optimal set S 2. How fast does the convergence to S take place The rst question has been more or less answered completely [AKvL97]. Basically there are two convergence results. The rst theorem assumes that for each T (t) the algorithm is run until equilibrium is reached. Then for lim t 1 T (t) 0 convergence to S in probability is obviously obtained. This convergence theorem is of limited values because there exists no ....

E.H. Aarts, H.M. Korst, and P.J. van Laarhoven. Simulated annealing. In E. Aarts and J.K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 121{ 136, Chichester, 1997. Wiley.

....needs an exponential effort (in the size of the problem) There are at least two approaches to reduce the computation: to approximate the Boltzmann distribution or to look for ADFs where the distribution can be computed in polynomial time. The first approach is used by Simulated Annealing [1]. FDA is based on the second approach. The distribution is factored into a product of marginal and conditional probabilities. They are defined as usual p( c i x) X y2X; c i y= c i x p(y) 3) p( b i xj c i x) p( b i x; c i x) p( c i x) 4) The main factorization theorem uses the ....

Aarts, E.H. & Korst, H.M. & van Laarhoven, P.J. (1997). Simulated Annealing. In Aarts, E. & Lenstra, J.K. (Eds.),Local Search in Combinatorial Optimization. Chichester:Wiley pp =121-136.

....cooling schedule, it is possible to find an optimal solution. However, such cooling schedules usually take exponential time to find an optimal solution. Thus faster cooling schedules that find sub optimal solutions are usually adopted. For a more thorough explanation of simulated annealing, see [1]. Similar to simulated annealing, tabu search improves on hill climbing by allowing worsening solutions to be selected from a neighborhood. At each point in the search, the best solution in the neighborhood is selected even if it is worse than the current solution. This means that when tabu ....

E. Aarts, J. Korst, and P. Laarhoven. Simulated annealing. In E. Aarts and Lenstra J. K., editors, Local Search in Combinatorial Optimization, pages 91-- 120. John Wiley & Sons Ltd., 1997.

....for Proposition 1 is difficult to prove for a general distribution. For a specific probability model, the Boltzmann distribution, convergence can be proven fairly easily. The Boltzmann distribution is often used in statistical physics and plays a major role in the analysis of simulated annealing (Aarts et al. 1997). Definition: The Gibbs or Boltzmann distribution of a function f is defined for u 1 by p(x) Exp u f(x) P y Exp u f(y) 10) where for notational convenience Exp u f(x) u f(x) F u : X y Exp u f(y) Remark: The Boltzmann distribution is usually defined as e Gammakg(x) Z. The ....

....ffl STEP 3: If termination criteria are not met, go to STEP 1. BEDA is similar to a simulated annealing algorithm. But it generates a population of points instead of a single point in each step using the exact Boltzmann distribution. Simulated annealing only approximates the Boltzmann distribution (Aarts 1997). For BEDA the probability distribution can be explicitly computed. We start with a lemma. Lemma: Let p(x) be given by Equation 10. If Boltzmann selection is used with basis v then the distribution of the selected points is given by p s (x) Exp u Deltav f(x) P y Exp u Deltav f(y) 12) ....

Aarts, E.H. & Korst, H.M. & van Laarhoven, P.J. (1997). Simulated Annealing. In Aarts, E. & Lenstra, J.K. (Eds.),Local Search in Combinatorial Optimization. Chichester:Wiley pp =121-136.

....schedule used. We initially used the most commonly known and used schedule, which is the geometric cooling, but later tried adaptive cooling, as well as the method of geometric reheating based on cost [3] A comprehensive discussion of the theoretical and practical details of SA is given in [1, 27, 32, 34]. It suffices here to say that the elementary operation in the Metropolis method for a combinatorial problem such as scheduling is the generation of some new candidate configuration, which is then automatically accepted if it lowers the cost (C) or accepted with probability exp( Gamma DeltaC=T ....

Aarts, E. H., J. Korst, and P. J. van Laarhoven, "Simulated annealing," in Local Search in Combinatorial Optimization, E. H. Aarts and J. K. Lenstra (eds.), John Wiley and Sons, 1997.

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E.H.L. Aarts, J. Korst and W. Michiels (2005). Simulated annealing. In: E.K. Burke and G. Kendall (eds.) (2005). Introductory Tutorials in Optimisation, Decision Support and Search Methodology. ISBN: 0387234608, Springer. Chapter 7, 187-211.

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Aarts, E. H. L., Van Laarhoven, P. J. M., Korst, J. H. M., "Simulated annealing", Local Search in Combinatorial Optmization, E. H. L. Aarts and J. K. Lenstra (eds.), John Wiley & Sons, 1997.

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E.H.L Aarts, J.H.M. Korst, and P.J.M. van Laarhoven. Simulated annealing. In E. Aarts and J.K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 91--120. John Wiley & Sons Ltd., 1997.

No context found.

E.H. Aarts, H.M. Korst, and P.J. van Laarhoven. Simulated annealing. In E. Aarts and J.K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 121{ 136, Chichester, 1997. Wiley.

No context found.

E.H.L Aarts, J.H.M. Korst, and P.J.M. van Laarhoven. Simulated annealing. In E. Aarts and J.K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 91--120. John Wiley & Sons Ltd., 1997.

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Aarts, E.H. & Korst, H.M. & van Laarhoven, P.J. (1997). Simulated Annealing. In Aarts, E. & Lenstra, J.K. (Eds.),Local Search in Combinatorial Optimization.pp.

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References Aarts, E.H. & Korst, H.M. & van Laarhoven, P.J. (1997). Simulated Annealing. In Aarts, E. & Lenstra, J.K. (Eds.),Local Search in Combinatorial Optimization. Chichester:Wiley pp =121-136.

No context found.

Aarts, E.H. & Korst, H.M. & van Laarhoven, P.J. (1997). Simulated Annealing. In Aarts, E. & Lenstra, J.K. (Eds.),Local Search in Combinatorial Optimization. Chichester:Wiley pp =121-136.

No context found.

E. H. L. Aarts and J. K. Lenstra, "Simulated Annealing," in Local Search in Combinatorial Optimization, (E. H. L. Aarts and J. K. Lenstra, eds.), ch. 1, pp. 1--17, Wiley, 1997.

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Emile H. L. Aarts, Jan H. M. Korst, and Peter J. M. van Laarhoven. Simulated annealing. In Aarts and Lenstra [AL97], pages 91-120.

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E. H. L. Aarts, J. H. M. Korst, and P. J. M. van Laarhoven. Simulated annealing. In E. H. L. Aarts and J. K. Lenstra, editors, Local Search in Combinatorial Optimization, pages 91-120. John Wiley & Sons, Chichester, 1997.

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