P. J. M. V. Laarhoven and E. H. L. Aarts, Simulated Annealing : Theory and Applications. D. Reidel Publishing Company, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....linear programming [2] In order to get the optimal solution, we restrict the linear programming to the 0 1 integer programming [1] We also show some experiment results. In the future, we may develop a new algorithm with the branch and bound strategy [4] the simulated annealing strategy [6] or the genetic strategy [7] or other strategies for solving NP complete problems. In this paper, we still have some open problems. Problem I: Is the vertex compression problem NP complete on general graphs Problem II: What is the tight bound of the number of searching iterations in our main ....

P. J. M. V. Laarhoven and E. H. L. Aarts, Simulated Annealing : Theory and Applications. D. Reidel Publishing Company, 1987.

....C 7 = 10 by Theorem 2. Thus, the allocation of 108 potentially independent vertices seems to be very well balanced. It is also obvious that larger independent sets cannot be balanced in this way. 4 Simulated annealing with a constant temperature schedule Simulated annealing (see, for example [9]) can be understood as a random relaxation of the iterative improvement algorithm [1] The moves to higher cost solutions are accepted only with a certain probability. This acceptance probability depends on the parameter, which is usually called the temperature. Sometimes very good solutions are ....

P.J.M.Laarhoven, E.H.L.Aarts, Simulated Annealing, Theory and Applications, D.Reidel Publishing Company, Dordrecht 1987.

....of starting point. It often gives unsatisfactory results because the error measure E 2D is highly non convex, i.e. the surface E 2D have many local minima. To obtain more reliable results, methods from stochastic optimization must be applied. We have chosen an approach of Simulated Annealing [9,10,17]. This approach is much more computationally expensive, but is less sensitive to the starting point, and usually produces better results, i.e. a set of parameters for which E 2D is smaller. A description of the procedure used is found in appendix A. It is relevant here to comment on the expected ....

P. J. M. Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications, D. Reidel Publishing Company, 1987

....has to be stopped before it has finished, we can hope that the results will be of better quality than the results obtained by GACO in the same situation. In future works we plan to study other ways to evaluate a chromosome and the use of other optimization techniques like simulated annealing [45] or tab u search [46] 47] ....

P.J.M. Van Laarhoven and E.H.L. Aarts, Simulated Annealing, Reidel Publishing Company, 1988.

....than simulated annealing. Here we present a numerical example which con#rms that it is possible to observe the convergence of y t(s) to the global minima in practical simulation and leave theoretical questions, for example to estimate the convergence rate of y t(s) 16,17] and other applications [4,18] as topics for further discussion. In terms of (2.23) the gain function is a solution of the following di#erential equation: a # (t) a 3 (t) # 2 # t 0 a(u)du c 1 a(0) # 2 log(c 1 ) 3.11) which can be numerically solved. Example 2. We choose a potential U (x) x 4 =4 x 3 =3 x ....

P.J.M. van Laarhoven, E.H.L. Aarts, Simulated Annealing: Theory and Applications, Reidel, D. Reidel Publishing Company, Dordrecht, 1987.

....of problem instances de ned using PCCs and ACs only. Instead, however, we concentrate on approximation algorithms suitable for all kinds of ESP instances. Speci cally, local search algorithms based on Iterated Descent (ID) Simulated Annealing (SA) and Tabu Search (TS) are described (see [16, 22, 35] and [2, 14, 15, 19] Evolutionary algorithms were tested in [25] and showed very poor performance due to a mal functioning crossover operator. Therefore, this type of search algorithm is not investigated in this paper. Neighbourhood Functions Local search techniques make use of a neighbourhood ....

P. J. M. van Laarhoven and E. H. L. Aarts. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, 1987.

....used to this end. Deterministic approaches converge to model configurations corresponding to local minima of the energy function. Initialization, close to the desired solution are therefore required [9, 11, 21] Stochastic schemes may be used to obtain optimal solutions but are often cpu expensive [1, 19, 18]. General purpose closed contours ( snakes and variants) controlled by elastic forces based on local curvature, inflating forces and image based potentials (created for instance by local edges) have been used to extract continuous contour lines [3, 10, 9, 15, 21, 23, 36] Their limits and ....

E.H.L. AARTS and P.J.M. van LAARHOVEN. -- Simulated Annealing: Theory and Applications. -- D. Reidel Publishing Company, 1987.

....st =T , so that the increases in energy that may be accepted decrease as T decreases. The expected cost of solutions sampled by the algorithm decreases also. If T is decreased sufficiently slowly, the algorithm will converge convergence in probability to the globally minimum energy states [25]. Final solution quality depends on the annealing schedule, the initial temperature and the rate at which the temperature is reduced. Thus, the behavior and convergence of simulated annealing is characterized by the probability distribution of sampled states at each stage of the algorithm. ....

....is reduced. Thus, the behavior and convergence of simulated annealing is characterized by the probability distribution of sampled states at each stage of the algorithm. Theoretical analyses of simulated annealing, whether based on statistical physics and on Markov chains, rely on this observation [25]. 3 2 Parallel Simulated Annealing with Simultaneous Moves In order to improve SA performance, many parallel versions of SA have been developed(see [1, 7, 13] for surveys) An approach that is application independent and allows the exploitation of a reasonable amount of parallelism is to ....

P.J.M. van Laarhoven and E.H.L. Aarts. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, Boston, 1987.

....a technique designed to achieve fruitful hybridisation of a spanning tree construction algorithm with stochastic iterative search. This method, which we call RPM (Randomised Primal Method) is employed in three stochastic, iterative search techniques: multi start hillclimbing, simulated annealing [10], and a genetic algorithm [11] The quality of solutions found by these techniques are compared with each other, and also with those achieved by the dual simplex algorithm of [8] and the upper bound generated by Narula and Ho s d Prim s method [3] These comparisons are made on a variety of ....

....in a given number, r of iterations. The best evaluation found so far is continually stored, and returned at the end. The advantage of MHC is its simplicity, requiring only one parameter to be set in addition to the stopping criteria. The second technique we employ, simulated annealing (SA) [10], is based on an 20 analogy with the physical process of annealing, in which a solid is driven into a lowenergy state by first melting it and then cooling it down slowly. Simulated annealing is characterised by its ability to accept transitions to more expensive solutions (in the case of ....

P.J.M. van Laarhoven and E.H.L. Aarts, Simulated Annealing: Theory and Applications, D. Reidel Publishing Company, Dordrecht, Netherlands, 1987.

....methods show that on average the algorithm based on the s distance reduced the registration time by a factor of three over the cross correlation and the scatter plot based methods. To obtain numerically a solution of the optimization problem (1) we have applied a simulated annealing algorithm [4] which belongs to the class of non deterministic optimization methods. In contrast to the deterministic algorithms deteriorations of the objective function can also be accepted. This allows to avoid being trapped in local minima. In Fig. 2 there is presented a CT CT data pair registered using ....

van Laarhoven P.J.M., Aarts E.H.J.: Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, Dordrecht (1987)

....the Hubble Space Telescope, and other constraint problems like the million queens, and 3 colourability. It is interesting to note that the performance of this procedure was significantly improved by heuristics for choosing a good initial assignment. GenSAT is an iterative improvement algorithm [vanLaarhoven Aarts 87] which uses a distribution of initial assignments to overcome poor start positions and local maxima. Simulated annealing is an alternative approach to these problems but is probably of little use in GenSAT given the low density of local maxima, and the size of the plateaus. 8 Further Work ....

P.J.M. van Laarhoven and E.H.L. Aarts. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, Dordrecht, Holland, 1987.

.... different types of graphs the performance of the algorithm considerably depends on T [18, 20] Choosing a good temperature is therefore an interesting open research problem which 12 is not unlike to the well known problem of finding a good cooling schedule for the simulated annealing algorithm [14]. Not surprisingly, temperature is also important parameter of the present algorithm. The fact that it is a single real number gives hope that it can in praxis be tuned by not too complicated and time consuming process. Furthermore, our first experience shows that it can be tuned relatively fast, ....

P.J.M. Laarhoven and E.H.L. Aarts, Simulating Annealing, Theory and applications, D. Reidel Publishing Company, Dordrecht, 1987.

....a set of relations on T . In the case of points, R usually includes a linear ordering relation to express the before after order. In the case of intervals, R may be defined to be the set of the thirteen binary interval relations of [1] or a set of other interval relations, for example, those of [30]. After a time structure S is assumed and axiomatized, a positional logic based on S can be defined as an extension to classic logic by introducing some operators to express temporal references to time. Positional logics date back to [23] where there was a single operator, called temporal ....

....properties such as decidability, complexity and expressiveness. Completeness is an important and difficult issue on its own, which justifies the interest of this paper. 2 Common sense time The nature, understanding and representation of time are, in all the history, very debatable. van Benthem [30] gave a model theoretic study of temporal ontology and temporal discourse. In temporal databases, the common sense calendar clock style time is widely used. For example, 1992 10 2 is a valid calendar clock style time to represent October 2, 1992. In this paper we choose the calendar clock style ....

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J. van Benthem, The Logic of Time, D. Reidel Publishing Company, 1983.

....chains, the outcome of a trial just depends on the outcome of the previous trial. Moreover, the probability of moving from one solution to another can be found, which leads to the definition of the transition probability matrix associated with any Markov chain. For more theoretical results see [33]. An important design factor of the simulated annealing methods is the cooling schedule, i.e. the scheme that controls the temperature. The scheme most commonly used is the geometric cooling rule, in which the temperature is held steady for some prespecified constant L number of trials, and is ....

P.J.M. van Laarhoven and E.H.L. Aarts. Simulated Annealing: Theory and Applications. D.Reidel Publishing Company, Dordrecht, 1987.

.... the well demonstrated good computational behaviour of point algebra [25] However, we conclude that we really did not have to choose between one kind of temporal logic or another, because in practice, each, or both, logic forms can satisfy naturally the needs of the application we have in mind [23]. On the other hand, although most interval logics allow us to express assertions about points, considered as primitive temporal objects, or as intervals of duration equal to zero, or as intervals with specific structures that are, in all cases, more complex than a simple instant) 4, 5] In this ....

....[4, 5] In this paper, we have opted to treat points and intervals jointly to obtain a logic that adequately describes ofchanges, events, states and processes and that can resolve efficiently the computational problems associated with these ontological entities. Bochman [5] and van Benthem [23] theoretically tried to combine both approaches but they did not intend to use the combination for computing. They conclude that 1. INTRODUCTION 747 there are several areas of peaceful coexistence within which points and intervals are mutually definable. Our option is based on the assumption ....

J. F. A. K. van Benthem. The Logic of Time. D. Reidel Publishing Company, 1983.

....following chapter explore approaches that do provide this advantage. 5.3 Building Sphere Trees with Simulated Annealing This section presents a second algorithm for building sphere trees. This algorithm use simulated annealing, a general technique for solving constrained optimization problems [LA87, PTVF92] The sphere trees this algorithm produces can fit objects more tightly than sphere trees produced by the octree method from the previous section. Building sphere trees with simulated annealing does have disadvantages: it can be slow and unreliable. The algorithm from this section is ....

....produces good results in a reasonable amount of time. The current section, like Section 5.2, focuses on polyhedral objects, but the general ideas should extend to other classes of objects. 5.3. 1 Basic Ideas The motivation for simulated annealing comes from the thermodynamics of liquids [LA87, PTVF92] The internal energy is lower in a liquid that cools slowly than in a liquid that cools quickly. Internal energy causes brittleness in a liquid that cools to a solid state. Noting this problem, metal workers increase the strength of a part cast from molten metal by cooling it slowly. ....

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Peter J. M. van Laarhoven and Emile H. L. Aarts. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, Dordrecht, Holland, 1987.

....a belief that Simulated Annealing usually finds high quality solutions in finite time as well. Empirical investigations seem to support this conjecture. Presently, a number of thorough texts on Simulated Annealing exist. Among those we point out the books by Aarts Korst [1] and Laarhoven Aarts [23]. Some of the most thorough experimental investigations on Simulated Annealing are found in the papers by Johnson et al. 19, 20] 2.2 Strategies for parallelizing Simulated Annealing At first sight, it may appear difficult to effectively parallelize the generic Simulated Annealing algorithm, ....

Laarhoven, P.J.M., Aarts, E.H.L., Simulated Annealing : Theory and Applications, D. Reidel Publishing Company, Dordrecht, 1987.

....several other performance parameters as well. We will again focus on the discussion of the case of uniform size communicating subcubes, since we have shown [8] that mapping variable size subcubes can always be reduced to a uniform size subcube mapping problem. The simulated annealing method [9] is shown to be an effective algorithm for finding near optimal solutions to NP hard task mapping problems [10, 11] In [11] we investigated a simulated annealing method optimization process for finding good sub optimal mappings for the problem (G; 0; n) The implementation of the simulated ....

P. J. M. Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications, D. Reidel Publishing Company, 1987.

....effet cette phase n est pas interactive. Dans ce souci, nous pensons utiliser des methodes basees sur des techniques de recuit simule . Ces techniques necessitent souvent de tres longs temps de calcul, mais leur convergence vers de tres bonnes solutions a e te montree (sous certaines conditions) vL et al..87] Un autre developpement important concerne la couche d entree. Deux voies sont peuvent e tre explorees. La premiere consiste a decouper la couche d entree en plusieurs sequences de microexperts. La sequence principale concerne des notions de base. Lorsque le systeme rencontre une difficulte , il ....

P.J.M. van Laarhoven et E.H.L. Aarts. -- Simulated annealing : theory and applications, Mathematics and Its Applications. -- Dordrecht, Holland, Reidel Publishing Company, 87.

....The study of time has attracted the attention of philosophers ever since the ancient times. More recently plilosophers, logicians and linguists initiated the study of temporal logic, motivated by temporal phenomena as they manifest themeselves in natural language [Pri57, Pri67, RU71, DWP81, vB83] In the last fifteen years, reasoning about time and change has also received considerable attention in a number of areas of computer science. These areas include artificial intelligence, database and information systems and computer aided verification. This trend is quite natural since many ....

J. van Benthem. The Logic of Time. D. Reidel Publishing Company, 1983.

....Annealing for type 2 conditioning because this problem is the same for which we have considered the approximated algorithms above. Simulated Annealing algorithms for type 2 conditional information Simulated annealing is an optimization technique to solve combinatorial optimization problems [50]. Our problem is to select a configuration of transparent nodes given rise to a minimum value of probability for a case of a given variable. The calculation of the maximum is completely analogous. If given T i = c i ; i = 1; n, and C = c 1 ; c n ) this determines a probability ....

P.J.M. Van Laarhoven P.J.M. and E.H.L. Aarts. Simulated Annealing. Reidel Publishing Company, Drodrecht, 1988.

....physicists, and logicians. It is its formal structure in the model theoretic sense which is of interest for us, and here the prevalent mathematical picture of standard time is that of a set of instants with a temporal precedence order ( earlier than ) satisfying certain obvious conditions [17]: 1) T ransitivity. 2) Irref lexivity (notice that transitivity and irreflexivity imply asymmetry) 3) Linearity. 4) Eternity (8x9y : y x; 8x9y : x y) 5) Density (8x; y : x y 9z : x z y) There are several non isomorphic models satisfying these axioms, the most obvious are ....

J. F. A. K. Van Benthem. The Logic of Time. D. Reidel Publishing Company, 1983.

....leading to better overall solutions. This is yet to be investigated fully, but preliminary experiments suggested that the representation employed here struck a generally more robust balance between time complexity and solution quality. 3 Experiments We investigated the use of GAs [7] SA [8], and stochastic hillclimbing (SH) on each of the test problems. In the following subsections we briefly overview the experimental setup, and summarise the results. Test Problems Three moderately sized test problems were developed, consisting of 20, 30, and 40 connections respectively. Figure 1 ....

P. J. M. van Laarhoven and E. H. L. Aarts. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, 1987.

....N (2) k) N (2) OE (k) The last equality completes the proof in this case. 1 For some details and pointers on the use of these neighborhoods in local search algorithms for the QAP the reader is referred to [15] For similar information related to the TSP the reader is referred to [1, 13]. A communication assignment problem on trees 7 Case 2. i 62 R(k) Clearly, in this case j 62 R Gamma (k) Since j 6= k this implies j 62 R(k) Thus (R Gamma (k) OE(R Gamma (k) and OE(R(v) R(v) for all v 2 S(k) Hence, similarly as in Case 1 we have: N (l) OE (k) N ....

P. J. M. van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications, D.Reidel Publishing Company, 1988.

....based on the author s work during the past year, some early results of which were reported in [5] and [6] III. Populations: real and virtual We note that populations consist of individuals within a temporal framework: in this case we use time intervals and temporal logic as outlined by e.g. [1]. In our context time is made up of base intervals that cannot be subdivided further. This has several important consequences for the genetic algorithm. Since we will be using time intervals for populations, it also makes sense to de ne tness as the probability that an individual exists in a ....

J.F.A.K. van Benthem. The Logic of Time. D. Reidel Publishing Company, Dordrecht, 1983.

....II and SA approaches for optimizing large join queries [12] 4.4 Optimizer Tuning The parameters used in this study for II, SA and TPO are given in Figures 4, 5 and 6 respectively. These parameters were chosen after extensive experimentation and by following guidelines given in the literature [1, 24, 23, 12]. TPO needed a lot of tuning effort compared to the other two algorithms. The performance of TPO depends on the performance of both the II and SA phases and hence more effort is needed to balance the two phases. Also, it was noticed that the performance of TPO is very sensitive to the initial ....

P. J. M. van Laarhoven and E. H. Aarts. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, 1987.

....when there is a negative auxiliary. Thus, Dowty contends that lexical monotonicity marking does not suffice to identify downward and upward positions. A mechanism for marking complex expressions for monotonicity is required. This is done by first adopting and then re elaborating van Benthem s ( vB86] vB87] and S anchez Valencia s [SV91] proposal of Marking Rules. Some of these rules, namely the Monotonicity Marking Rules, allow for the possibility 12 The generalization across types goes as follows: a. A function z 2 D (ff;fi) is upward monotone iff for every x; y 2 D ff , x ff y ....

....in terms of the elements via which the law of distributivity is entered, i.e. the bottom elements or the lump sum information. I think I do not misinterpret his proposal by saying that Verkuyl suggests that processing instructions A third condition, called Quantity, following here van Benthem s [vB86] terminology, allows one to draw a distinction between determiners which are expressions of quantity, e.g. some, no, three, and the others, e.g. my, Chloe s. It defines the topic neutrality of the determiner. Determiners that form logical quantifiers satisfy this condition. Definition A ....

Johan van Benthem. Essays in Logical Semantics. Studies in Linguistics and Philosophy. D. Reidel Publishing Company, 1986.

....time points, one has to consider whether intervals 3 Recently, Web90] presented an extension of situation calculus which can cope with concurrent actions and dates. More on this in section 4.1. 4 There are philosophical theories which also allow time to branch into the past or even be cyclic [vB83] 5 Details are provided in sections 4 and 5. are open or closed. For example, if P is the proposition representing the fact John runs the race then we intuitively expect that there will be two time intervals T1 and T2 such that T2 is exactly after T1, P is true over T1 and :P is true over ....

J. van Benthem. The Logic of Time. D. Reidel Publishing Company, 1983.

....the cost function being minimized (as it will be show in the next section) 3 Problem Representation and Definitions 3.1 The Optimization Algorithm We present here the optimization algorithm used by the scheduling process. The reader not familiar with the Simulated Annealing process can refer to [20]. Figure 2 describes schematically the Simulated Annealing algorithm. Particularities of our simulated annealing algorithm are as follows : Generic Simulated Annealing Algorithm Begin S : Initial Solution T : Initial Temperature While (stopping criterion is not satisfied) do Begin While (not yet ....

....direction of the design space (area or performance) ffl The schedule of the temperature, determined empirically, is as follows : Tk = T init Theta a k . Where the parameter a depends on the size of the problem and k is the number of moves performed from the beginning. As indicated in [20], the simulated annealing method is well suited for this problem (the transformation from a high level behavioural description to a structural one) because of the very large amount of data when image processing algorithms are considered (our system is mainly oriented towards this kind of ....

P.J.M. van Laarhoven and E.H.L. Arts. Simulated Annealing: Theory and Applications. D.Reidel Publishing Company, 1988.

....or devising appropriate reproduction methods because, in some cases like in ordering problems, inappropriate reproduction methods may give invalid genotypes, Gol89] DS87] 1.2. 2 SIMULATED ANNEALING The Simulated Annealing (SA) method is an emulation of the cooling down process of solids, [vA87]. In SA, the search will start at a high temperature where random search takes the major role of exploring the space. The temperature will decrease as time passes, which reduces the amount of exploration but exploitation will take over as the major part of the search process. Having a possibility ....

P. J. M. van Laarhoven and E. H. L. Aarts. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, 1987.

.... Federal Department of Science and Technology (BMFT) PARAWAN project 413 5839 ITR 9007 BO 1 Introduction Simulated annealing (SA) was first presented by Kirkpatrik et al. 13] for solving hard combinatorial optimization problems and has proven to be a good technique for a lot of applications [2, 11, 12, 14, 15, 16]. The disadvantage of this probabilistic approach is a large amount of computation time for obtaining a near optimal solution. Several attempts on parallelizing SA can be found in the literature for small global memory multiprocessor systems [1, 6, 7, 20] as well as for small distributed memory ....

P.J.M. van Laarhoven, E. Aarts: Simulated Annealing. Theory and Applications. D. Reidel Publishing Company, 1987

....paper we explore the use of simulated annealing, for solving arbitrary integer problems. 2. 2 Solving Using Simulated Annealing Simulated Annealing (SA) is a general purpose meta heuristic method that has been applied successfully to a number of combinatorial optimisation problems [1] 6] 8] 14] [20]. The theory of simulated annealing is derived from the physics of annealing substances. Simulated annealing seeks to minimise an energy function, which in combinatorial optimisation is the objective function. At the beginning of the annealing run there is a high likelihood of accepting any ....

P. van Laarhoven and E. Aarts, Simulated Annealing: Theory and Applications, D Reidel Publishing Company, 1987

....this behavior by setting the initial temperature to a value that accepts a fraction of the moves equal to twice the fraction of random moves that cause improvement. Other than in setting the initial temperature, we use a conventional cooling schedule and a conventional stopping rule [L88] AL87] The maximum number of moves considered at each temperature step is 20 times the number of STSs. The temperature is multiplied by 0.95 as soon as this number of moves have been attempted, or when 25 of this number have been accepted. The procedure terminates when less than 5 of the moves are ....

E. H. L. Aarts and P. J. M. Van Laarhoven. Simulated Annealing: Theory and Applications. 1987. D. Reidel Publishing Company.

....global optimum unless started from its vicinity. To solve this discrete optimization problem we have used the method of simulated annealing (SA) 7] which is a computer simulation of chemical annealing with a temperature parameter T used instead of the true temperature. Under certain conditions [8] this method is able to localize the global minimum of an arbitrary cost function. Simulated annealing uses stochastic relaxation to generate samples which with time (and temperature reduction) converge to the global optimum. We have used the Metropolis algorithm [9] to generate such samples. Let ....

....a safeguard of 1 bit. 3 Note that the frequency above is assumed to be normalized with respect to the sampling frequency. Parameters of the annealing schedule have been chosen experimentally. We have selected the initial temperature T 0 =0.5 to obtain the acceptance ratio of about 0. 8 [8] at the beginning of the relaxation process. Realizing the need for a finer temperature control later in the process, we have slowed down temperature reduction by using three values of ff (ff 1 = 0:9850; ff 2 = 0:9990; ff 3 = 0:9995) Temperature thresholds for switching ff have been chosen ....

P. J. M. van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, 1987.

.... the stochastic technique of Rinnooy Kan and Timmer [27] Stochastic techniques also have the advantage of being easy to parallelize [4] Additional possible approaches to the global optimization problem would be the tunneling algorithm of Levy and Montalvo [21] or a simulated annealing approach [30]. In addition, there are various optimization tools that could improve the performance of the local optimizations. A quasi Newton approach could be used so that instead of refactoring the Hessian matrix at each step, the factorization would be approximated and updated in linear time. Also, ....

P. J. M. van Laarhoven and E. H. L. Aarts, Simulated Annealing: Theory and Applications, D. Reidel Publishing Company, Boston, MA, 1987.

....between the events in one process. We have to cope with many problems including that of bad (deviating or faulty) clocks[KO87] Therefore we might have a closer look at the notion of time to find another solution: 2.4. 1 Virtual Time Lemma 1 (Benthem) Time must satisfy certain obvious conditions[Ben83] 1. Transitivity ( V xyz:x y y z x z) 2. Irreflexivity ( 1) and (2) imply asymmetry) 3. Linearity 4. Eternity ( V x W y:y x; V x W y:x y) 5. Density ( V xy:x y W z:x z y) Leslie Lamport found out that a partial ordering ( called happened before ) can be ....

J. F. A. K. Van Benthem. The Logic of Time. D. Reidel Publishing Company, 1983.

....the vertices of the task graph onto processors in a manner that optimizes some cost criterion. This problem is known to be NP complete except under a few special situations [10, 26] Hence satisfactory sub optimal solutions obtainable in a reasonable amount of computation time are generally sought [5,7 11,14,16,18 22]. In this paper, a very efficient algorithm, based on the Kernighan Lin graph bisection heuristic [11] is proposed for the task allocation problem in the context of a hypercube parallel computer. The effectiveness of the algorithm is evaluated by comparing the quality of mappings obtained with ....

....based on the Kernighan Lin graph bisection heuristic [11] is proposed for the task allocation problem in the context of a hypercube parallel computer. The effectiveness of the algorithm is evaluated by comparing the quality of mappings obtained with those derived using simulated annealing [4, 12, 14] on the same sample problems. The approach proposed in this paper uses a recursive divide and conquer strategy. The optimality criterion used is the total weighted inter processor communication cost under the mapping, subject to the constraint that the computational loads on the processors are ....

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van Laarhoven, P. J. M., and Aarts, E. H. L. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, 1987.

....or the near global minimum of the network energy function, the final state will represent a solution of good quality. Otherwise, a poor solution is likely to be obtained [47] To overcome this local minima problem, several effective approaches have been reported. Earlier, simulated annealing [21, 45] has been devised for solving combinatorial optimization problem. The key idea is from the analogy with statistical thermodynamics. When liquid freezes and crystallizes with very slow cooling, the material structure achieves the minimum state of the thermodynamic energy. This is because there ....

P.J.M. van Laarhoven and E.H.L. Aarts. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, 1987.

....(the first and last respectively) The initial ASAP scheduling is not critical due to the optimization method. The convergence proof of the Simulated Annealing process being assumed by a random initial solution constructed after a full perturbation of all nodes and a slow enough cooling schedule [11]. 4.3 Scheduling algorithm Once an arbitrary solution has been given, a first optimization procedure is run to find the optimal scheduling of the data flow graph on a synchronous machine. Module selection is achieved simultaneously. This is done by using a Simulated Annealing based stochastic ....

P.J.M. van Laarhoven and E.H.L. Arts. Simulated Annealing: Theory and Applications. D.Reidel Publishing Company, 1988.

....technique is based on the following. ffl Physical optimization technique such as Simulated Annealing and Genetic Algorithms have shown to be succesfull in finding near optimal solutions for discrete optimization problems that show NP completeness in their solution space, see for example [1] and [4]. ffl The parallelizability of Genetic Algorithms is much better (in general) than e.g. Simulated Anealing. ffl It is relatively simple to build genetic operators and add these modularly to a genetic algorithm kernel. ffl For example Fox et al. see [3] and [2] have shown that genetic ....

P. J. M. van Laarhoven and E. H. Aarts. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, 1987.

.... space; they find an optimal solution, provided they are given enough time incomplete or approximate algorithms which, leaving out completeness, try to find quickly good solutions in an opportunistic way; these methods are generally based on greedy repair schemes and randomization techniques [7, 6]; although they often produce very good quality results, they cannot guarantee a distance to the optimal valuation. Earth Observation Satellite Scheduling Problems as VCSPs These problems can be casted as additive VVCSPs by : ffl associating a variable v with each photograph p; associating with ....

P. J. M. van Laarhoven and E. H. L. Aarts. Simulated Annealing : Theory and Applications. D. Reidel Publishing Company, 1987.

....of algorithms are described in the following section. 2.2 Non linear relaxation algorithms 2.2. 1 Stochastic relaxation Since the seminal work of Kirkpatrick et al. 24] on simulated annealing, stochastic relaxation has been intensively studied and used in large scale optimization problems [1, 16]. Stochastic relaxation algorithms theoretically guarantee convergence towards the global minimum of highly non linear and non convex objective functions. The final solution theoretically does not depend on the initial state of the system. This class of algorithm thus provides robust solutions ....

....on temperature T . The annealing schedule is defined by a controlled decrease of temperature T . If the temperature is decreased adequately (i.e. slowly enough) one can show that the sampling process converges towards the fundamental states of the system i.e. the minimum energy states (see [1, 16] for convergence theorems) A typical example of a stochastic relaxation algorithm is described in Fig. 2. The algorithm presented in Fig. 2 is based on a sampling process called the Gibbs sampler , proposed by Geman and Geman in [16] for the optimization of MRF related global energy functions. ....

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E.H.L. AARTS and P.J.M. van LAARHOVEN. -- Simulated Annealing: Theory and Applications. -- D. Reidel Publishing Company, 1987.

....of algorithms are described in the following section. 2.2 Non linear relaxation algorithms 2.2. 1 Stochastic relaxation Since the seminal work of Kirkpatrick et al. 28] on simulated annealing, stochastic relaxation has been intensively studied and used in large scale optimization problems [1, 18]. Stochastic relaxation algorithms theoretically guarantee convergence towards the global minimum of highly non linear and non convex objective functions. The final solution theoretically does not depend on the initial state of the system. This class of algorithm thus provides robust solutions ....

....on temperature T . The annealing schedule is defined by a controlled decrease of temperature T . If the temperature is decreased adequately (i.e. slowly enough) one can show that the sampling process converges towards the fundamental states of the system i.e. the minimum energy states (see [1, 18] for convergence theorems) A typical example of a stochastic relaxation algorithm is described in Fig. 2. The algorithm presented in Fig. 2 is based on a sampling process called the Gibbs sampler , proposed by Geman and Geman in [18] for the optimization of MRFrelated global energy functions. ....

[Article contains additional citation context not shown here]

E.H.L. AARTS and P.J.M. van LAARHOVEN. -- Simulated Annealing: Theory and Applications. -- D. Reidel Publishing Company, 1987.

....global optimum unless started from its vicinity. To solve this discrete optimization problem we have used the method of simulated annealing (SA) 8] which is a computer simulation of chemical annealing with a temperature parameter T used instead of the true temperature. Under certain conditions [9] this method is able to localize the global minimum of an arbitrary cost function. Simulated annealing uses stochastic relaxation to generate samples which with time (and temperature reduction) converge to the global optimum. We have used the Metropolis algorithm [10] to generate such samples. The ....

P. van Laarhoven and E. Aarts, Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, 1987.

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P. Laarhoven and F. Aarts, Simulated annealing: theory and applications, D. Reidel Publishing Company, Dordrecht, 1987.

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P. J. M. van Laarhoven and E. H. L. Aarts. Simulated Annealing: Theory and Applications. D. Reidel Publishing Company, Dordrecht, Holland, 1987.

No context found.

P. van Laarhoven and E. Aarts. Simulated Annealing: Theory and Applications. D.Reidel Publishing Company, 1987.

No context found.

P.J.M. van Laarhoven, E.H.L. Aarts [1987] Simulated annealing: theory and applications, D. Reidel Publishing Company, Dordrecht, Holland.

No context found.

P.J.M. van Laarhoven, E.H.L. Aarts [1987] Simulated annealing: theory and applications, D. Reidel Publishing Company, Dordrecht, Holland.

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