Annealing Schedule Research Articles

Stepwise-overlapped parallel annealing and its application to floorplan designs

A new parallel annealing scheme, stepwise-overlapped parallel annealing, is proposed. This can provide a massive speedup using a multiprocessor system with a large number of processors. It decomposes the annealing process by means of Markov chains. The annealing scheme of the systolic algorithm proposed by Aart et al. is improved. The improved annealing schedule keeps a good temperature profile even when a large number of processors are used. The communication pattern is also enhanced. The new parallel annealing algorithm is applied to floorplan design problems. Experimental results show that the new parallel annealing algorithm is highly effective for a large number of processors. The experimental results of the proposed algorithm are compared with those of other parallel annealing algorithms and the distributed genetic algorithm.

Heuristic technique for processor and link assignment in multicomputers

A graph-based solution to the mapping problem using the simulated annealing optimization heuristic is developed. An automated two-phase mapping strategy is formulated: process annealing assigns parallel processes to processing nodes, and connection annealing schedules traffic connections on network data links so that interprocess communication conflicts are minimized. To evaluate the quality of generated mappings. cost functions suitable for simulated annealing that accurately quantify communications overhead are derived. Communication efficiency is formulated to measure the quality of assignments when the optimal mapping is unknown. The mapping scheme is implemented using the hypercube as a host architecture, and results for several image graphs are presented. >

Application of simulated annealing to deconvolution in astronomical speckle imaging

Monte-Carlo type simulated annealing has been investigated as an optimization procedure for reconstructing high spatial resolution astronomical images. In particular, the annealing method is shown to be a powerful technique for phase retrieval in connection with Knox-Thompson speckle correlation data. An annealing schedule is proposed and optimum annealing parameters identified.

A combined multistart-annealing algorithm for continuous global optimization

The application of simulated annealing to the global optimization of a function on a compact subset of R d is discussed. For the Langevin algorithm the class of convergent schedules depends on some a priori knowledge about the form of the function. It is shown that this problem disappears by using the simplest annealing algorithm of jump type, which can also be improved by performing local searches between two consecutive jump times. The resulting algorithm is essentially a multistart technique controlled by an annealing schedule.

A note on the effect of neighborhood structure in simulated annealing

The simulated annealing method is a neighborhood search algorithm that can be used as a heuristic for many combinatorial problems. Recent research has concentrated on the viability of the approach and the appropriate algorithm parameter settings to use in implementation. In this note we consider a problem specific parameter; the neighborhood structure. We motivate the importance of considering the neighborhood by appealing to results on the convergence rate of simulated annealing and previous empirical results. We test several neighborhood structures on four different problems: the traveling salesman problem, the quadratic assignment problem, the quadratic selection problem and the stochastic quadratic selection problem. Our results suggest that for these problem classes and the particular annealing schedule used, small neighborhoods are better.

Constrained simulated annealing for optimized radiation therapy treatment planning

A variation of simulated annealing optimization called ‘constrained simulated annealing’ is used with a simple annealing schedule to automatically optimize beam weights and beam angles in radiation therapy treatment planning. This optimization technique permits the straightforward utilization of any objective function and any set of dose constraints, even those described by non-analytic functions. Constrained simulated annealing is demonstrated using an objective function which minimizes the probability of normal tissue complications subject to the constraint that the entire target volume receive a tumoricidal dose within specified maximum and minimum limits. Target volume dose constraints are determined by points located on the perimeter of the target volume. Probabilities of normal tissue complication are based on published normal tissue complication probability functions and computed from dose-volume histograms calculated on points spread throughout the normal anatomy.

Algorithmic efficiency of simulated annealing for heat exchanger network design

Heat exchanger network synthesis by simulated annealing, a new multivariable optimization method based on the mathematical theory of Markov chains, has recently been reported by Dolan et al. ( Foundations of Computer- Aided Process Operations, CACHE, Elsevier, New York, 1987; AIChE Jl 35, 725, 1989). Two aspects of the algorithm strongly affect computation time: the evaluation of the change in cost between different randomly generated states and the annealing temperature schedule. This paper describes a new implementation of the simulated annealing algorithm that efficiently treats the first aspect through the use of a linked-list data structure to calculate changes in cost directly, resulting in a speed increase of two orders of magnitude over earlier implementations of the algorithm. The second aspect is addressed through the use of the annealing schedule of Aarts and van Laarhoven ( Philips J. Res. 40, 193, 1985). This new implementation of the algorithm is used to generate a new low-cost solution to the 7SP4 problem (Papoulias and Grossmann, Comput. Chem. Engng 7, 707, 1983; Floudas et al., AIChE Jl 32, 276, 1986).

A stepwise-overlapped parallel simulated annealing algorithm

This paper proposes a parallel annealing algorithm, called stepwise-overlapped annealing, that can be efficiently implemented to a multiprocessor system with a large number of processors such as hypercube computers. It is an improved algorithm of the systolic annealing that was proposed by Aarts et al. [8]. We introduce modifications for correcting the temperature decrement strategy and also enhance the communication pattern. Instead of the temperature decrement at each subchain, it calculates the temperature decrement at the start of each Markov chain with the standard deviation of a complete Markov chain previously processed. It is based on an annealing schedule of polynomial time complexity. Experimental results show high efficiencies even when a large number of processors are used. The merit of this parallel annealing algorithm is a simple communication pattern and thus less communication overhead. This parallel annealing algorithm can also effectively replace the high temperature region of the application-dependent parallel simulated annealing algorithms.

A step‐wise‐overlapped parallel annealing algorithm on a message‐passing multiprocessor system

AbstractThis paper proposes a parallel annealing algorithm, called step‐wise‐overlapped parallel annealing, that can provide a massive speed‐up utilizing a multiprocessor system with a large number of processors. We improve the parallel annealing scheme of the systolic algorithm that was proposed by Aart et al. Instead of the temperature decrement at each subchain, it decides the decrement ratio at the start of each Markov chain using the standard deviation of the cost distribution in the previous Markov chain of the full length. Thus the improved annealing schedule keeps a good temperature profile even with a large number of processors. We also enhance the communication pattern.The new parallel annealing algorithm has a simple communication pattern and thus less communication overheads. The decomposition strategy of this parallel annealing algorithm is independent of application problems. Experimental results of the step‐wise‐overlapped parallel annealing algorthm for the travelling salesman problems show high efficiencies even when a large number of processors are used; it produces near optimal solutions with a speedup of 70.8 by using 128 processors. It can be implemented efficiently on a message‐passing multiprocessor system with a large number of processors, such as a hypercube computer.

Optimization of physical data tables by simulated annealing

A simulated annealing program, HMCTAB, has been developed to optimize equation of state data tables for use in large physics simulation codes. A cost function dependent on table error and table size is defined and is used to accept or reject randomly chosen table grid configurations. An annealing schedule reduces the ‘‘temperature’’ parameter and drives the grid configuration toward the optimum. The result is a much smaller table with acceptable error.

Very fast simulated re-annealing

An algorithm is developed to statistically find the best global fit of a nonlinear nonconvex cost-function over a D-dimensional space. It is argued that this algorithm permits an annealing schedule for “temperature” T decreasing exponentially in annealing-time k, T = T 0 exp(– ck 1/ D ). The introduction of re-annealing also permits adaptation to changing insensitivities in the multi-dimensional parameter-space. This annealing schedule is faster than fast Cauchy annealing, where T = T 0/ k, and much faster than Boltzmann annealing, where T = T 0/1 n k. Applications are being made to fit empirical data to Lagrangians representing nonlinear Gaussian–Markovian systems.

Inversion of wave field data by simulated annealing

Simulated annealing is a new Monte-Carlo optimization method that (if properly used) does not get stuck in local minima of the objective function. This feature is attractive for the inversion of wave field data where the lack of low-frequency energy makes cycle skipping a problem. To gain experience with the method, it was applied to a simple problem: determining a sound-speed profile c(z) from recordings of two shots at unequal distances from a vertical array. For a nearly stratified ocean this problem is equivalent to a single shot, recorded on two vertical arrays. A profile c(z), propagating data from the near array to the far array, is assumed and then the propagated data are compared with the actual data at the second array. If the propagated and actual data agree then c(z) is a good profile. If the sound-speed profile has, say, 15 parameters with, say, 10 possible values for each parameter then the number of possible profiles is 1015. In tests with synthetic data, simulated annealing gave a nearly correct profile with a few hours of iteration (on a desk-side workstation). Experiments are currently going on with different annealing schedules. Results so far suggest that critical temperature (Tcr) is difficult to determine, and so annealing strategies which do not require a prior estimate of Tcr are more efficient than those which do. [Work supported by ONR.]

On the Complexity of Computing the Volume of a Polyhedron

We show that computing the volume of a polyhedron given either as a list of facets or as a list of vertices is as hard as computing the permanent of a matrix.

Implementation of an adaptive, constant thermodynamic speed simulated annealing schedule

We present a new implementation of simulated annealing. It calculates its own cooling schedule from thermodynamic information computed enroute. Our schedule proceeds at constant “thermodynamic speed” to minimize the entropy produced along the way. It is based on finite time thermodynamics and is, in some sense, optimal. We use ensembles over the entire configuration space to compute thermodynamic averages. Ensembles provide good statistics for the thermodynamic process as well as a direct, instantaneous measures of the nature of the configuration space with Hamming distances. We compare our implementation with some others on a random graph problem. It is found to produce superior results.

Simulated annealing with constant thermodynamic speed

Arguments are presented to the effect that the optimal annealing schedule for simulated annealing proceeds with constant thermodynamic speed, i.e., with dT dt = -(vT) (ϵ C ) , where T is the temperature, ϵ is the relaxation time, C is the heat capacity, t is the time, and v is the (constant) thermodynamic speed. Experimental results on a graph partitioning problem which can be solved exactly are shown to be consistent with this conjecture.

Laser Deposition of Gold

ABSTRACTMetallic gold was deposited on several different substrates by laser pyrolysis of a goldcontaining ink. The gold was deposited in the form of lines by translating the substrate during laser pyrolysis; linewidths ranged from 10 Am to 1.5 mm. This process was performed in open air. Prior to annealing, the films contain 40 to 50 % carbon impurity and the resistivity is extremely high. After a 1 hour anneal in air, the carbon content is reduced to < 5 %, and the resistivity is reduced to roughly 13 times bulk gold. Further improvement may be possible with a different annealing schedule.

Transport in refractory metals and their interaction with SiO 2: Comparison of tungsten and molybdenum

We have investigated sputtered and electron-beam-evaporated thin films of tungsten and molybdenum deposited onto 100 Å SiO 2. These two refractory metals have comparable room temperature resistivities (5–6 μΩ cm) and a work function at the midgap between n + and p + polycrystalline silicon. Therefore both can be considered for application as a gate electrode in submicron very large scale integration technology. We have probed their interaction with SiO 2 using Auger spectroscopy, cross-sectional transmission electron microscopy (CTEM) and with current-voltage ( I-V) characteristics of molybdenum and tungsten metal/oxide/ semiconductor (MOS) capacitors as a function of the annealing temperature. We have also measured electrical resistivity in the 4.2–300K temperature range to ascertain the differences and the similarities between the two. We find that, in terms of resistivity, the difference between the two metals is slight. Although at room temperature, ρ Mo is 10% higher than ρ w, at liquid nitrogen, molybdenum is around 30% more conductive after a 900–1000°C anneal. The interface with SiO 2 appears in CTEM to be very smooth for both. Auger depth profiling, however, reveals some interface interaction for molybdenum, but not tungsten. This is confirmed with leakage and breakdown measurements on an MOS capacitor structure 32 mm in diameter. After anneals at and above 900°C, molybdenum capacitors on 100 Å oxide are all shorted. The same annealing schedule produces a reasonable distribution of breakdown voltages for tungsten capacitors.

A statistical mechanical study of Boltzmann machines

Hinton and Sejnowski (1983) have described recently a novel statistical mechanical system which they named the Boltzmann machine. The interesting property of Boltzmann machines is that they can learn to recognise the structure in a set of patterns simply by being shown an example subset of patterns. In this paper some numerical simulations of Boltzmann machines are reported. It is found that the annealing schedule proposed by Ackley, Hinton and Sejnowski (1985) is adequate to obtain a Boltzmann distribution of states, on which the key part of the algorithm depends, but it is clear that the algorithm will require massive computations for large networks. It is also found that there is a window of annealing temperatures at which learning is possible, and the sensitivity of the learning rate to temperature can be understood in terms of the density of states at low energies. Direct calculations of the partition function in small instances of Boltzmann machines are used to characterise the number of states which are thermally accessible for particular annealing schedules. Finally, since Boltzmann machines bear some resemblance to models of disordered magnetic systems, a comparison is made with results for the Sherrington-Kirkpatrick spin-glass model. Both systems support multiple metastable states (i.e. stable with respect to single spin flips), but, in contrast to the SK spin glass, Boltzmann machines exhibit a random distribution of low-energy states in terms of Hamming distance.

Criteria for an optimum simulated annealing schedule for problems of the travelling salesman type

The simulated annealing algorithm for optimisation problems such as the travelling salesman problem is reviewed. The concept of the autocorrelation function for cost functions is introduced and it is shown how numerical experiments to measure this quantity can provide criteria as to how rapidly a system can be annealed close to equilibrium. From this the authors obtain an optimum annealing schedule of general applicability.

Partitioning concurrent VLSI simulation programs onto a multiprocessor by simulated annealing

Efficiently loading concurrent programs onto multiprocessor architectures is a graph partitioning problem where both the edges and vertices are weighted. The corresponding optimisation problem is computationally NP-hard, and the optimal solution can only be found by exhaustively examining all possible partitioning configurations. Near-optimal solutions can be found by using heuristic algorithms such as iterative improvement and simulated annealing. The simulated annealing heuristic is experimentally evaluated against simple iterative improvement for graphs representing the concurrent simulation programs of four VLSI circuits where the vertices were weighted. A simple cost function and an annealing schedule are presented for partitioning the graphs onto a star network of identical processors. Experimental results show that simulated annealing produces a better solution than simple iterative improvement but at the expense of considerable computer running times. It is suggested that the time required for simulated annealing to give better solutions than iterative improvement depends on the nature of distributions of weighted vertices and edges in the concurrent simulation graph as well as its size.