Use Of Simulated Annealing Research Articles

Improved Coverings of a Square with Six and Eight Equal Circles

In a recent article, Tarnai and Gáspár used computer simulations to find thin coverings of a square with up to ten equal circles. We will give improved coverings with six and eight circles and a new, thin covering with eleven circles, found by the use of simulated annealing. Furthermore, we present a combinatorial method for constructing lower bounds for the optimal covering radius.

Optimal Ground‐Water Remediation Design Using Multiple Control Technologies

AbstractCombined optimization‐simulation models for designing ground‐water remediation systems generally focus on design strategies that use only one remedial technology, typically pumping. In practice, many field remediation programs use pumping along with one or more additional ground‐water control technologies, such as drains, trenches, slurry walls, and low permeability caps. Simulated annealing provides a flexible optimization framework that can incorporate a number of different remedial technologies into the design process. Using simulated annealing, additional remedial technologies can be added to or subtracted from the optimization at any time. This flexibility can provide for remedial design evaluations that are more consistent with current field implementations. The use of simulated annealing is demonstrated by a series of hypothetical remediation design problems that incorporate four different remedial technologies. The computed optimal design solution depends on the relative costs of the remedial tools as specified by the cost function and on the effects that each tool has on the system behavior. A sensitivity analysis can reveal which costs are critical to the outcome of the optimization.

Use of simulated annealing and neural nets for the eco-techno-economic synthesis of mineral and metallurgical flowsheets

The principal objective of this paper is to introduce simulated annealing to the synthesis of flowsheets in metallurgy and minerals processing. This optimisation methodology will be discussed initially followed by the development of synthesis models for minerals processing and metallurgical flowsheets incorporated in the simulated annealing framework. In a recent paper by the authors a methodology was developed by which complex metallurgical process routes can be synthesised as a function of various ecological, technological and economical aspects. In that paper, however, the process routes were based on the flow of one element only. Therefore, a further objective of this paper is to expand this proposed eco-techno-economic synthesis procedure to incorporate any number of elements by the introduction of simulated annealing as the optimisation procedure.

Variants of simulated annealing for the examination timetabling problem

This paper is concerned with the use of simulated annealing in the solution of the multi-objective examination timetabling problem. The solution method proposed optimizes groups of objectives in different phases. Some decisions from earlier phases may be altered later as long as the solution quality with respect to earlier phases does not deteriorate. However, such limitations may disconnect the solution space, thereby causing optimal or near-optimal solutions to be missed. Three variants of our basic simulated annealing implementation which are designed to overcome this problem are proposed and compared using real university data as well as artificial data sets. The underlying principles and conclusions stemming from the use of this method are generally applicable to many other multi-objective type problems.

Packing 16, 17 or 18 circles in an equilateral triangle

We present new, efficient packings for 16, 17 and 18 congruent circles in an equilateral triangle. The results have been found by the use of simulated annealing and a quasi-Newton optimization technique, supplemented with some human intelligence.

The stochastic inversion of magnetics and resistivity data using the simulated annealing algorithm1

AbstractSimulated annealing is a stochastic combinatorial optimization technique, based on ideas from statistical mechanics, thermodynamics and multivariable probability theory. This paper presents the use of simulated annealing as a means of inversion for both linear magnetics and non‐linear resistivity problems. The subsurface is viewed as being constructed of smaller elemental blocks which possess either uniform internal magnetization or conductivity, enabling larger structures to be modelled. Simulated annealing is employed to calculate the distribution of the particular physical property which causes a measured anomalous field curve.A general description of simulated annealing and its application is given, followed by specific descriptions of its application to the magnetics and resistivity cases.For the magnetics case the subsurface consists of 2D prismatic elements as the basis for the forward model. Synthetic model data is used to test the algorithm and an example of actual field data; a survey across an igneous dike is used to demonstrate the use of the method with real data. In the resistivity case, the finite‐element method is used to generate the forward models. Synthetic vertical profiling data is used to test the application of the simulated annealing method to the resistivity case. Actual data from an archaeological survey is used to show again the use of the method with real data.Simulated annealing is shown to be capable of inverting both the linear and non‐linear methods of magnetic surveying and resistivity surveying respectively.

Phase optimization of a kinoform by simulated annealing

The design of a kinoform by the use of simulated annealing is discussed. The simulated annealing process is applied to decrease the reconstruction noise and to adjust the phase distribution of the kinoform to the configuration of the recording device. A liquid-crystal spatial light modulator is used to display the kinoform. The reconstructed image of the optimized kinoform is found to be in good agreement with the computed image. Some experimental results obtained with a liquid-crystal spatial light modulator are presented. The phase quantization effect of the kinoform is discussed.

Routeing winter gritting vehicles

When roads may become dangerously slippery due to frost, ice or snow, local authorities treat the roads by spreading a de-icing agent (usually salt) on them. In order to treat a road, a winter gritting vehicle must travel down the road once, spreading salt on to both sides of the carriageway. An application is described where routes were constructed for gritters in a local authority area. The formulation of the model is presented which involves dealing with multiple depot locations, limited vehicle capacities, and roads with different priorities (for example, some must be treated within two hours and others within four hours of the start of gritting). The objective function to be optimised depends on both the total distance travelled, and the number and capacity of the gritters. The solution method is a heuristic algorithm, which involves, as a first stage, the optimal solution of an unconstrained Chinese Postman Problem for the network, and followed by the use of Simulated Annealing for the constrained problem.

Estimation of seismoacoustic properties of the ocean bottom by matched-field inversion

Matched-field processing of acoustic field data provides a straightforward but powerful method for estimating the elastic properties of the ocean bottom. The success of the inversion depends in part on having an efficient algorithm for searching the multidimensional parameter space of ocean bottom models. This paper considers the use of simulated annealing as a search algorithm for matched-field inversion (MFI), and presents results of inversions for data obtained from the PACIFIC ECHO experiments. A method is described for adaptively guiding the annealing process by adding a feedback loop that assesses the significance of the matched-field correlations for each parameter. The search is guided to regions of the parameter space associated with above-average correlations. Simulations for a vertical line array (VLA) are presented to demonstrate the limits on performance of MFI with respect to uncertainties in experimental geometry, and low signal-to-noise ratio. The method is applied to VLA data from thin-sediment PACIFIC ECHO environments where the age of the upper oceanic crust varied from 0.1 to 66 million years. The MFI results indicate an age dependence of the compressional and shear wave speeds of the basalt, and the values are significantly lower than those obtained for thickly sedimented crust.

Design of Binary Computer Generated Holograms by Simulated Annealing

Abstract The simulated annealing algorithm allows optimal solutions to the binary hologram design problems to be located. When compared with sub-optimal techniques such as direct binary search it requires a significantly longer optimization time. We compare simulated annealing and direct binary search for the design of fanout holograms. Over a large range of design parameters no significant improvement is obtained by the use of simulated annealing. When diffraction efficiencies are maximized however metastable states are observed and simulated annealing results in a 6·6% increase in diffraction efficiency and a tenfold reduction in reconstruction error.

The use of simulated annealing in chromosome reconstruction experiments based on binary scoring.

We present a method of combinatorial optimization, simulated annealing, to order clones in a library with respect to their position along a chromosome. This ordering method relies on scoring each clone for the presence or absence of specific target sequences, thereby assigning a digital signature to each clone. Specifically, we consider the hybridization of oligonucleotide probes to a clone to constitute the signature. In that the degree of clonal overlap is reflected in the similarity of their signatures, it is possible to construct maps based on the minimization of the differences in signatures across a reconstructed chromosome. Our simulations show that with as few as 30 probes and a clonal density of 4.5 genome equivalents, it is possible to assemble a small eukaryotic chromosome into 33 contiguous blocks of clones (contigs). With higher clonal densities and more probes, this number can be reduced to less than 5 contigs per chromosome.

Simulated Annealing with a Temperature Dependent Penalty Function

We formulate the problem of permuting a matrix to block angular form as the combinatorial minimization of an objective function. We motivate the use of simulated annealing (SA) as an optimization tool. We then introduce a heuristic temperature dependent penalty function in the simulated annealing cost function, to be used instead of the real objective function being minimized. Finally we show that this temperature dependent penalty function version of simulated annealing consistently outperforms the standard simulated annealing approach, producing, with smaller running times, better solutions. We believe that the use of a temperature dependent penalty function may be useful in developing SA algorithms for other combinatorial problems. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

Optimization of brachytherapy dose distributions by simulated annealing.

An algorithm based on the method of simulated annealing is presented for optimizing brachy-therapy dose distributions. The algorithm accommodates either static configurations of multiple sources or single stepping sources, hence in principle can be used to optimize both low- and high-dose rate treatments delivered with remote afterloading equipment. Required inputs include the specification of target dose rates and dose rate limits, expressed in absolute or relative terms, at operator selected points near the treatment site. The influence of the dose rate limits can be adjusted continuously through the use of one or more penalty factors. The algorithm generates a set of integer weights, one for each available source position, which are interpreted in terms of configuration occupancy numbers for static source arrangements and relative dwell times for stepping sources. Application is made to several variations of a hypothetical low-dose rate vaginal vault planning problem involving one rectal and six applicator calculation points. The algorithm's performance for different source strengths, annealing schedules, target dose rates, dose rate limits, and values of a single penalty factor lambda was examined. With a simple annealing schedule and value of lambda = 25, the algorithm found solutions of high quality for all problem variants. The CPU time required for optimization on a Vax 11/750 computer ranged from 2 min for a single configuration to 25 min for a solution consisting of four configurations. These results support the use of simulated annealing for clinical planning of low dose rate vaginal treatments, and encourage investigation of other applications in brachytherapy.

Structure and molecular model refinement of Rhizomucor miehei triacyglyceride lipase: a case study of the use of simulated annealing in partial model refinement

Structure and molecular model refinement of <i>Rhizomucor miehei</i> triacyglyceride lipase: a case study of the use of simulated annealing in partial model refinement

Optimization of signal distribution networks using simulated annealing

The author discusses the use of simulated annealing for optimizing signal distribution networks consisting of multiplexers, switches, buses and end-devices or users. A linear algebraic approach is developed for application of simulated annealing to problems of this kind. The author shows how such an approach allows for the optimization of general capacity-constrained signal distribution networks containing multiple levels of demultiplexers, switches, and buses, with linear and nonlinear objective functions. Examples include both linear and nonlinear objective functions. >

Composite stock cutting through simulated annealing

This paper explores the use of Simulated Annealing as an optimization technique for the problem of Composite Material Stock Cutting. The shapes are not constrained to be convex polygons or even regular shapes. However, due to the composite nature of the material, the orientation of the shapes on the stock is restricted. For placements of various shapes, we show how to determine a cost function, annealing parameters and performance.

Monte Carlo simulation for folded structure of peptides

We have carried out Monte Carlo simulations to predict tertiary structure of a few peptides with the use of simulated annealing. The simulation is made in a completely unrestricted manner using generic potential energy parameters determined for each amino acid as input. For the isolated C-peptide fragment of ribonuclease A we found that the α-helix appears close to the ground state of this peptide in agreement with the indication from the experiment. We have also succeeded in reproducing the α-helix propensity for several amino acid residues in homopolymer simulations.

An improved annealing scheme for the QAP

Recently there has been some interest in the use of Simulated Annealing to obtain ‘good’ solutions to a number of combinatorial problems. This paper reports on the use of this method applied to the Quadratic Assignment Problem (i.e. the assignment of inter-communicating objects to locations to minimize the total cost of communication between them). The result is a much-improved annealing scheme for this problem which performs well on a range of examples, finding improved solutions for several of the largest problems available in the literature and requiring only modest amounts of computational effort.

The use of simulated annealing for clustering data in databases

PDRT is a prototype design tool which is currently being developed for database workload capture and analysis with an emphasis on performance. A major feature of this tool is a clustering facility which can be used to optimise the proximity between inter-related tuples on a hierarchy of secondary storage devices in order to enhance retrieval performance. As a step towards obtaining a good clustering method we have previously shown that simulated annealing, which is a derivative of the Metropolis Monte Carlo optimisation algorithm, provides an effective solution to this NP-complete placement problem. In this paper we discuss and evaluate new “flavours” of this heuristic methodology found in the literature and investigate the effect of the initial configuration upon the final result.

Synthesis of electrostatic lenses by simulated annealing

The use of simulated annealing is proposed for automatic design of electrostatic lenses with given first-order properties and minimum aberrations. The synthesis of a high-quality lens for focusing an ion beam produced by a liquid-metal source is shown as an example.