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Journal articles on the topic 'Fast simulated annealing'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Bonilla-Petriciolet, Adrián, Juan Carlos Tapia-Picazo, Carlos Soto-Becerra, and Javier Gerson Zapiain-Salinas. "Perfiles de comportamiento numérico de los métodos estocásticos simulated annealing y very fast simulated annealing en cálculos termodinámicos." Ingeniería, investigación y tecnología 12, no. 1 (January 1, 2011): 51–62. http://dx.doi.org/10.22201/fi.25940732e.2011.12n1.006.

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2

Szu, Harold, and Ralph Hartley. "Fast simulated annealing." Physics Letters A 122, no. 3-4 (June 1987): 157–62. http://dx.doi.org/10.1016/0375-9601(87)90796-1.

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3

Henrique Cardoso Camelo, Pedro, and Rafael Lima De Carvalho. "Multilayer Perceptron optimization through Simulated Annealing and Fast Simulated Annealing." Academic Journal on Computing, Engineering and Applied Mathematics 1, no. 2 (June 10, 2020): 28–31. http://dx.doi.org/10.20873/uft.2675-3588.2020.v1n2.p28-31.

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The Multilayer Perceptron (MLP) is a classic and widely used neural network model in machine learning applications. As the majority of classifiers, MLPs need well-defined parameters to produce optimized results. Generally, machine learning engineers use grid search to optimize the hyper-parameters of the models, which requires to re-train the models. In this work, we show a computational experiment using metaheuristics Simulated Annealing and Fast Simulated Annealing for optimization of MLPs in order to optimize the hyper-parameters. In the reported experiment, the model is used to optimize two parameters: the configuration of the neural network layers and its neuron weights. The experiment compares the best MLPs produced by the SA and FastSA using the accuracy and classifier complexity as comparison measures. The MLPs are optimized in order to produce a classifier for the MNIST database. The experiment showed that FastSA has produced a better MLP, using less computational time and less fitness evaluations.

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4

Camelo, Pedro Henrique Cardoso, and Rafael Lima De Carvalho. "Multilayer Perceptron optimization through Simulated Annealing and Fast Simulated Annealing." Academic Journal on Computing, Engineering and Applied Mathematics 1, no. 2 (June 10, 2020): 28–31. http://dx.doi.org/10.20873/ajceam.v1i2.9474.

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The Multilayer Perceptron (MLP) is a classic and widely used neural network model in machine learning applications. As the majority of classifiers, MLPs need well-defined parameters to produce optimized results. Generally, machine learning engineers use grid search to optimize the hyper-parameters of the models, which requires to re-train the models. In this work, we show a computational experiment using metaheuristics Simulated Annealing and Fast Simulated Annealing for optimization of MLPs in order to optimize the hyper-parameters. In the reported experiment, the model is used to optimize two parameters: the configuration of the neural network layers and its neuron weights. The experiment compares the best MLPs produced by the SA and FastSA using the accuracy and classifier complexity as comparison measures. The MLPs are optimized in order to produce a classifier for the MNIST database. The experiment showed that FastSA has produced a better MLP, using less computational time and less fitness evaluations.

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5

Ingber, L. "Very fast simulated re-annealing." Mathematical and Computer Modelling 12, no. 8 (1989): 967–73. http://dx.doi.org/10.1016/0895-7177(89)90202-1.

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6

Lee, Chung-Yeol, Sun-Young Lee, Soo-Min Lee, Jong-Seok Lee, and Cheol-Hoon Park. "Fast Simulated Annealing with Greedy Selection." KIPS Transactions:PartB 14B, no. 7 (December 31, 2007): 541–48. http://dx.doi.org/10.3745/kipstb.2007.14-b.7.541.

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7

Guo, Hong, Martin Zuckermann, R. Harris, and Martin Grant. "A Fast Algorithm for Simulated Annealing." Physica Scripta T38 (January 1, 1991): 40–44. http://dx.doi.org/10.1088/0031-8949/1991/t38/010.

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8

Szu, H. H., and R. L. Hartley. "Nonconvex optimization by fast simulated annealing." Proceedings of the IEEE 75, no. 11 (1987): 1538–40. http://dx.doi.org/10.1109/proc.1987.13916.

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9

Lu, Zhiwu, Yuxin Peng, and Horace H. S. Ip. "Combining multiple clusterings using fast simulated annealing." Pattern Recognition Letters 32, no. 15 (November 2011): 1956–61. http://dx.doi.org/10.1016/j.patrec.2011.09.022.

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10

Lee, Chang-Yong, and Dongju Lee. "Determination of initial temperature in fast simulated annealing." Computational Optimization and Applications 58, no. 2 (December 24, 2013): 503–22. http://dx.doi.org/10.1007/s10589-013-9631-y.

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11

Thompson, M., and J. K. Fidler. "Fast antenna tuning using transputer based simulated annealing." Electronics Letters 36, no. 7 (2000): 603. http://dx.doi.org/10.1049/el:20000502.

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12

Harada, Ryuhei, Tomotake Nakamura, and Yasuteru Shigeta. "A Fast Convergent Simulated Annealing Algorithm for Protein-Folding: Simulated Annealing Outlier FLOODing (SA-OFLOOD) Method." Bulletin of the Chemical Society of Japan 89, no. 11 (November 15, 2016): 1361–67. http://dx.doi.org/10.1246/bcsj.20160244.

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13

Liu, Hsiao-Chung, and Jeng-Sheng Huang. "Pattern recognition using evolution algorithms with fast simulated annealing." Pattern Recognition Letters 19, no. 5-6 (April 1998): 403–13. http://dx.doi.org/10.1016/s0167-8655(98)00025-7.

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14

Prémont, Guy, and Yunlong Sheng. "Fast design of circular-harmonic filters using simulated annealing." Applied Optics 32, no. 17 (June 10, 1993): 3116. http://dx.doi.org/10.1364/ao.32.003116.

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15

Kuperman, W. A., Michael D. Collins, John S. Perkins, and N. R. Davis. "A fast simulated‐annealing algorithm for time‐domain beamforming." Journal of the Acoustical Society of America 87, S1 (May 1990): S154. http://dx.doi.org/10.1121/1.2028050.

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16

Palubeckis, Gintaras. "Fast simulated annealing for single-row equidistant facility layout." Applied Mathematics and Computation 263 (July 2015): 287–301. http://dx.doi.org/10.1016/j.amc.2015.04.073.

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17

Fiannaca, Antonino, Giuseppe Di Fatta, Riccardo Rizzo, Alfonso Urso, and Salvatore Gaglio. "Simulated annealing technique for fast learning of SOM networks." Neural Computing and Applications 22, no. 5 (December 28, 2011): 889–99. http://dx.doi.org/10.1007/s00521-011-0780-6.

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18

Mendivil, F., R. Shonkwiler, and M. C. Spruill. "Restarting search algorithms with applications to simulated annealing." Advances in Applied Probability 33, no. 1 (March 2001): 242–59. http://dx.doi.org/10.1017/s0001867800010727.

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Some consequences of restarting stochastic search algorithms are studied. It is shown under reasonable conditions that restarting when certain patterns occur yields probabilities that the goal state has not been found by the nth epoch which converge to zero at least geometrically fast in n. These conditions are shown to hold for restarted simulated annealing employing a local generation matrix, a cooling schedule Tn ∼ c/n and restarting after a fixed number r + 1 of duplications of energy levels of states when r is sufficiently large. For simulated annealing with logarithmic cooling these probabilities cannot decrease to zero this fast. Numerical comparisons between restarted simulated annealing and several modern variations on simulated annealing are also presented and in all cases the former performs better.

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19

Furao, Shen, and Osamu Hasegawa. "Fractal Image Coding with Simulated Annealing Search." Journal of Advanced Computational Intelligence and Intelligent Informatics 9, no. 1 (January 20, 2005): 80–88. http://dx.doi.org/10.20965/jaciii.2005.p0080.

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The main shortcomings of fractal image coders are (1) the slow speed for searching domain block pool, and (2) known fast algorithms leading to a loss of image quality. We propose efficient fractal image coding using simulated annealing method. Compared to previous schemes, our proposal greatly increases the search speed of domain block pool with almost no image quality loss. Experimental results indicate the high feasibility of the proposed method, which is, furthermore, extendable to other fractal coders.

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20

Srigutomo, Wahyu, Mohammad Heriyanto, and Muhamad Hilmi Aufa. "Gravity Inversion of Talwani Model using Very Fast Simulated Annealing." Journal of Mathematical and Fundamental Sciences 51, no. 2 (August 2019): 177–90. http://dx.doi.org/10.5614/j.math.fund.sci.2019.51.2.7.

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21

Fakheri Tabrizi, Aysa, Laleh Behjat, William Swartz, and Logan Rakai. "A fast force-directed simulated annealing for 3D IC partitioning." Integration 55 (September 2016): 202–11. http://dx.doi.org/10.1016/j.vlsi.2016.06.003.

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22

Pouliot, Jean, Daniel Tremblay, Jean Roy, and Santo Filice. "Optimization of permanent 125I prostate implants using fast simulated annealing." International Journal of Radiation Oncology*Biology*Physics 36, no. 3 (October 1996): 711–20. http://dx.doi.org/10.1016/s0360-3016(96)00365-3.

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23

Pospichal, Jiri, and Vladimir Kvasnicka. "Fast evaluation of chemical distance by a simulated-annealing algorithm." Journal of Chemical Information and Modeling 33, no. 6 (November 1, 1993): 879–85. http://dx.doi.org/10.1021/ci00016a010.

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24

Ryu, Seun, Guang Lin, Xin Sun, Mohammad Khaleel, and Dongsheng Li. "Adaptive multiple super fast simulated annealing for stochastic microstructure reconstruction." International Journal of Theoretical and Applied Multiscale Mechanics 2, no. 4 (2013): 287. http://dx.doi.org/10.1504/ijtamm.2013.062161.

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25

Leite, Nuno, Fernando Melício, and Agostinho C. Rosa. "A fast simulated annealing algorithm for the examination timetabling problem." Expert Systems with Applications 122 (May 2019): 137–51. http://dx.doi.org/10.1016/j.eswa.2018.12.048.

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26

Saab, Youssef. "A Fast Clustering-Based Min-Cut Placement Algorithm With Simulated-Annealing Performance." VLSI Design 5, no. 1 (January 1, 1996): 37–48. http://dx.doi.org/10.1155/1996/58084.

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Placement is an important constrained optimization problem in the design of very large scale (VLSI) integrated circuits [1–4]. Simulated annealing [5] and min-cut placement [6] are two of the most successful approaches to the placement problem. Min-cut methods yield less congested and more routable placements at the expense of more wire-length, while simulated annealing methods tend to optimize more the total wire-length with little emphasis on the minimization of congestion. It is also well known that min-cut algorithms are substantially faster than simulated-annealing-based methods. In this paper, a fast min-cut algorithm (ROW-PLACE) for row-based placement is presented and is empirically shown to achieve simulated-annealing-quality wire-length on a number of benchmark circuits. In comparison with Timberwolf 6 [7], ROW-PLACE is at least 12 times faster in its normal mode and is at least 25 times faster in its faster mode. The good results of ROW-PLACE are achieved using a very effective clustering-based partitioning algorithm in combination with constructive methods that reduce the wire-length of nets involved in terminal propagation.

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27

Wang, Lei, and Yongqiang Liu. "Application of Simulated Annealing Particle Swarm Optimization Based on Correlation in Parameter Identification of Induction Motor." Mathematical Problems in Engineering 2018 (July 8, 2018): 1–9. http://dx.doi.org/10.1155/2018/1869232.

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The strengths and weaknesses of correlation algorithm, simulated annealing algorithm, and particle swarm optimization algorithm are studied in this paper. A hybrid optimization algorithm is proposed by drawing upon the three algorithms, and the specific application processes are given. To extract the current fundamental signal, the correlation algorithm is used. To identify the motor dynamic parameter, the filtered stator current signal is simulated using simulated annealing particle swarm algorithm. The simulated annealing particle swarm optimization algorithm effectively incorporates the global optimization ability of simulated annealing algorithm with the fast convergence of particle swarm optimization by comparing the identification results of asynchronous motor with constant torque load and step load.

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28

Xu, Yueshu, Qian Ye, and Guoxiang Meng. "Hybrid phase retrieval algorithm based on modified very fast simulated annealing." International Journal of Microwave and Wireless Technologies 10, no. 9 (June 22, 2018): 1072–80. http://dx.doi.org/10.1017/s1759078718000971.

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AbstractThe Misell algorithm is one of the most widely used phase retrieval holography methods for large reflector antennas to measure surface deformation. However, it usually locks in a local minimum because it heads downhill from an initial estimation without any consideration whether it heads for a global minimum or not. The core problem of the Misell algorithm is to find an initial estimation near the global minimum to avoid local stagnation. To cope with the problem, we construct a hybrid Misell algorithm, named modified very fast simulated annealing (MVFSA)-Misell algorithm, to search for the global minimum with a high efficiency. The algorithm is based on the combination of the MVFSA algorithm and Misell algorithm. Firstly, the MVFSA is utilized to obtain a rough position near the global minimum in limited steps. Then, the Misell algorithm starts from the rough position to converge to the global minimum with high speed and accuracy. The convergence characteristic of the proposed algorithm was discussed in detail through digital simulation. Simulation results show that the algorithm can reach global minimum in a very short time. Unlike the traditional Misell algorithm, the hybrid algorithm is not influenced by initial phase estimation.

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29

Ding, Xinqiang, Yujin Wu, Yanming Wang, Jonah Z. Vilseck, and Charles L. Brooks. "Accelerated CDOCKER with GPUs, Parallel Simulated Annealing, and Fast Fourier Transforms." Journal of Chemical Theory and Computation 16, no. 6 (May 6, 2020): 3910–19. http://dx.doi.org/10.1021/acs.jctc.0c00145.

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30

Tung-Chieh Chen and Yao-Wen Chang. "Modern floorplanning based on B/sup */-tree and fast simulated annealing." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 25, no. 4 (April 2006): 637–50. http://dx.doi.org/10.1109/tcad.2006.870076.

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31

Mageras, G. S., and R. Mohan. "Application of fast simulated annealing to optimization of conformal radiation treatments." Medical Physics 20, no. 3 (May 1993): 639–47. http://dx.doi.org/10.1118/1.597012.

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32

Nguyen, Luan T., and Tamara Nestorović. "Unscented hybrid simulated annealing for fast inversion of tunnel seismic waves." Computer Methods in Applied Mechanics and Engineering 301 (April 2016): 281–99. http://dx.doi.org/10.1016/j.cma.2015.12.004.

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33

Balasaraswathi M and Kalpana B. "Fast and Effective Classification using Parallel and Multi-start PSO." Journal of Information Technology Research 11, no. 2 (April 2018): 13–30. http://dx.doi.org/10.4018/jitr.2018040102.

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PSO being a swarm based algorithm, can efficiently lend itself to operate on huge data. This article presents a technique that performs classification using PSO. An initial discussion is carried out describing PSO as a classifier. Three variants of PSO are proposed here; the first variant hybridizes PSO using Simulated Annealing and the next two variants parallelizes PSO. The two parallel variants of PSO are; Parallel PSO and Multistart PSO. Parallel PSO operates by parallelizing the operation of each of the particles and Multistart PSO runs several normal versions of PSO embedded with Simulated Annealing in parallel. The multi-start version is implemented to eliminate the problem of local optima. Experiments were conducted to identify the scalability and efficiency of PSO and its variants on huge and imbalanced data.

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34

Nascimento, V. B., V. E. de Carvalho, C. M. C. de Castilho, B. V. Costa, and E. A. Soares. "The fast simulated annealing algorithm applied to the search problem in LEED." Surface Science 487, no. 1-3 (July 2001): 15–27. http://dx.doi.org/10.1016/s0039-6028(01)01096-2.

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35

Li, Xin, Toshio Koike, and Mahadevan Pathmathevan. "A very fast simulated re-annealing (VFSA) approach for land data assimilation." Computers & Geosciences 30, no. 3 (April 2004): 239–48. http://dx.doi.org/10.1016/j.cageo.2003.11.002.

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36

Yuping, Z., J. Shouwei, and Z. Chunli. "A very fast simulated re-annealing algorithm for the leather nesting problem." International Journal of Advanced Manufacturing Technology 25, no. 11-12 (March 29, 2004): 1113–18. http://dx.doi.org/10.1007/s00170-003-1966-6.

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37

Sharma, S. P., and P. Kaikkonen. "Global Optimisation of Time Domain Electromagnetic Data Using Very Fast Simulated Annealing." Pure and Applied Geophysics 155, no. 1 (June 1, 1999): 149–68. http://dx.doi.org/10.1007/s000240050259.

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38

Akram, Kashif, Khurram Kamal, and Alam Zeb. "Fast simulated annealing hybridized with quenching for solving job shop scheduling problem." Applied Soft Computing 49 (December 2016): 510–23. http://dx.doi.org/10.1016/j.asoc.2016.08.037.

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39

Shibata, Hiroki, Hiroshi Ishikawa, and Yasufumi Takama. "Crystalizing Effect of Simulated Annealing on Boltzmann Machine." Journal of Advanced Computational Intelligence and Intelligent Informatics 23, no. 3 (May 20, 2019): 474–84. http://dx.doi.org/10.20965/jaciii.2019.p0474.

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This paper proposes a method to estimate the posterior distribution of a Boltzmann machine. Due to high feature extraction ability, a Boltzmann machine is often used for both of supervised and unsupervised learning. It is expected to be suitable for multimodal data because of its bi-directional connection property. However, it needs a sampling method to estimate the posterior distribution, which becomes a problem during an inference period because of the computation time and instability. Therefore, it is usually converted to feedforward neural networks, which means to lose its bi-directional property. To deal with these problems, this paper proposes a method to estimate the posterior distribution of a Boltzmann machine fast and stably without converting it to feedforward neural networks. The key idea of the proposed method is to estimate the posterior distribution using a simulated annealing on non-uniform temperature distribution. The advantage of the proposed method against Gibbs sampling and conventional simulated annealing is shown through experiments with artificial dataset and MNIST. Furthermore, this paper also gives the mathematical analysis of Boltzmann machine’s behaviour with regard to temperature distribution.

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40

Jhang, Kyoung-Son, Soonhoi Ha, and Chu Shik Jhon. "Simulated Annealing Approach to Crosstalk Minimization in Gridded Channel Routing." VLSI Design 7, no. 1 (January 1, 1998): 85–95. http://dx.doi.org/10.1155/1998/81296.

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The inter-wire spacing in a VLSI chip becomes closer as the VLSI fabrication technology rapidly evolves. Accordingly, it becomes important to minimize crosstalk caused by the coupling capacitance between adjacent wires in the layout design for the fast and safe VLSI circuits. We present a simulated annealing approach based on segment rearrangement to crosstalk minimization in an initially gridded channel routing. The proposed technique is compared with previous track-oriented techniques, especially a track permutation technique whose performance is bounded by an exhaustive track permutation algorithm. Experiments showed that the presented technique is more effective than the track permutation technique.

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41

Myong, Seung Yeop. "Annealing Kinetic Model Using Fast and Slow Metastable Defects for Hydrogenated-Amorphous-Silicon-Based Solar Cells." Advances in OptoElectronics 2007 (June 5, 2007): 1–8. http://dx.doi.org/10.1155/2007/30569.

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The two-component kinetic model employing “fast” and “slow” metastable defects for the annealing behaviors in pin-type hydrogenated-amorphous-silicon- (a-Si:H-) based solar cells is simulated using a normalized fill factor. Reported annealing data on pin-type a-Si:H-based solar cells are revisited and fitted using the model to confirm its validity. It is verified that the two-component model is suitable for fitting the various experimental phenomena. In addition, the activation energy for annealing of the solar cells depends on the definition of the recovery time. From the thermally activated and high electric field annealing behaviors, the plausible microscopic mechanism on the defect removal process is discussed.

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42

Lee, Chang-Yong. "Fast simulated annealing with a multivariate Cauchy distribution and the configuration’s initial temperature." Journal of the Korean Physical Society 66, no. 10 (May 2015): 1457–66. http://dx.doi.org/10.3938/jkps.66.1457.

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43

LIU Ying, 刘莹, 马剑强 MA Jian-qiang, 何挺 HE Ting, 李保庆 LI Bao-qing, and 褚家如 CHU Jia-ru. "Hybrid simulated annealing-hill climbing algorithm for fast aberration correction without wavefront sensor." Optics and Precision Engineering 20, no. 2 (2012): 213–19. http://dx.doi.org/10.3788/ope.20122002.0213.

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44

Jean, Pouliot, Tremblay Daniel, Roy Jean, and Coté Carl. "2211 125I prostate implants: Automatic optimization of dose distribution using fast simulated annealing." International Journal of Radiation Oncology*Biology*Physics 39, no. 2 (January 1997): 346. http://dx.doi.org/10.1016/s0360-3016(97)80977-7.

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45

Yang, Kaifang, Shuai Wan, Yanchao Gong, and Yan Feng. "A fast algorithm of bitstream extraction using distortion prediction based on simulated annealing." Journal of Visual Communication and Image Representation 24, no. 7 (October 2013): 752–59. http://dx.doi.org/10.1016/j.jvcir.2013.04.013.

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46

Ryden, Nils, and Choon Byong Park. "Fast simulated annealing inversion of surface waves on pavement using phase-velocity spectra." GEOPHYSICS 71, no. 4 (July 2006): R49—R58. http://dx.doi.org/10.1190/1.2204964.

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The conventional inversion of surface waves depends on modal identification of measured dispersion curves, which can be ambiguous. It is possible to avoid mode-number identification and extraction by inverting the complete phase-velocity spectrum obtained from a multichannel record. We use the fast simulated annealing (FSA) global search algorithm to minimize the difference between the measured phase-velocity spectrum and that calculated from a theoretical layer model, including the field setup geometry. Results show that this algorithm can help one avoid getting trapped in local minima while searching for the best-matching layer model. The entire procedure is demonstrated on synthetic and field data for asphalt pavement. The viscoelastic properties of the top asphalt layer are taken into account, and the inverted asphalt stiffness as a function of frequency compares well with laboratory tests on core samples. The thickness and shear-wave velocity of the deeper embedded layers are resolved within 10% deviation from those values measured separately during pavement construction. The proposed method may be equally applicable to normal soil site investigation and in the field of ultrasonic testing of materials.

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47

Zhang, Peng, Javid Shiriyev, Mrinal K. Sen, and Mukul M. Sharma. "Inversion of downhole electrical measurements for proppant mapping using very fast simulated annealing." GEOPHYSICS 85, no. 1 (January 1, 2020): D13—D22. http://dx.doi.org/10.1190/geo2018-0749.1.

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Proppant mapping is critical for optimizing fracture treatment design and improving wells’ productivity. An electrode-based resistivity tool concept was developed earlier for proppant mapping in cased-hole wells. An array of insulating gaps is installed and cemented in place as a permanent part of the casing string. The electrical measurements are performed by imposing a voltage across each insulating gap, one at a time, before and after hydraulic fracture operations. The voltages across other insulating gaps near the transmitter gap are recorded. The method relies on direct excitation of the casing, which is expected to overcome the severe limitations of induction tools in cased-hole wells. A forward model based on a finite volume method has been developed to simulate the tool’s response to one or multiple fractures. To enable the implementation of such a practical system in multistage fractured horizontal wells, a fast and robust inversion approach is required. To that end, we have developed a divide-and-conquer approach based on a global optimization algorithm very fast simulated annealing (VFSA). Specifically, the original inverse problem is divided into subproblems and each subproblem can be solved separately using VFSA. The results indicate that our approach can invert the data and output widths and radii of multiple fractures without requiring a large number of forward simulations. The robustness of the inverse solver is also tested by adding Gaussian noise to the synthetic data. We tested example cases that demonstrate that when up to 5% noise is introduced, VFSA still provides very accurate inversion results with moderate uncertainties. Inversion results with some more realistic conditions, e.g., tilted fractures, complex fractures, and so on, are also presented.

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48

Gielis, G., and C. Maes. "A simple approach to time-inhomogeneous dynamics and applications to (fast) simulated annealing." Journal of Physics A: Mathematical and General 32, no. 29 (January 1, 1999): 5389–407. http://dx.doi.org/10.1088/0305-4470/32/29/301.

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49

Srivastava, R. P., and M. K. Sen. "Fractal-based stochastic inversion of poststack seismic data using very fast simulated annealing." Journal of Geophysics and Engineering 6, no. 4 (October 23, 2009): 412–25. http://dx.doi.org/10.1088/1742-2132/6/4/009.

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50

Manwar, Rayyan, Mohsin Zafar, Adrian Podoleanu, and Mohammad Avanaki. "An Application of Simulated Annealing in Compensation of Nonlinearity of Scanners." Applied Sciences 9, no. 8 (April 22, 2019): 1655. http://dx.doi.org/10.3390/app9081655.

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Galvo scanners are popular devices for fast transversal scanning. A triangular signal is usually employed to drive galvo scanners at scanning rates close to the inverse of their response time where scanning deflection becomes a nonlinear function of applied voltage. To address this, the triangular signal is synthesized from several short ramps with different slopes. An optimization algorithm similar to a simulated annealing algorithm is used for finding the optimal signal shape to drive the galvo scanners. As a result, a significant reduction in the nonlinearity of the galvo scanning is obtained.

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