Abstract
Two-dimensional generalization of the original peak finding algorithm suggested earlier is given. The ideology of the algorithm emerged from the well-known quantum mechanical tunneling property which enables small bodies to penetrate through narrow potential barriers. We merge this “quantum” ideology with the philosophy of Particle Swarm Optimization to get the global optimization algorithm which can be called Quantum Swarm Optimization. The functionality of the newborn algorithm is tested on some benchmark optimization problems.
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Z. K. Silagadze, “A New Algorithm for Automatic Photopeak Searches,” Nucl. Instrum. Methods Phys. Res., Sect. A 376, 451–454 (1996).
W. Feller, An Introduction in Probability Theory and Its Applications (Wiley, New York, 1966), Vol. 1.
M. N. Achasov et al., “Medium Energy Calorimetry at SND: Techniques and Performances on Physics,” in Proc. of “Calorimetry in High Energy Physics,” Lisbon, 1999 (World Sci., Singapore, 2000), pp. 105–120.
A. V. Bannikov, G. A. Chelkov, and Z. K. Silagadze, “B 0 s → D − s a + 1 (D − s → ϕπ−, D − s → K*0 K −) Decay Channel in the ATLAS B 0 s Mixing Studies,” JINR Preprint No. E1-98-29 (Dubna, 1998).
A. O. Griewank, “Generalized Descent for Global Optimization,” J. Optim. Theory Appl 34, 11–39 (1981).
J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” in Proc. of IEEE Conf. on Neural Networks (Perth, 1995), pp. 1942–1948.
J. Kennedy, R. C. Eberhart, and Y. Shi, Swarm Intelligence. Morgan Kaufmann Publishers (San Francisco, 2001).
K. E. Parsopoulos and M. N. Vrahatis, “Recent Approaches to Global Optimization Problems through Particle Swarm Optimization,” Natural Computing 1, 235–306 (2002).
A. Gide, The Tractate of Narcissus (Theory of Symbol), Transl. by A. Mangravite, in The Book of Masks; Atlas Arkhive Two: French Symbolist and Decadent Writing of the 1890s (Atlas Press, London, 1994).
X. P. Xie, W. J. Zhang, and Z. L. Yang, “Solving Numerical Optimization Problems by Simulating Particle-Wave Duality and Social Information Sharing,” in Intern. Conf. on Artificial Intelligence (Las Vegas, USA, 2002), pp. 1163–1169.
A. V. Levy and A. Montalvo, “The Tunneling Method for Global Optimization,” SIAM J. of Sci. Stat. Comp. 6, 15–29 (1985).
For a review and references see, for example, T. Kadowaki, “Study of Optimization Problems by Quantum Annealing,” Ph.D. Thesis (Department of Physics, Institute of Technology, Tokyo, 1998).
P. Liu and B. J. Berne, “Quantum Path Minimization: An Efficient Method for Global Optimization,” J. Chem. Phys. 118, 2999–3005 (2003).
C. Jansson and O. Knuppel, “A Global Minimization Method: The Multi-Dimensional Case,” Technical Report 92-1 (TU Harburg, Hamburg, 1992).
C. Jansson and O. Knuppel, “Numerical Results for a Self-Validating Global Optimization Method,” Technical Report 94-1 (TU Harburg, Hamburg, 1994).
R. J. Van Iwaarden, “An Improved Unconstrained Global Optimization Algorithm,” PhD Thesis (Univ. of Colorado at Denver, Denver, 1996).
V. Chichinadze, “The ω-Transform for Solving Linear and Nonlinear Programming Problems,” Automata 5, 347–355 (1969).
H.-P. Schwefel, Numerical Optimization of Computer Models (Wiley, Chichester, 1981).
D. H. Ackley, A Connectionist Machine for Genetic Hill-climbing (Kluwer, Boston, 1987).
E. E. Easom, “A Survey of Global Optimization Techniques,” M. Eng. Thesis (Univ. Louisville, KY, Louisville, 1990).
H.-M. Voigt, J. Born, and I. Santibanez-Koref, “A Multi-valued Evolutionary Algorithm,” Technical Report TR-92-038 (Intern. Comp. Sci. Inst., CA, Berkeley, 1992).
S. Nagendra, “Catalogue of Test Problems for Optimization Algorithm Verification,” Technical Report 97-CRD-110 (General Electric Company, 1997).
A. A. Giunta, “Aircraft Multidisciplinary Design Optimization Using Design of Experiments Theory and Response Surface Modeling Methods,” MAD Center Report, 97-05-01 (Virginia Polytechn Inst. and State Univ. Blacksburg, VA, 1997).
A. D. Bukin, “New Minimization Strategy for Non-Smooth Functions. Budker Inst. of Nucl. Phys,” Preprint No. BUDKER-INP-1997-79 (Novosibirsk, 1997).
M. Styblinski and T. Tang, “Experiments in Nonconvex Optimization: Stochastic Approximation with Function Smoothing and Simulated Annealing,” Neuron Networks, 3, 467–483 (1990).
D. Whitley et al., “Evaluating Evolutionary Algorithms,” Artif. Intell. 85, 245–276 (1996).
K. Madsen and J. Zilinskas, “Testing Branch-and-Bound Methods for Global Optimization,” IMM Technical Report 05 (Techn. Univ. of Denmark, 2000).
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Silagadze, Z.K. Finding two-dimensional peaks. Phys. Part. Nuclei Lett. 4, 73–80 (2007). https://doi.org/10.1134/S154747710701013X
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DOI: https://doi.org/10.1134/S154747710701013X