Global minimum search using DMC algorithm with continuous weights

• Autorzy: Kazimirski J. K.
• Języki publikacji: EN

Abstrakty

EN

In this study we presented an algorithm for an unconstrained optimization of a continuous objective function, inspired by the Diffusion Monte Carlo method using a weight-based implementation. In this algorithm a cloud of replicas explores the solution space. Replicas are moved and evaluated after each step. Each replica carries an additional parameter (weight) which reflects the quality of its local solution. This parameter is updated after each step. Most inefficient replicas, i.e. replicas with the lowest weights, are occasionally replaced with their highest weight counterparts. In our study we present the basic implementation of the algorithm and compare its performance with other approaches, including the previously used implementation of DMC algorithm with a fluctuating population.

Słowa kluczowe

EN

DMC algorithm; diffusion Monte Carlo; continuous objective function; minimum search

PL

algorytm DMC; metoda Monte Carlo; funkcja ciągłego celu; wyszukiwanie minimalne

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2011
• Tom: Vol. 16
• Strony: 117--122
• Opis fizyczny: Bibliogr. 12 poz., tab.

Twórcy

autor

Kazimirski J. K.

• European University of Informatics and Economy ul. Białostocka 22, 03-741 Warsaw, Poland

Bibliografia

• [1] P.M. Pardalos, M.G.C. Resende (Eds). Handbook of Applied Optimization. Oxford University Press, Oxford 2002.
• [2] C.A. Floudas, P.M. Pardalos. Encyclopedia of Optimization. 2nd edition, Springer, New York 2008.
• [3] D.E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Boston 1989.
• [4] J. Arabas. Lectures on Evolutionary Algorithms. WNT, Warszawa 2001. (In Polish).
• [5] J. B. Anderson. A random-walk simulation of the Schrödinger equation H+3. J. Chem. Phys., 63(4), 1499-1503, 1975.
• [6] M.A. Suhm, R.O. Watts. Quantum Monte-Carlo studies of vibrational-states in molecules and clusters. Phys. Rep., 204(4), 293-329, 1991.
• [7] J.K. Kazimirski, V. Buch. Search for low energy structures of water clusters (H2O)(n), n=20-22, 48, 123, 293. J. Phys. Chem. A, 107(46), 9762-9775, 2003.
• [8] J.K. Kazimirski. Computational Study of Hydrogen Bonded Systems. PhD thesis, The Hebrew University, Jerusalem 2004.
• [9] M. Jaszczuk, M. Stopiński. Search of global minimum using the diffusion Monte Carlo method. Master's thesis, Wyższa Szkoła Menedżerska w Warszawie, 2008. (In Polish).
• [10] J.K. Kazimirski. Global optimization using diffusion Monte Carlo approach. Studia i Materiały. Europejska Wyższa Szkoła Informatyczno-Ekonomiczna w Warszawie, 2011. (Submitted for publication).
• [11] T. Bäck. Evolutionary Algorithms in Theory and Practice. Oxford University Press, Oxford 1996.
• [12] A. Törn, A. Zilinskas. Global Optimization. Lecture Notes in Computer Science, vol. 350. Springer, Berlin 1989.