Virtual particles and search for global minimum

Abstract The models and computational techniques stemming from natural sciences — so-called natural solvers — become more and more popular as the methods of last resort in investigations of irreducible problems of universal character. In the paper, the author uses the concept of a virtual particle (VIP) model. It covers the broad range of natural solvers, which use VIPs as basic objects. The main features of particles paradigm proposed: simplicity, decomposition ability, and built-in message-passing way of communication, make it attractive as a universal approach for mapping different problems on parallel platform. In course of the paper, molecular dynamics (MD) is proposed as a pure VIP model. In dependence of the level of abstraction the particle can be defined as atom, cluster of molecules, piece of matter, object or UNIX process. MD applications as a method of search for global minimum in multi-dimensional function domain is discussed. The features extraction problem considered, shows the advantages of this technique. It is also shown that Hopfield nets can be mapped onto a particle model. The locality of the particles paradigm is discussed on the base of the spatial genetic algorithm.

[1]  Gerhard W. Dueck,et al.  Threshold accepting: a general purpose optimization algorithm appearing superior to simulated anneal , 1990 .

[2]  Stefan Brode,et al.  An optimized MD program for the vector computer cyber 205 , 1986 .

[3]  David A. Yuen,et al.  Molecular Simulation of Mixing Fluids and Microhydrodynamic Instabilities , 1996, HPCN Europe.

[4]  Holian,et al.  Fracture simulations using large-scale molecular dynamics. , 1995, Physical review. B, Condensed matter.

[5]  Witold Dzwinel,et al.  Comparison of noise diagnostic systems based on pattern recognition and discriminant methods , 1995 .

[6]  R. Battiti,et al.  Local search with memory: benchmarking RTS , 1995 .

[7]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[8]  Marco Villani,et al.  PARALLEL ARCHITECTURES AND INTRINSICALLY PARALLEL ALGORITHMS: GENETIC ALGORITHMS , 1994 .

[9]  Marco Tomassini,et al.  The Parallel Genetic Cellular Automata: Application to Global Function Optimization , 1993 .

[10]  Lester Ingber,et al.  Simulated annealing: Practice versus theory , 1993 .

[11]  Witold Dzwinel,et al.  Pattern recognition via molecular dynamics on vector supercomputers and networked workstations , 1995, HPCN Europe.

[12]  Witold Dzwinel,et al.  Pattern recognition application for surveillance of abnormal conditions in a nuclear reactor , 1991 .

[13]  John E. Straub,et al.  Finding the needle in the haystack: algorithms for conformational optimization , 1996 .

[14]  Witold Dzwinel,et al.  Spatial Genetic Algorithm and Its Parallel Implementation , 1996, PARA.

[15]  David M. Beazley,et al.  Message-Passing Multi-Cell Molecular Dynamics on the Connection Machine 5 , 1994, Parallel Comput..

[16]  Witold Dzwinel.  Particles Paradigm and Optimization Problems , 1996, HPCN Europe.

[17]  David A. Yuen,et al.  Macro-Scale Simulations Using Molecular Dynamics Method , 1995 .

[18]  Witold Dzwinel,et al.  How to make sammon's mapping useful for multidimensional data structures analysis , 1994, Pattern Recognit..

[19]  Clementi,et al.  Eddy formation in obstructed fluid flow: A molecular-dynamics study. , 1986, Physical review letters.

[20]  D. C. Rapaport,et al.  The Art of Molecular Dynamics Simulation , 1997 .

[21]  L. Libersky,et al.  High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response , 1993 .

[22]  Thomas P. Trappenberg,et al.  Development of massively parallel applications , 1994 .

[23]  Nigel P. Topham,et al.  Performance of the decoupled ACRI-1 architecture: the perfect club , 1995, HPCN Europe.

[24]  Hans J. Herrmann,et al.  Simulation of granular media , 1992 .

[25]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[26]  David E. Goldberg,et al.  Parallel Recombinative Simulated Annealing: A Genetic Algorithm , 1995, Parallel Comput..

[27]  Ciriyam Jayaprakash,et al.  Simple models of self-organized criticality , 1995 .

[28]  Christian Laugier,et al.  Simulating physical interactions between an articulated mobile vehicle and a terrain , 1993, Robotics Auton. Syst..

[29]  H. Schuster.  Deterministic chaos: An introduction , 1984 .

[30]  David E. Goldberg,et al.  A Note on Boltzmann Tournament Selection for Genetic Algorithms and Population-Oriented Simulated Annealing , 1990, Complex Syst..

[31]  Peter M. A. Sloot,et al.  A dynamic load balancing system for parallel cluster computing , 1996, Future Gener. Comput. Syst..

[32]  Jack Sklansky,et al.  An overview of mapping techniques for exploratory pattern analysis , 1988, Pattern Recognit..

[33]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[34]  Rapaport.  Molecular-dynamics study of Rayleigh-Bénard convection. , 1988, Physical review letters.

[35]  J. J. Hopfield,et al.  “Neural” computation of decisions in optimization problems , 1985, Biological Cybernetics.

[36]  R. Battiti,et al.  Simulated annealing and Tabu search in the long run: A comparison on QAP tasks☆ , 1994 .

[37]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[38]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[39]  Jacek Kitowski,et al.  “Checker Board” Periodic Boundary Conditions in Molecular Dynamics Codes , 1991 .