Monte Carlo dynamics in global optimization

Chen, C N; Chou, C. I.; Hwang, Chii‐Ruey; Kang, Jiexiang; Lee, T K; Li, S P

doi:10.1103/physreve.60.2388

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…The last ingredient that we include in this algorithm is from an observation in a recent work [11]. It was [11] observed that the average first passage time to reach the global optimum of an optimization problem in Monte Carlo simulation was a U-shape temperature dependent curve. At the optimal temperature, the avereage first passage time to find the global optimal will be the shortest.…”

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confidence: 99%

A Guided Monte Carlo Method for Optimization Problems

2002

Int. J. Mod. Phys. C

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We introduce a new Monte Carlo method by incorporating a guided distribution function to the conventional Monte Carlo method. In this way, the efficiency of Monte Carlo methods is drastically improved. To further speed up the algorithm, we include two more ingredients into the algorithm. First, we freeze the sub-patterns that have high probability of appearance during the search for optimal solution, resulting in a reduction of the phase space of the problem, a concept inspired by the renormalization group equation method in statistical physics. Second, we perform the simulation at a temperature which is within the optimal temperature range of the optimization search in our algorithm. We use this algorithm to search for the optimal path of the traveling salesman problem and the ground state energy of the Anderson-Edwards spin glass model and demonstrate that its performance is comparable with more elaborate and heuristic methods.

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confidence: 99%

A Guided Monte Carlo Method for Optimization Problems

2002

Int. J. Mod. Phys. C

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“…(12). This is the reason why the distributions of first passage times for rather general global optimization problems with quadratic cost functions [44] is the same as the form of the distribution of energy states which we find from our simulations.…”

Section: Universality Of the Energy Historgrams And The Ornstein-umentioning

confidence: 49%

“…(See Ref. [3], Table Ia,b for the values of the fitting parameters) It should be mentioned that the same energy distributions may be fit equally well (or better near the point E 0 and in the far tail) by the "inverse Gaussian" [44], where the probability density is given by,…”

Section: B Distribution Of Energy Statesmentioning

confidence: 99%

Hydrophobic models of protein folding and the thermodynamics of chain-boundary interactions

Erzan

Tüzel

2003

Braz. J. Phys.

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We review some results concerning the energetic and dynamical consequences of taking a generic hydrophobic model of a random polypeptide chain, where the effective hydrophobic interactions are represented by Hookean springs. Then we present a set of calculations on a microscopic model of hydrophobic interactions, investigating the behaviour of a hydrophobic chain in the vicinity of a hydrophobic boundary. We conclude with some speculations as to the thermodynamics of pre-biotic functions proteins may have discharged very early on in the evolutionary past. I IntroductionThe approach of a statistical physicist to biological problems is different from that of a biologist, in the same way that the approach of a physicist to any natural phenomenon is different from that of an engineer. The difference seems to lie in regarding any given instance of a particular phenomenon not as the product of an ingenious design, but only as a member of a very large ensemble of possible realizations of a generic rule, all governed by the same laws of physics. To a statistical physicist, a biological molecule is not, first and foremost, a high precision tool custom-made to perform a highly specialized task; it is rather a member of a very large set of possible outcomes of random processes, which, under nonequilibrium conditions, have conspired to produce a certian, albeit very improbable result. Moreover, as has already been thoroughly underlined by Eigen [1] and Maynard-Smith [2], biological entities typically correspond to sharply peaked probability distributions ("quasispecies") about some point in biological phase space, rather than unique solutions to some optimization problem. This distribution is of course reflected in the genetic code, and also must translate itself to the proteins that make up the organism.Another source of deviations from perfect order is thermal noise. We would like to stress that the protein in its native state must essentially correspond to a self-organized system, i.e., the "native state" should be concieved of as the attractor of a dynamics [3]. This typically corresponds not to a unique conformation but to a set of conformations to which the trajectory of the phase point representing the molecule is confined after asymptotically long times (which may already be achieved in microseconds).In this paper we will first review a simple model involving discrete torsional degrees of freedom [3]. The hydrophobic interactions driving the folding of the polypeptide chain [4,5] are modeled by Hookean springs connecting pairs of hydrophobic residues. [6][7][8][9][10][11][12] This system, with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional OrnsteinUhlenbeck [13,14] process, quite independently of the nature of the sequence of hydrophobic and polar residues, or the dimensionality of the space. It can be shown to obey the so called Wigner distribution [15][16][17][18][19] over a very large range of energies relative ...

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Tüzel

Erzan

2000

Journal of Statistical Physics

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Monte Carlo dynamics in global optimization

Cited by 5 publications

References 15 publications

A Guided Monte Carlo Method for Optimization Problems

A Guided Monte Carlo Method for Optimization Problems

Hydrophobic models of protein folding and the thermodynamics of chain-boundary interactions

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