Список цитируемой литературы:
1. Машины и оборудование газонефтепроводов; Учеб. пособие для вузов/ Ф. М. Мустафин, Н. И. Коно-
валов, Р. Ф. Гильметдинов и др. — 2-е изд., перераб. и доп. — Уфа: Монография, 2002- с.234
CALCULATION OF WORKING PARAMETERS OF A COMPRESSOR STATION WITH A
GAS TURBINE INSTALLATION
Sheveleva D. A., Sivashenko V. A.
Omsk State Technical University, Omsk, Russia
The gas industry is developing rapidly. This requires the development of new methods to
improve the reliability and economic efficiency of the construction and operation of compressor
stations and the linear part of gas pipelines. In recent years, one of these methods is the construction
and reconstruction of compressor stations with gas pumping units driven by aircraft engines, they can
dramatically reduce the time of construction and reconstruction of compressor stations and reduce the
amount of necessary investment.
Keywords: compressor station, productivity, efficiency
123
УДК 519.68
SIMULATED ANNEALING METHOD: TEMPERATURE SCHEDULE
Burova E. M.
Lomonosov Moscow State University, Moscow, Russia
The annealing algorithm is one of the stochastic methods for finding extremums of functions
based on the simulation of the metal quenching process. The physical basis of the method is
described.
Keywords: stochastic optimization, simulated annealing
The idea of using the Monte Carlo method to simulate the equilibrium position of a set of atoms
at a given temperature (T) was proposed by N. Metropolis [1]. This method is based on the fact that,
according to Boltzmann's law, the probability of any configuration of atoms is exp(-E(i)/(k T)), where
E(i) is the energy corresponding to the configuration #i, k is the Boltzmann constant. Consequently,
lower–energy configurations are most likely at a given temperature. Then you can try to generate
these configurations randomly in order to obtain a configuration with minimal energy. Since the
number of possible configurations is large, Metropolis proposed a heuristic for finding a low–energy
configuration. At each step of the algorithm, the atom is given a small displacement and the resulting
energy change ΔE is calculated. If ΔE≤0, the new location is accepted and this configuration is
considered as the starting point of the next step. The case ΔE≥0 step is carried out in a probabilistic
way.
In a physical situation, the temperature slowly decreases, allowing atoms to move into a state
with minimal energy. This makes it possible to use temperatures in the case of an arbitrary
combinatorial problem as a control parameter.
Metropolis adaptation, combined with the method of temperature change, called the method of
simulated annealing or the simple method of annealing. The Metropolis method is easily adaptable for
solving combinatorial optimization problems [2]. By using the cost function instead of energy and
defining a configuration with many parameters, you can generate many configurations of the
optimization problem. The temperature is used as a control parameter measured in the same units as
the cost function. The process of simulating annealing thus consists in bringing the system to be
optimized to a high temperature and then changing the temperature in small steps until the system
cools. At each temperature, the simulation must continue long enough for the system to reach
equilibrium. The simulation of the temperature reduction process is called the annealing schedule.
The method can use different temperature drops, temperature schedule, for example:
T
i
= T
0
/ln(i+1),
T
i
= T
0
/ i.
T
i
= T
0
exp(-β i), β– parameter.
The method of simulated annealing differs from iterative improvement in that it is possible to
exit the local optimum. There is a significant drawback of the method–calculations take a long
time [3].
The algorithm requires a large number of iterations. In the conditions of their limitation, the
value of the local optimum is given.
Areas of application of simulation of the annealing method: optimization of functions,
combinatorial optimization, mathematical modeling in physics and chemistry, economics, finance,
engineering and other fields.
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Figure.1. The block diagram of the algorithm
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