4 research outputs found
Ruteo de helicΓ³pteros modelado con tasa de falla estocΓ‘stica en flotas heterogΓ©neas
The use of helicopters in the logistics sector is very frequent to transport people and products to places that,
due to geographical conditions, it is difficult to access by other kind of transport. The vehicle routing problem
is a combinatorial optimization problem that aims to optimize the deliveries of any type of transport and it has
been widely studied in literature since 1950s. Despite the vast quantity of studies found in VRP, it is important
to consider simultaneously different real-industry characteristics in the problem making its solution closer to
reality. Therefore, this project aims to solve the helicopters routing problem that minimizes the total traveling
time simultaneously, considering: the use of a heterogeneous fleet, stochastic failure and repair times, demands
of pickup and delivery, and helicopters maximum storage capacity.
The problem is solved in three phases. Firstly, a Mixed Linear Programming (MILP) is proposed for the
deterministic case. Secondly a Tabu Search algorithm is developed for the deterministic case. Thirdly, a
simheuristic that hybridizes Tabu Search and Monte Carlo simulation procedures is designed to solve the
stochastic counterpart of the problem. The performance of the simheuristic for small instances was calculated
in comparison with the simulation of the deterministic solutions of MILP model. Additionally, for medium and
large instances, the performance of simheuristic is evaluated in comparison with the simulation of deterministic
solutions given by a modified nearest neighbour algorithm. Results show that the simheuristic improves an
average of 18,56% the results of expected traveling times of simulated solutions of MILP model, and improves
an average of 27.66% the simulated solutions of nearest neighbour algorithm.Ingeniero (a) IndustrialPregrad
A multi-start ILS-RVND algorithm with adaptive solution acceptance for the CVRP
Gokalp, Osman/0000-0002-7604-8647; UGUR, Aybars/0000-0003-3622-7672WOS: 000518599800044This study proposes a novel hybrid algorithm based on Iterated Local Search (ILS) and Random Variable Neighborhood Descent (RVND) metaheuristics for the purpose of solving the Capacitated Vehicle Routing Problem (CVRP). the main contribution of this work is that two new search rules have been developed for multi-starting and adaptive acceptance strategies, and applied together to enhance the power of the algorithm. A comprehensive experimental work has been conducted on two common CVRP benchmarks. Computational results demonstrate that both multi-start and adaptive acceptance strategies provide a significant improvement on the performance of pure ILS-RVND hybrid. Experimental work also shows that our algorithm is highly effective in solving CVRP and comparable with the state of the art.Scientific and Technological Research Council of Turkey (TUBITAK) 2211 National Graduate Scholarship ProgramTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK)Author Osman Gokalp acknowledges the support of Scientific and Technological Research Council of Turkey (TUBITAK) 2211 National Graduate Scholarship Program
A multi-start ILSβRVND algorithm with adaptive solution acceptance for the CVRP
This study proposes a novel hybrid algorithm based on Iterated Local Search (ILS) and Random Variable Neighborhood Descent (RVND) metaheuristics for the purpose of solving the Capacitated Vehicle Routing Problem (CVRP). The main contribution of this work is that two new search rules have been developed for multi-starting and adaptive acceptance strategies, and applied together to enhance the power of the algorithm. A comprehensive experimental work has been conducted on two common CVRP benchmarks. Computational results demonstrate that both multi-start and adaptive acceptance strategies provide a significant improvement on the performance of pure ILSβRVND hybrid. Experimental work also shows that our algorithm is highly effective in solving CVRP and comparable with the state of the art. Β© 2019, Springer-Verlag GmbH Germany, part of Springer Nature
ΠΠ΄ΡΠΆΠΈΠ²ΠΎ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ΅ ΠΈΠ½ΡΠ΅ΠΊΡΠΈΠ²Π½ΠΈΠΌ ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ ΠΎΡΠΏΠ°Π΄ΠΎΠΌ Ρ Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½ΠΎΠΌ ΡΠΈΡΡΠ΅ΠΌΡ Π‘ΡΠ±ΠΈΡΠ΅
ΠΡΠ΅Π΄ΠΌΠ΅Ρ ΡΠ°Π΄Π° ΡΠ΅ ΡΠ°Π³Π»Π΅Π΄Π°Π²Π°ΡΠ΅ ΠΈ ΠΎΡΠ΅Π½Π° ΡΡΠ°ΡΠ° Ρ Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½ΠΎΠΌ ΡΠΈΡΡΠ΅ΠΌΡ Π‘ΡΠ±ΠΈΡΠ΅, ΡΠ° ΠΎΡΠ²ΡΡΠΎΠΌ
Π½Π° ΠΏΡΠ°Π²ΡΠ΅ Π³Π΅Π½Π΅ΡΠΈΡΠ°ΡΠ° ΠΈ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ ΠΎΡΠΏΠ°Π΄ΠΎΠΌ. Π‘ΡΡΡΠΈΠ½Π° ΡΠ΅ ΠΎΠ³Π»Π΅Π΄Π° Ρ ΡΠ²ΠΎΡΠ΅ΡΡ
ΡΠ°Π²ΡΠ΅ΠΌΠ΅Π½ΠΎΠ³ ΠΊΠΎΠ½ΡΠ΅ΠΏΡΠ° ΠΌΠ΅Π½Π°ΡΠΌΠ΅Π½ΡΠ° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΎΠ³ ΠΎΡΠΏΠ°Π΄Π° Ρ ΡΠΈΡΡ Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½Π΅ Π·Π°ΡΡΠΈΡΠ΅
ΡΡΠ°Π½ΠΎΠ²Π½ΠΈΡΡΠ²Π° ΠΈ Π·Π°ΠΏΠΎΡΠ»Π΅Π½ΠΈΡ
Ρ Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½ΠΎΠΌ ΡΠΈΡΡΠ΅ΠΌΡ Π‘ΡΠ±ΠΈΡΠ΅, ΡΠ· ΠΈΠ΄Π΅Π½ΡΠΈΡΠΈΠΊΠ°ΡΠΈΡΡ ΡΠ²ΠΈΡ
ΠΏΠΎΡΡΠ΅Π±Π½ΠΈΡ
ΠΌΠ΅ΡΠ° ΠΈ ΠΏΠΎΡΡΡΠΏΠ°ΠΊΠ°, ΠΊΠ°ΠΊΠΎ Π±ΠΈ ΡΠ΅ ΠΏΡΡ ΠΎΠ΄ Π³Π΅Π½Π΅ΡΠΈΡΠ°ΡΠ° Π΄ΠΎ ΠΊΠΎΠ½Π°ΡΠ½Π΅ Π΄ΠΈΡΠΏΠΎΠ·ΠΈΡΠΈΡΠ΅
ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΎΠ³ ΠΎΡΠΏΠ°Π΄Π° (Π°ΠΊΡΠ΅Π½Π°Ρ Π½Π° ΠΈΠ½ΡΠ΅ΠΊΡΠΈΠ²Π½ΠΈ ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈ ΠΎΡΠΏΠ°Π΄) ΡΠ²Π΅ΠΎ Π½Π° Π½Π°ΡΠΌΠ°ΡΡ ΠΌΠΎΠ³ΡΡΡ
ΠΎΠΏΠ°ΡΠ½ΠΎΡΡ.
ΠΠΎΡΡΠΎΡΠΈ Π²ΠΈΡΠ΅ Π΄Π΅ΡΠΈΠ½ΠΈΡΠΈΡΠ° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΎΠ³ ΠΎΡΠΏΠ°Π΄Π° ΠΊΠΎΡΠ΅ ΡΠ΅ ΡΠΌΠ°ΡΡΠ°ΡΡ ΠΏΡΠΈΡ
Π²Π°ΡΡΠΈΠ²ΠΈΠΌ ΠΏΡΠΈΠ»ΠΈΠΊΠΎΠΌ
ΠΊΠ°ΡΠ΅Π³ΠΎΡΠΈΠ·Π°ΡΠΈΡΠ΅ ΠΈ ΡΠ°Π·Π²ΡΡΡΠ°Π²Π°ΡΠ° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΎΠ³ ΠΎΡΠΏΠ°Π΄Π° ΠΊΠΎΡΠΈ Π½Π°ΡΡΠ°ΡΠ΅ Ρ Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½ΠΈΠΌ
ΡΡΡΠ°Π½ΠΎΠ²Π°ΠΌΠ°. ΠΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈ ΠΎΡΠΏΠ°Π΄ ΡΠ΅ Π΄Π΅ΡΠΈΠ½ΠΈΡΠ΅ ΠΊΠ°ΠΎ: βΡΠ°Π² ΠΎΡΠΏΠ°Π΄, ΠΎΠΏΠ°ΡΠ°Π½ ΠΈΠ»ΠΈ Π½Π΅ΠΎΠΏΠ°ΡΠ°Π½, ΠΊΠΎΡΠΈ
ΡΠ΅ Π³Π΅Π½Π΅ΡΠΈΡΠ΅ ΠΏΡΠΈ ΠΏΡΡΠΆΠ°ΡΡ Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½ΠΈΡ
ΡΡΠ»ΡΠ³Π° (Π΄ΠΈΡΠ°Π³Π½ΠΎΡΡΠΈΠΊΠ°, ΠΏΡΠ΅Π²Π΅Π½ΡΠΈΡΠ°, Π»Π΅ΡΠ΅ΡΠ΅ ΠΈ
ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠ° Ρ ΠΎΠ±Π»Π°ΡΡΠΈ Ρ
ΡΠΌΠ°Π½Π΅ ΠΈ Π²Π΅ΡΠ΅ΡΠΈΠ½Π°ΡΡΠΊΠ΅ ΠΌΠ΅Π΄ΠΈΡΠΈΠ½Π΅)". ΠΡΡΠ³ΠΈΠΌ ΡΠ΅ΡΠΈΠΌΠ°, ΠΏΠΎΠ΄
ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ ΠΎΡΠΏΠ°Π΄ΠΎΠΌ ΡΠ΅ ΠΏΠΎΠ΄ΡΠ°Π·ΡΠΌΠ΅Π²Π° ΡΠ°Π² ΠΎΡΠΏΠ°Π΄ ΠΊΠΎΡΠΈ Π½Π°ΡΡΠ°ΡΠ΅ Ρ ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ ΡΡΡΠ°Π½ΠΎΠ²Π°ΠΌΠ°
(Π΄ΡΠΆΠ°Π²Π½ΠΈΠΌ ΠΈΠ»ΠΈ ΠΏΡΠΈΠ²Π°ΡΠ½ΠΈΠΌ), ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠΊΠΈΠΌ ΡΠ΅Π½ΡΡΠΈΠΌΠ° ΠΈΠ»ΠΈ Π»Π°Π±ΠΎΡΠ°ΡΠΎΡΠΈΡΠ°ΠΌΠ°.
ΠΠ²Π°Ρ ΠΎΡΠΏΠ°Π΄ ΠΏΡΠ΅Π΄ΡΡΠ°Π²ΡΠ° Ρ
Π΅ΡΠ΅ΡΠΎΠ³Π΅Π½Ρ ΠΌΠ΅ΡΠ°Π²ΠΈΠ½Ρ, ΠΏΡΠΈ ΡΠ΅ΠΌΡ 10-25% ΡΠΈΠ½ΠΈ ΠΎΠΏΠ°ΡΠ°Π½ ΠΎΡΠΏΠ°Π΄
ΡΠΈΠ·ΠΈΡΠ°Π½ ΠΏΠΎ Π·Π΄ΡΠ°Π²ΡΠ΅ ΡΡΠ΄ΠΈ ΠΈ ΠΆΠΈΠ²ΠΎΡΠ½Ρ ΡΡΠ΅Π΄ΠΈΠ½Ρ ΠΈ Π½Π°ΡΡΠ°ΡΠ΅ ΠΏΡΠΈΠ»ΠΈΠΊΠΎΠΌ ΠΏΠΎΡΡΠ°Π²ΡΠ°ΡΠ° Π΄ΠΈΡΠ°Π³Π½ΠΎΠ·Π°,
Π»Π΅ΡΠ΅ΡΠ° ΠΈΠ»ΠΈ ΠΏΡΡΠΆΠ°ΡΠ° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠ΅ Π½Π΅Π³Π΅, ΠΊΠ°ΠΎ ΠΈ ΠΏΡΠΈΠ»ΠΈΠΊΠΎΠΌ ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠ° ΠΊΠΎΡΠ° ΡΠ΅ ΡΠΏΡΠΎΠ²ΠΎΠ΄Π΅ Ρ
Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½ΠΈΠΌ ΡΡΡΠ°Π½ΠΎΠ²Π°ΠΌΠ° Π½Π°ΡΡΠ½Π΅, ΡΠ΅ΡΠ°ΠΏΠΈΡΡΠΊΠ΅, Π΄ΠΈΡΠ°Π³Π½ΠΎΡΡΠΈΡΠΊΠ΅ ΠΈΠ»ΠΈ ΡΠ»ΠΈΡΠ½Π΅ ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠ΅
Π΄Π΅Π»Π°ΡΠ½ΠΎΡΡΠΈ. ΠΠΎΠΌΠ΅Π½ΡΡΠΈ ΠΎΡΠΏΠ°Π΄ ΠΏΠΎΠ΄ΡΠ°Π·ΡΠΌΠ΅Π²Π° ΡΠ°Π² ΠΎΡΠΏΠ°Π΄ ΠΊΠΎΡΠΈ Π½Π°ΡΡΠ°ΡΠ΅ ΠΏΡΠΈΠ»ΠΈΠΊΠΎΠΌ ΠΏΡΡΠΆΠ°ΡΠ°
Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½ΠΈΡ
ΡΡΠ»ΡΠ³Π°, ΠΊΠ°ΠΊΠΎ Ρ Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½ΠΈΠΌ ΡΡΡΠ°Π½ΠΎΠ²Π°ΠΌΠ° ΠΈΠ»ΠΈ Π²Π°Π½ ΡΠΈΡ
(ΠΊΡΡΠ½Π° Π½Π΅Π³Π°), Ρ
Π΄ΠΎΠΌΠΎΠ²ΠΈΠΌΠ° Π·Π° ΡΠΌΠ΅ΡΡΠ°Ρ ΡΡΠ°ΡΠΈΡ
Π»ΠΈΡΠ°, ΠΈΠ»ΠΈ Ρ ΡΡΡΠ°Π½ΠΎΠ²Π°ΠΌΠ° Ρ ΠΊΠΎΡΠΈΠΌΠ° ΡΠ΅ ΠΏΡΡΠΆΠ° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠ° Π½Π΅Π³Π°
Ρ Π±ΠΈΠ»ΠΎ ΠΊΠΎΠΌ ΠΎΠ±Π»ΠΈΠΊΡ.
ΠΡΠΎΠ±Π»Π΅ΠΌΠ°ΡΠΈΠΊΠ° ΠΏΡΠ΅Π΄ΠΌΠ΅ΡΠ° (ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ°) ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠ° ΡΠ°ΡΡΠΎΡΠΈ ΡΠ΅ ΠΈΠ· ΡΠ»Π΅Π΄Π΅ΡΠΈΡ
Π±ΠΈΡΠ½ΠΈΡ
ΡΠ΅Π³ΠΌΠ΅Π½Π°ΡΠ°:
- ΡΠ°Π³Π»Π΅Π΄Π°Π²Π°ΡΠ΅ ΡΡΠ°ΡΠ° ΠΎΠ΄ΡΠΆΠΈΠ²ΠΎΡΡΠΈ Ρ ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ ΠΎΡΠΏΠ°Π΄ΠΎΠΌ Ρ
Π . Π‘ΡΠ±ΠΈΡΠΈ,
- Π°Π½Π°Π»ΠΈΠ·Π° Π·Π°ΡΠ΅Π΄Π½ΠΈΡΠΊΠ΅ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠ΅ ΠΠ£ ΠΈ ΡΠ΅Π½ΠΎΠ³ ΡΡΠΈΡΠ°ΡΠ° Π½Π° ΠΏΠΎΠ»ΠΈΡΠΈΠΊΡ ΠΎΠ΄ΡΠΆΠΈΠ²ΠΎΠ³
ΡΠΏΡΠ°Π²ΡΠ°ΡΠ° ΠΎΡΠΏΠ°Π΄ΠΎΠΌ Ρ Π Π΅ΠΏΡΠ±Π»ΠΈΡΠΈ Π‘ΡΠ±ΠΈΡΠΈ. ΠΠΎΡΠ΅Π±Π½ΠΎ ΡΠ΅ ΠΈΠ·ΡΡΠ°Π²Π°ΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈ,
Π°ΡΠΏΠ΅ΠΊΡΠΈ ΠΈ Π½Π°ΡΠΈΠ½ΠΈ ΡΡΠΈΡΠ°ΡΠ° Π½Π° ΠΎΠ΄ΡΠΆΠΈΠ²ΠΎΡΡ Ρ ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ
ΠΎΡΠΏΠ°Π΄ΠΎΠΌ Ρ Π Π΅ΠΏΡΠ±Π»ΠΈΡΠΈ Π‘ΡΠ±ΠΈΡΠΈ,
- ΠΏΡΠ΅Π΄ΠΌΠ΅Ρ ΠΈΠ·ΡΡΠ°Π²Π°ΡΠ° ΠΎΠ±ΡΡ
Π²Π°ΡΠ° ΠΏΡΠΎΠΌΠ΅Π½Π΅ Ρ Π°Π»ΠΎΠΊΠ°ΡΠΈΡΠΈ ΠΈ ΡΡΡΡΠΊΡΡΡΠΈ ΡΡΠ°Π½ΠΎΠ²Π½ΠΈΡΡΠ²Π°
ΠΈ ΡΠ°Π΄Π½Π΅ ΡΠ½Π°Π³Π΅ ΠΈ ΡΠΈΡ
ΠΎΠ² ΡΡΠΈΡΠ°Ρ Π½Π° ΠΎΠ΄ΡΠΆΠΈΠ²ΠΎ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ΅ ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ ΠΎΡΠΏΠ°Π΄ΠΎΠΌ.
ΠΠΎΡΠ΅Π±Π½Π° ΠΏΠ°ΠΆΡΠ° ΠΏΠΎΡΠ²Π΅ΡΠ΅Π½Π° ΡΠ΅ ΠΏΡΠΎΡΡΠ°Π²Π°ΡΡ ΡΡΠ΅Π½Π΄ΠΎΠ²Π° ΠΈ ΡΠ΅ΡΡΡΡΠ° Ρ ΡΡΠ½ΠΊΡΠΈΡΠΈ
ΠΎΠΏΡΠΈΠΌΠ°Π»Π½ΠΎΠ³ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ°,
- ΠΏΡΠ΅Π΄ΠΌΠ΅Ρ ΠΈΡΡΡΠ°ΠΆΠΈΠ²Π°ΡΠ° Ρ Π΄ΠΈΡΠ΅ΡΡΠ°ΡΠΈΡΠΈ ΠΎΠ±ΡΡ
Π²Π°ΡΠΈΠΎ ΡΠ΅ ΠΏΠΈΡΠ°ΡΠ° ΡΡΠΈΡΠ°ΡΠ°
ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΡΠΊΠΎΠ³ ΡΠ°Π·Π²ΠΎΡΠ° ΠΎΠΏΡΠ΅ΠΌΠ΅ ΠΈ ΠΏΠΎΡΡΡΠΎΡΠ΅ΡΠ° Π·Π° Π·Π±ΡΠΈΡΠ°Π²Π°ΡΠ΅ ΠΎΡΠΏΠ°Π΄Π° Π½Π° ΠΆΠΈΠ²ΠΎΡΠ½Ρ
Π’Π°ΠΊΠΎΡΠ΅, Π½Π΅ΠΎΠΏΡ
ΠΎΠ΄Π½ΠΎ ΡΠ΅ ΠΏΠΎΠ²Π΅Π·Π°ΡΠΈ Π΅ΠΊΠΎΠ½ΠΎΠΌΡΠΊΠ΅ ΡΠ°ΠΊΡΠΎΡΠ΅ ΠΈ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΡ
ΡΡΠΌΠ΅ΡΠ°Π²Π°ΡΠ° ΠΎΠ΄ΡΠΆΠΈΠ²ΠΎΠ³ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ° ΠΎΡΠΏΠ°Π΄ΠΎΠΌ,
- ΡΠ°Π³Π»Π΅Π΄Π°Π²Π° ΡΠ΅ Π·Π°ΠΊΠΎΠ½ΡΠΊΠ° ΡΠ΅Π³ΡΠ»Π°ΡΠΈΠ²Π° Π·Π° ΠΌΡΠ»ΡΠΈΡΡΠ½ΠΊΡΠΈΠΎΠ½Π°Π»Π½ΠΎ ΠΎΠ΄ΡΠΆΠΈΠ²ΠΎ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ΅
ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ ΠΎΡΠΏΠ°Π΄ΠΎΠΌ Π Π‘ ΡΠΏΠΎΡΠ΅Π΄Π½ΠΎ ΡΠ° Π΄ΠΈΡΠ΅ΠΊΡΠΈΠ²Π°ΠΌΠ° ΠΠ£ Ρ ΡΠΎΡ ΠΎΠ±Π»Π°ΡΡΠΈ ΠΈ
- Ρ ΠΈΠ·ΡΡΠ°Π²Π°ΡΡ ΡΠ°ΠΊΡΠΎΡΠ°, ΠΏΡΠ°Π²Π°ΡΠ° ΠΈ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΎΠ΄ΡΠΆΠΈΠ²ΠΎΠ³ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ
ΠΎΡΠΏΠ°Π΄ΠΎΠΌ Ρ Π Π΅ΠΏΡΠ±Π»ΠΈΡΠΈ Π‘ΡΠ±ΠΈΡΠΈ, ΡΠ°Π³Π»Π΅Π΄Π°Π²Π°ΡΡ ΡΠ΅ ΠΈ ΡΡΡΠ°ΡΠ΅Π³ΠΈΡΠ΅ ΠΈ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠ° ΠΠ£ Ρ
ΠΎΠ±Π»Π°ΡΡΠΈ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ° ΠΎΡΠΏΠ°Π΄ΠΎΠΌ.
ΠΡΠ½ΠΎΠ²Π½ΠΈ ΡΠΈΡ ΡΠ°Π΄Π° ΡΠ΅ ΡΡΠ²ΡΠ΄ΠΈΡΠΈ ΠΊΠΎΡΠΈ ΡΡ ΡΠΎ ΠΈΠ½Π΄ΠΈΠΊΠ°ΡΠΎΡΠΈ ΠΊΠΎΡΠΈ ΠΈΠΌΠ°ΡΡ Π½Π°ΡΠ²Π΅ΡΠΈ ΡΡΠΈΡΠ°Ρ Π½Π°
ΡΠΏΡΠ°Π²ΡΠ°ΡΠ΅ ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ ΠΎΡΠΏΠ°Π΄ΠΎΠΌ Ρ Π‘ΡΠ±ΠΈΡΠΈ.
ΠΠ°ΡΡΠ½ΠΈ ΡΠΈΡ ΠΎΠ³Π»Π΅Π΄Π° ΡΠ΅ Π½Π΅ ΡΠ°ΠΌΠΎ Ρ ΡΠΎΠΌΠ΅ Π΄Π° Π΄Π΅ΡΠΈΠ½ΠΈΡΠ΅ΠΌΠΎ ΠΏΡΠΎΠ±Π»Π΅ΠΌ ΠΈ ΠΎΡΠΊΡΠΈΡΠ΅ΠΌΠΎ ΡΠ»Π°Π±Π΅ βΡΠ°ΡΠΊΠ΅β,
Π²Π΅Ρ Π΄Π° ΠΈΡΡΠ΅ Ρ ΠΌΡΠ»ΡΠΈΡΠ΅ΠΊΡΠΎΡΡΠΊΠΎΡ ΡΠ°ΡΠ°Π΄ΡΠΈ ΡΡΠΎ Π²ΠΈΡΠ΅ ΡΠ΅ΡΠΈΠΌΠΎ, Π° ΡΠ²Π΅ ΡΠ° Π·Π°Π΄Π°ΡΠΊΠΎΠΌ ΠΏΠΎΠ΄ΠΈΠ·Π°ΡΠ°
Π½ΠΈΠ²ΠΎΠ° ΠΈ ΠΊΠ²Π°Π»ΠΈΡΠ΅ΡΠ° ΠΏΡΡΠΆΠ΅Π½Π΅ Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½Π΅ ΡΡΠ»ΡΠ³Π΅, ΠΌΠΈΠ½ΠΈΠΌΠΈΠ·Π°ΡΠΈΡΠ΅ ΠΎΡΠΏΠ°Π΄Π° ΠΈ Π·Π°ΡΡΠΈΡΠΈ ΠΆΠΈΠ²ΠΎΡΠ½Π΅
ΡΡΠ΅Π΄ΠΈΠ½Π΅ ΠΈ ΡΠ²Π΅ΡΠΊΡΠΏΠ½ΠΎΠ³ Π·Π΄ΡΠ°Π²ΡΠ° ΡΡΠ°Π½ΠΎΠ²Π½ΠΈΡΡΠ²Π° Π‘ΡΠ±ΠΈΡΠ΅.
ΠΡΠΏΠΈΡΠΈΠ²Π°Π½Π΅ ΡΡ ΡΠ΅ΠΊΡΠ½Π΄Π°ΡΠ½Π΅ Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½Π΅ ΡΡΡΠ°Π½ΠΎΠ²Π΅ ΠΈΡΡΠΎΠ³ Π½ΠΈΠ²ΠΎΠ° Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½Π΅ Π·Π°ΡΡΠΈΡΠ΅ ΠΈΠ· ΡΡΠΈ
Π£ΠΏΡΠ°Π²Π½Π° ΠΎΠΊΡΡΠ³Π° Π Π΅ΠΏΡΠ±Π»ΠΈΠΊΠ΅ Π‘ΡΠ±ΠΈΡΠ΅, ΠΊΠΎΡΠ΅ ΠΈΠΌΠ°ΡΡ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ½ΠΎ ΠΈΡΡΠΈ Π±ΡΠΎΡ Π³ΡΠ°Π²ΠΈΡΠΈΡΠ°ΡΡΡΠ΅Π³
ΡΡΠ°Π½ΠΎΠ²Π½ΠΈΡΡΠ²Π°, Π° ΡΠ»ΠΈΡΠ½Π΅ ΡΡ ΠΈΠ»ΠΈ ΠΈΡΡΠ΅ ΠΏΠΎ ΠΎΠ±ΠΈΠΌΡ Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½ΠΈΡ
ΡΡΠ»ΡΠ³Π°, ΠΊΠ°ΠΏΠ°ΡΠΈΡΠ΅ΡΠ°, Π±ΡΠΎΡΠ°
ΠΏΠΎΡΡΠ΅ΡΠ°, ΠΎΡΡΠ²Π°ΡΠ΅Π½ΠΈΡ
Π±ΠΎΠ»Π½ΠΈΡΠΊΠΈΡ
Π΄Π°Π½Π° Ρ Ρ
ΠΈΡΡΡΡΠΊΠΈΠΌ Π³ΡΠ°Π½Π°ΠΌΠ° Π·Π΄ΡΠ°Π²ΡΡΠ²Π΅Π½Π΅ Π·Π°ΡΡΠΈΡΠ΅ ΠΏΡΠ΅
ΡΠ²Π΅Π³Π°. ΠΡΠΈΠΊΠ°Π·Π°Π½Π΅ ΡΡ ΡΠ΅Π½Π΄Π΅Π½ΡΠΈΡΠ΅ Π΄ΠΎΡΠ°Π΄Π°ΡΡΠ΅Π³ ΡΠΏΡΠ°Π²ΡΠ°ΡΠ° ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΈΠΌ ΠΎΡΠΏΠ°Π΄ΠΎΠΌ Ρ
Π Π΅ΠΏΡΠ±Π»ΠΈΡΠΈ Π‘ΡΠ±ΠΈΡΠΈ ΠΈ ΡΠΈΡ
ΠΎΠ² ΡΡΠΈΡΠ°Ρ Π½Π° Π΄Π΅Π³ΡΠ°Π΄Π°ΡΠΈΡΡ ΠΈ Π·Π°Π³Π°ΡΠ΅ΡΠ΅ ΠΆΠΈΠ²ΠΎΡΠ½Π΅ ΡΡΠ΅Π΄ΠΈΠ½Π΅.
ΠΠΎΡΡΠΈΠ³Π½ΡΡΠ° ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΡΠΊΠΎΠ³ ΡΠ°Π·Π²ΠΎΡΠ° ΠΎΠΏΡΠ΅ΠΌΠ΅ Π·Π° Π·Π±ΡΠΈΡΠ°Π²Π°ΡΠ΅ ΠΌΠ΅Π΄ΠΈΡΠΈΠ½ΡΠΊΠΎΠ³ ΠΎΡΠΏΠ°Π΄Π° ΡΠ°Π·ΠΌΠ°ΡΡΠ°Π½Π΅
ΡΡ Ρ ΡΡΠ½ΠΊΡΠΈΡΠΈ ΠΏΠΎΠ²Π΅Π·ΠΈΠ²Π°ΡΠ° Π΅ΠΊΠΎΠ½ΠΎΠΌΡΠΊΠΈΡ
ΠΈ Π΅ΠΊΠΎΠ»ΠΎΡΠΊΠΈΡ
ΡΠΈΡΠ΅Π²Π°