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THE COUNTRIES OF CENTRAL ASIA IN THE APPLICATION OF
MATHEMATICAL MODELS AND OPTIMIZATION APPROACHES OF ISSUE
KOMMIVOYAJYOR
Zilolaxon Xabibulloxonovna Mamatova
Fergana state university , associate professor,
pedagogical sciences doctor of philosophy (PhD)
E-mail:
mamatova.zilolakhon@gmail.com
ORCID ID
Lobarxon Olimova Sherzodjon kizi
Fergana state university student
E-mail:
lobarxonkamolova0104@gmail.com
Annotatsiya:
In this article the theoretical basis of the issues of the central asian countries
and its cities of kommivoyajor tatbiqi lit. Various optimization approaches, including
traditional, and an intuitive graphical methods are considered. Also, how can these issues in
charging through mathematical modeling of logistics system analysis. Is characterized by
practical examples, and / orassessed the effectiveness of rning.
Keywords:
kommivoyajor the issue of optimization, logistics, central asia, the mathematical
model and the algorithm.
To enter.
Of the central asian countries and issues of mutual economic optimization of
transport and communication kommivoyajor effective approach in the planning and
development plays an important role. These issues, among various cities and states to find the
shortest or cheapest route when directed, reduce logistics costs, save time, and allows optimal
distribution of resources. The practice of using mathematical modeling and algorithm can be
successful in the modern charging this issue. This article kommivoyajor solution of the issue
of the taking of the city, the state in central asia is an analysis of the approach.
Methods of charging:
Bruteforce (Full review),dina programming (Held-Karp
algorithm),ochko'z algorithm (Greedy Algorithm),genetik algorithm, simulyatsiyalangan
tavlanish (simulated annealing), chiziqli be programming and chess (Branch and bound)
Objective:
the purpose of this article — kommivoyajor issues of theoretical and
practical aspects of a study, analysis and optimization of central asia without cover the city
with the help of the mathematical model of the approach is to develop effective solutions.
Also, the indications of this issue in the field of logistics and route planning to reduce costs of
transport through the show we learn that opportunities for improvement.
The standard option.
Will put bring the concept of the table. To do this, the table is coming
from the line of earlier, that is, each row of the table of elements of the same row is removed
the small isolated respectively. After that we also do other than follow the column of the table
were the same, and come to the table columns. All are listed on the table are referred to as
rows and columns are listed. The smallest the sum of h elements were defined by the table of
rows and columns, bring it charts the coefficient is called. As an example, below and across
central asia train travel, let's see the schedule:
Enter the world belgilashlarz.
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1.Tashkent-Astana – 1210 km
Tashkent-Bishkek– 480 km
Tashkent-Ashgabat – 1700 km
TashkentDushanbe – 320 km
Tashkent-Nukus – 1050 km
2.Astana -Tashkent – 1210 km
Astana - Bishkek – 950 km
Astana - Ashgabat – 1900 km
Astana - finance department – 1400 km
Astana - Nukus – 1600 km
3. Bishkek -Tashkent – 480 km
None –Astana – 950 km
None - Ashgabat – 2000 miles
Bishkek - Dushanbe – 790 km
None - Nukus – 1200 km
4. Ashgabat -tashkent – 1700 km
Ashgabat - Astana – 1900 km
Ashgabat - None – 2000 miles
Ashgabat - finance department – 1150 km
Ashgabat - Nukus – 800 miles
5. Dushanbe -Tashkent – 320 km
Dushanbe - Astana – 1400 km
Dushanbe - None – 790 km
Dushanbe - Ashgabat – 1150 km
Dushanbe - Nukus – 1100 km
6. Nukus -Tashkent – 1050 km
Nukus, republic of - Astana – 1600 km
Nukus - None – 1200 km
Nukus - Ashgabat – 800 miles
Nukus - Dushanbe – 1100 km
High represented the approximate distance between the capital cities of the central
asian countries.
B/S
T
O
B
A
D
N
Satrbo'yicha
min
T
1210
480
1700
320
1050
320
O
1210
950
1900
1400
1600
950
B
480
950
2000
790
1200
480
A
1700
1900
2000
1150
800
800
D
320
1400
790
1150
1100
320
N
1050
1600
1200
800
1100
800
1 table.
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1-row table to bring his will write out the smallest element to the right side of the
corresponding row and the row of the element following it isolated from 2-you will be able to
schedule.
B/S
T
O
B
A
D
N
T
890
160
1380
0
730
O
260
0
950
450
650
B
0
470
1520
310
720
A
900
1100
1200
350
0
D
0
1080
470
Per 830
780
N
250
800
400
0
300
min
on
column
0
470
0
0
0
0
2-table
The yield on the 2-of the table the column themselves bring order to the table under
the column to en fit'vewritten a small element of g and eliminate the columnare isolated from
mentlar, as a result, the following 3-table is formed.
B/S
T
O
B
A
D
N
A T
420
160
1380
(460)
0
730
O
260
(420)
0
950
450
650
B
(0)
0
(470)
0
1520
310
720
A
900
630
1200
350
(1000)
0
D
(470)
0
610
470
PER 830
780
N
250
330
400
(1080)
0
300
(1080)
0
NA
C
=
AN
C
=
3-the table
3-the table is listed, there is at least one element in every row and column zero. The
following charts coefficient h equal to the number of people you bring
320 950 480 800 320 800 0 470 0 0 0 0 4140
h
=
+
+
+
+
+
+ +
+ + + + =
1
320 950 480 800 320 800 0 470 0 0 0 0 4140
h
=
+
+
+
+
+
+ +
+ + + + =
`
1
1
1080 5220
h
h
= +
=
4140
5220
4140
1-picture.
In general, the network consists of two important stages of the method of limits and is from:
1) tarmoqlash;
2) determine the lower limit.
Both stages is conducted in parallel for solving the issue. For the implementation of this
stage, the following sequence must complete the work. A) primary come to the table; B) to
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determine h koeffitsenti to come; C) to determine the level of zero elements in the table given;
D) on the basis of this level tarmoqlash implementation; E) determine the lower limits of
tarmoqlanish the results of the cycle components; f) reduce the size of the table to one; and g)
the full cycle of harvest remain to keep from; H) this process (2x2) continue until the table is
formed; I) determine the final results corresponding to a cycle network; (J) all limits (ho ba)
to compare; K) is a necessity the results can restore the table to the minimum boundary
tarmoqlash fit to continue.
During the application of this method, all the calculations are conducted using the table
given, and its results will go far in showing graf configured separately. Perfect at the end of
this process(lowest cost) cycle is determined.
If doiracha graf consists of combined mutual, each one of them will determine a certain
xossali collection cycle. This doiracha written by the border-while the number of the same
circle indicates that belongs to a cycle corresponding to the lower limit of the costs. Part 1 of
the primary graf-picture is in view. Thus, the first cycle of primary package which includes
all doiracha define the number of cycle costs go on a voluntary means that h is small. Seen in
the example above, h=4140 was, therefore, costs 4140 it's not a cycle that is small.
Which is great bc most of the level is situated zerotry
i
and superior
j
being found are
( , )
i j
on there. Mabodo, if nollar is a multiple senior level, one of them optional is selected.
Thus, the right side in the city doiracha ij city to pass to the insideof the div of the entire
cycle ofthe package and it means ng,
( , )
i j
defined byis justified, in the left side doiracha esa,
on the contrary, I from j city chinaevery transition to its own into unable route of the
collection meansdi and it
( , )
i j
with be determined.
Most of the level katta 1080 with zero element
(1080)
54
0
c
=
is, therefore, tarmoqlanish
grafi1-picture view is. Left doiracha bring costs to a minimum coefficient
4140
h
=
to zero,
the greatest level of 1080 , which is formed by adding 5220 number is recorded.
'
1
( )
h
In the
right side to determine the lower limit of costs doiracha compatible 3-table 5-row and 4-
remove the column(off) will be sent(therefore, the size of the table is reduced to one). Thus,it
should be noted that this particular, of course, the city preserved the order of the numbers(and
written) remain ,otherwise the case of the confusion stems from. After that,all he prohibited
the harvest of the full cycle,the issue
(
i
j
i i
j
® ®
®
mark i-from the city to the j-means to
the city) is the loss of to do this,
ji
c
the elements
to change the sign will be recorded two
45
c
=
).
Again he made the statements we can continue our work.
B/S
T
O
B
D
N
A T
420
160
0
730
0
O
260
0
450
650
0
B
0
0
310
720
0
A
900
630
1200
350
350
D
0
610
470
780
0
4-the table
B/S
T
O
B
D
N
A T
420
160
0
730
O
260
0
450
650
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B
0
0
310
720
A
550
80
850
0
D
0
610
470
780
0
0
0
0
650
5 table
B/S
T
O
B
D
N
A T
420
160
(80)
0
80
O
260
(160)
0
450
(70)
0
B
(0)
0
(80)
0
310
70
A
550
80
850
(80)
0
D
(130)
0
610
470
130
(160)
0
OB
C
=
BO
C
=
6table
2
h
= 4140+350+650=5140
'
2
h
=
2
h
+=160=5300
B/S
T
O
D
N
T
420
0
80
0
B
0
310
70
0
A
550
80
0
0
D
0
610
130
0
0
80
0
70
3
2
80 70 5290
h h
=
+
+
=
`
3
3
340 5630
h
h
=
+
=
Table 7
B/S
T
O
D
N
T
340
(10)
0
10
B
(0)
0
310
(10)
0
A
550
(340)
0
(0)
0
D
(60)
0
530
60
(340)
0
AO
C
=
OA
C
=
Table 8
B/S
T
D
N
T
0
10
B
0
310
0
D
0
60
In this table row in column b and change the schedule because of the lack of unlimited n stir
B/S
T
D
N
T
0
10
0
B
0
310
0
D
0
60
0
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0
0
10
4
3
10 5290 10 5390
h
h
= +
=
+
=
`
4
4
320 5710
h
h
=
+
=
Table 9
B/S
T
D
N
T
(310)
0
(50)
0
B
(310)
0
310
D
(50)
0
50
(310)
0
BT
C
=
TB
C
=
Table 10
B/S
B
N
T
0
0
D
50
50
Table 11
B/S
B
N
T
0
D
0
0
0
Table 12
B/S
B
N
T
0
D
0
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the shortest path (optimal route):
T
D
N
A
O
B
T
® ® ® ® ® ®
Minimum distance: km-5230
Conclusion.
Kommivoyajyor issues of mathematical modeling of many real-life
problems and used for the optimization of a classic issue. Due to the complexity of much of
the calculation of the optimal solution found, in many cases the approximate algorithm or
approach heuristik apply.
Used literature:
1. Applegate, D. L., Bixby, R. E., Chvátal, V., & Cookie, J. W. (2007). Travel I Am Your
Sales Problem: A Computational Study. Princeton University Press.
2. Gavrilov, T. A. & Kudryavtsev, Yu. V. (2016). Issledovanie v upravlenii I ekonomika
operation. Focusing sp.: Peters.
3. Bazarbaev, J. K. (2019). Matematicheskoe modelirovanie I optimizasiya logisticheskix
prosessov. Almaty: Kaz.
4. Cormen T. H., Leiserson C. E., Rivest, R. L., & From Stem, C. (2009). Introduction to
Algorithms (3rd ed.). MITCH Press.
5. Nazarov, A. X. & Toshmatov, F. T. (2021). Operations research: theory and practice.
Tashkent: Economics publishing house.
6. Makhmudov, Sh. M. (2022). “Kommivoyajor issues modern solution methods”. TDIU
scientific journal, №4, 115-120-page.
7. Laporta, G. (1992). "The problem is that I am your sales travel: an overview of exact and
approximate Algorithms". European journal of operational research, 59(2), 231-247.
INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE
ISSN: 2692-5206, Impact Factor: 12,23
American Academic publishers, volume 05, issue 04,2025
Journal:
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page 1255
8. Operating issledovaniya: who zada president, methods, and models. Pod red. V. V.
Shevchenko. – M.: I finans statistics, 2017.
9. Islamov, A. N. (2023). “Central asia identify the optimal way of logistics at the
mathematical principles”. Applied mathematics and computer science, №2, 78-85-page.
