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28Electronic scientific and practical journal
INTELLECTUALIZATION OF LOGISTICS AND SUPPLY CHAIN MANAGEMENT
I I vi WWW.SMART-SCM.ORG linpj ISSN 2708-3195
¡1—1 I DOI.ORG/10.467S3/SM ART-SCM/2020-3
fQ E ectronic scientific and practical izollectijn
jintellectuali7atiqn of logistics ]j and supply chain management
Electronic scientific and practical publication in economic sciences
ISSN 2708-3195
DOI: https://doi.org/10.46783/smart-scm/2020-3
Released 6 times a year
№ 3 (2020) October 2020
Kyiv - 2020
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Editor in Chief: Deputy editors-in-chief:
Hryhorak M. Yu. - Doctor of Economics, Ass. Professor. Koulyk V. A. - PhD (Economics), Professor. Marchuk V. Ye. - Doctor of Tech. Sci., Ass. Professor.
Technical editor: Executive Secretary:
Harmash O. M. - PhD (Economics), Ass. Professor. Davidenko V. V. - PhD (Economics), Ass. Professor.
Members of the Editorial Board:
SWIEKATOWSKI Ryszard - Doctor of Economics, Professor (Poland); POSTAN M. Ya. - Doctor of Economics, Professor;
TRUSHKINA N. V. - PhD (Economics), Corresponding Member of the Academy;
KOLOSOK V. M. - Doctor of Economics, Professor;
ILCHENKO N. B. - Doctor of Economics, Ass. Professor;
SOLOMON D. I. - Doctor of Economics, Professor (Moldova);
ALKEMA V. H. - Doctor of Economics, Professor;
Henryk DZWIGOt - PhD (Economics), Professor (Poland);
SUMETS O. M. - Doctor of Economics, Ass. Professor;
STRELCOVA Stanislava - PhD (Economics), Ass. Professor, (Slovakia);
RISTVEJ Jozef (Mr.) PhD (Economics), Professor, (Slovakia);
ZAMIAR Zenon - Doctor of Economics, Professor, (Poland);
SMERICHEVSKA S. V. - Doctor of Economics, Professor;
GRITSENKO S. I. - Doctor of Economics, Professor;
KARPENKO O. O. - Doctor of Economics, Professor;
PATKOVSKYI S. A. - Business practitioner.
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In 2020, the International Center for Periodicals (ISSN International Center, Paris) included the Electronic Scientific and Practical Edition "Intellectualization of Supply Chain Management" in the international register of periodicals and provided it with a numerical code of international identification: ISSN 2708-3195 (Online).
Recommended for dissemination on the Internet by the Academic Council of the Department of Logistics NAU (No. 7 of February 26, 2020). Released 6 times a year. Editions references are required. The view of the editorial board does not always coincide with that of the authors.
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Contents
INTRODUCTION 6
FEDOROV E. E. Doctor of Technical Science, Associate Professor, Professor of Department Robotics and Specialized Computer Systems, Cherkasy State Technological University (Ukraine), NIKOLYUK P. K., Doctor of Physics and Mathematics Sciences, Professor, Professor of Department Computer Sciences and Information Technologies, VasiT Stus Donetsk National University (Ukraine), NECHYPORENKO O. V., PhD, Associate Professor, Associate Professor of Department Robotics and Specialized Computer Systems, Cherkasy State Technological University (Ukraine), CHIOMA E. V., Student of Department Computer Sciences and Information Technologies, VasiT Stus Donetsk National University (Ukraine)
INTELLECTUALIZATION OF A METHOD FOR SOLVING A LOGISTICS PROBLEM TO OPTIMIZE COSTS WITHIN THE FRAMEWORK OF LEAN PRODUCTION TECHNOLOGY 7 - 17
HRYHORAK M. Yu. Doctor of Science in Economics, Associate Professor, Head of
Logistics Department of National Aviation University (Ukraine), LEHA V. O., Students
of Logistics Department of National Aviation University (Ukraine)
CORPORATE CULTURE REENGINEERING STRATEGY OF A MULTINATIONAL LOGISTICS
COMPANY 18 - 28
HOBELA V. V. PhD of Economics, Senior Lecturer of the Department of Management of Lviv State University of Internal Affairs (Ukraine)
LOGISTICS AS A SUPPLY TOOL ECOLOGICAL AND ECONOMIC SECURITY OF THE STATE 29 - 37
BUGAYKO D. O. PhD in Economics, Associate Professor, Acting Director International Cooperation and Education Institute, Instructor of ICAO Institute of National Aviation University (Ukraine), KHARAZISHVILI Yu. M., Doctor of Economic Sciences, Senior Researcher, Chief Researcher of Institute of Industrial Economics of the National Academy of Sciences (Ukraine), ANTONOVA A. O., PhD in Technical Sciences, Associate Professor, Associate Professor of Air Transportation Management Department of National Aviation University (Ukraine), ZAMIAR ZENON Doctor of Technical Sciences, Professor, Vice-Rector the International University of Logistics and Transport in Wroclaw (Poland)
IDENTIFICATION OF AIR TRANSPORT ECOLOGICAL COMPONENT LEVEL IN THE CONTEXT OF ENSURING SUSTAINABLE DEVELOPMENT OF THE NATIONAL ECONOMY 38 - 53
TADEUSZ POPKOWSKI, PhD eng., Professor, The International University of Logistics and Transport (Wroclaw, Poland), BUGAYKO D. O. PhD in Economics, Associate Professor, Acting Director International Cooperation and Education Institute, Instructor of ICAO Institute of National Aviation University (Ukraine) MODERN CHALLENGES OF DANGEROUS AND EXTRAORDINARY GOODS
TRANSPORTATIONS 54 - 61
A®
This work is licensed under a Creative Commons Attribution 4.0 International License
SAVCHENKO L.V. PhD of Technical Sciences, Associate Professor, Associate Professor of Logistics Department of National Aviation University (Ukraine), Davydenko V.V., PhD of Economics, Associate Professor, Associate Professor of Logistics Department of National Aviation University (Ukraine) EFFICIENCY OF DIGITAL COMMUNICATIONS IN THE LOGISTICS BUSINESS: EVALUATION INDICATORS _____________________________________________________________________________________________________________________________________________________________________________________________ 62 - 73
KOULIK V^. PhD (Economics), Professor, Professor of Logistics Department National Aviation University (Ukraine), Honored Worker of National Education of Ukraine, Honorary employee of aviation transport of Ukraine (Ukraine), ZAHARCHUK A.P. Assistant of the Logistics Department of National Aviation University (Ukraine)
PROBLEMS OF MANAGEMENT IN THE SYSTEM OF SPIRAL DYNAMICS OF SUPPLY CHAINS 74 - 82
MOLCHANOVA K.M. Senior lecturer at the Department of Logistics National Aviation University (Ukraine), TRUSHKINA N.V. PhD (Economics), Associate Professor, Senior Research Fellow, Regulatory Policy and Entrepreneurship Development Institute of Industrial Economics of the National Academy of Sciences of Ukraine (Ukraine), KATERNA O.K. PhD (Economics), Associate Professor, Associate Professor at the Department of Foreign Economic Activity Enterprise Management National Aviation University (Ukraine)
DIGITAL PLATFORMS AND THEIR APPLICATION IN THE AVIATION INDUSTRY 83 - 98
EVENTS AND SCIENTIFIC CONFERENCES
Marcin PAWÇSKA - THE JUBILEE INAUGURATION OF THE 2020/2021 ACADEMIC YEAR at
The International University of Logistics and Transport in Wrociaw............................................ 99 - 105
Yevhen KRYKAVSKYY, Nataliya HAYVANOVYCH - XIII International Scientific and Practical Conference "MARKETING AND LOGISTICS IN THE SYSTEM OF MANAGEMENT" at Lviv Polytechnic National University........................................................................................................ 106 - 108
Mariia HRYHORAK, Lidiia SAVCHENKO, Oksana OVDIIENKO - LOGISTICS - RELEVANT, GLOBAL, VIRTUAL AND REAL!...................................................................................................................... 109 - 111
UDC 004.023, 330.45 DOI: https://doi.org/10.46783/smart-scm/2020-3-1
JEL Classification: C61, M 15. Received: 13 October 2020
Fedorov E. E. Doctor of Technical Science, Associate Professor, Professor of Department Robotics and Specialized Computer Systems, Cherkasy State Technological University (Ukraine)
ORCID - 0000-0003-3841-7373 Researcher ID - AA0-6744-2020
Scopus author id: 47161087200, 47161155900, 57205185819
Nikolyuk P. K., Doctor of Physics and Mathematics Sciences, Professor, Professor of Department Computer Sciences and Information Technologies, VasiT Stus Donetsk National University (Ukraine)
ORCID - 0000-0002-0286-297X Researcher ID - H-3223-2017 Scopus author id: -
Nechyporenko O. V., PhD, Associate Professor, Associate Professor of Department Robotics and Specialized Computer Systems, Cherkasy State Technological University (Ukraine)
ORCID - 0000-0002-3954-3796 Researcher ID -Scopus author id: -
Chioma E. V., Student of Department Computer Sciences and Information Technologies, VasiT Stus Donetsk National University (Ukraine)
ORCID - 0000-0002-0286-297X Researcher ID -Scopus author id: -
INTELLECTUALIZATION OF A METHOD FOR SOLVING A LOGISTICS PROBLEM TO OPTIMIZE COSTS WITHIN THE FRAMEWORK OF LEAN PRODUCTION TECHNOLOGY
Eugene Fedorov, Peter Nikolyuk, Olga Nechporenko, Esta Chioma. "Intellectualization of a method for solving a logistics problem to optimize costs within the framework of Lean Production technology". In the article, within the framework of intellectualization of the Lean Production technology, it is proposed to optimize the costs arising from the insufficient efficiency of placing goods in the warehouse by creating an optimization method based on the immune metaheuristics of the T-cell model, which allows solving the knapsack constrained optimization problem. The proposed metaheuristic method does not require specifying the probability of mutation, the number of mutations, the number of selected new cells and allows using only binary potential solutions, which makes discrete optimization possible and reduces computational complexity by preventing permanent transformations of real potential solutions into intermediate binary ones
and vice versa. An immune metaheuristic algorithm based on the T-cell model has been created, intended for implementation on the GPU using the CUDA parallel information processing technology. The proposed optimization method based on immune metaheuristics can be used to intellectualize the Lean Production technology. The prospects for further researches are to test the proposed methods on a wider set of test databases.
Keywords: lean manufacturing, immune metaheuristics, T-cell model, conditional optimization, knapsack problem.
€вген Федоров, Петро Школюк, Ольга Нечипоренко, Еста Ч'юма. "1нтелектуальна реал'1зац'я методу лог'ктичного ршення для оптим'!зацн витрат за технологию Lean Rroduction". У cmammi в рамках Ытелектуал'вацП технологи Lean Rroduction пропонуеться оптим'вувати витрати, що виникають в результатi в'1дсутност'1 ефективнот розмщення товар 'т на складi, шляхом створення методу оnmuмiзацil'на основi ¡мунно!метаевристики моделi Т-клimин, що дозволяе виршити проблему умовноl оптим'вацИ' про рюкзак. Запропонований метаевр'!стичний метод не вимагае задання ймов'рностi мутаци, к'тькост'1 мута^й, к'тькост'1 в 'дбраних нових клтин i дозволяе використовувати тльки бнарн поmенцiйнi ршення, що робить можливою дискретну опmимiзацiю i знижуе обчислювальну складн'!сть шляхом запобгання постЮнЮ трансформаци фiзuчнuх потенцЮних ршень в промiжнi бнарн i зворотн'!. Створено '¡мунний алгоритм метаевристики на основi моделi T-клimuн, призначений для впровадження на GPU за допомогою технологи паралельноlобробки нформаци CUDA. Запропонований метод опmuмiзацil'на основi iмунноl' метаевристики може бути використаний для iнmелекmуалiзацil' технологи Lean Rroduction. Перспективи подальших дослiджень включають тестування запропонованих метод1в на бльш широкому наборi тестових баз даних.
Кпючов'1 слова: ощадливе виробництво, iMyHHa метаевристика, модель Т-^тин, умовна опти1^зафя, задача про рюкзак.
Евгений Федоров, Петр Николюк, Ольга Нечипоренко, Эста Чиома. "Интеллектуализация метода решения логистической задачи для оптимизации затрат в рамках технологии Lean Production". В статье в рамках интеллектуализации технологии Lean Production предлагается оптимизация затрат, возникающих вследствие недостаточной эффективности размещения товаров на складе, посредством создания метода оптимизации на основе иммунной метаэвристики модели Т-клеток, который позволяет решать задачу условной оптимизации о рюкзаке. Предложенный метаэвристический метод не требует задания вероятности мутации, количества мутаций, количества отбираемых новых клеток и позволяет использовать только бинарные потенциальные решения, что делает возможной дискретную оптимизацию и снижает вычислительную сложность за счет предотвращения постоянных преобразований вещественных потенциальных решений в промежуточные бинарные и обратно. Создан иммунный метаэвристический алгоритм на основе модели Т-клеток, предназначенный для реализации на GPU посредством технологии параллельной обработки информации CUDA. Предложенный метод оптимизации на основе иммунной метаэвристики может использоваться для интеллектуализации технологии Lean Production. Перспективы дальнейших исследований заключаются в тестировании предложенных методов на более широком наборе тестовых баз данных.
Ключевые слова: бережливое производство, иммунная метаэвристика, модель Т-клеток, условная оптимизация, задача о рюкзаке.
Introduction. At present many worldwide companies are optimizing their business processes based on Lean Production technology. The concept of Lean Production is that it clearly identifies seven groups of
costs that do not create value for final buyers, and therefore, the primary efforts of any company should be directed to minimizing these costs. However, the problem of finding models to minimize these costs is quite
complicated and requires searching for the new solutions. As a result, the relevance of the development of methods for the intellectualization of Lean Production technology, which is based on the solution of optimization problems, significantly increases.
Literature and research review. Highly computationally complex optimization methods that find an accurate solution. Optimization methods that find an approximate solution through directional search have a high probability of hitting a local extremum. Random search methods do not guarantee convergence. Consequently, there is a problem of insufficient efficiency of optimization methods, which needs to be addressed.
Metaheuristics (or modern heuristics) [25] are used to find an accelerate quasi-optimal solution optimization problems and reduce the probability of hitting a local extremum. Metaheuristics empowered of heuristics by combining heuristic methods based on a high-level strategy [6-9].
The current metaheuristics have one or more of the following disadvantages:
- there is only an abstract description of the method or the description of the method is focused on solving only a certain problem [10];
- the influence of the iteration number on the process of finding a solution is not taken into account [11];
- the convergence of the method is not guaranteed [12];
- it is not possible to use non-binary potential solutions [13];
- the procedure for determining the values of parameters is not automated [14];
- it is not possible to solve the problems of conditional optimization [15];
- the lack of accuracy of the method [16].
In this regard, the problem of
constructing effective metaheuristic optimization methods arises [17].
One of the popular metaheuristics are immune metaheuristics [18, 19], among which the T-cell model [20] can be
distinguished, which allows solving constrained optimization problems.
Aims and Objectives. The aim of the work is to optimize the costs arising from the insufficient efficiency of placing goods in the warehouse by creating an optimization method based on immune metaheuristics that solves the knapsack problem.
To achieve the goal, the following tasks were put and decided:
1. Conduct an analysis of existing optimization methods aimed at optimizing costs within the framework of lean manufacturing technology.
2. Create an immune metaheuristic method based on the T-cell model for solving the knapsack problem.
3. Create an algorithm of the immune metaheuristic method based on the T-cell model, intended for implementation on the GPU using the CUDA technology.
4. Conduct a numerical study.
Results, analysis, and discussion.
Optimization of costs associated with inefficient placement of goods in a warehouse can be reduced to the problem of a knapsack. To solve this problem, the work proposes an immune metaheuristic - a modified model of T cells that uses imitation of annealing.
As a function of the goal F, it is proposed to use the inverse function of income
Г
F ( x)
M
л
-i
I
V i=i
VjXj
^ min
x
v
where ■ is the income from the goods of the j -th type, defined,
w ■ j
■ - weight of goods of the J -th type,
defined,
x
■ - goods presence of the ■ -th type (corresponds to the T-cell),
M - the number of types of goods.
As a limit, it is proposed to use the following function
Figure 1 — The structure of the proposed immune metaheuristic method for solving the
knapsack problem
g ( x) = max
M
o S
j=i
wjxj -W
setting the probability of mutation of
where W - is the maximum total weight of all goods, defined.
The structure of the proposed immune metaheuristic method is shown in Fig. 1.
The proposed metaheuristic method makes possible to find the quasi-optimal number of placed goods and consists of the following blocks:
Block 1 - Initialization:
- setting the number of the current iteration n to one;
- setting the number of iterations N,;
- setting the cell length — ;
- setting the size of the subpopulation of
new cells Lv ;
- setting the number of selected new
cells, taking into account the restrictions L1v L1V = LV/4
as
V
- setting the number of selected new cells without taking into account the
. . .. L2V L2V = LV /4 restrictions V as V V ;
- setting the number of mutations of
each executive cell Ne as Ne = N ,
- setting the size of the subpopulation of
memory cells L— as Lm Lv /4 ;
- setting the number of mutations of
each memory cell N— as N— = N,
- setting a static tolerance A— for a subpopulation of memory cells;
- setting the probability of mutation of
E 1
P =-
executive cells as — ;
memory cells as
pM = — M .
- randomly create the best cell x
* / * * \ X = (Xl5"-5 XM ),
x* = il, U(0,1) < 0.5 j \0, U(0,1) > 0.5
where U (0,1) - is a function that returns a uniformly distributed random number in
the range of [0'1].
Block 2 - Creation of a subpopulation of
new cells pV V
x
P = {(xk,)}, k e 1, Lv
xk = ( xk1,---, xk—), [1, U(0,1) < 0.5 k [0, U(0,1) > 0.5
sk =max{0, g ( xk )} Block 3 - Calculation of the dynamic tolerance value ^V for a subpopulation P
1 LV
a v = sk
L
V k=1
If AV <A —, then AV =0.1
Block 4 - Creation of a subpopulation of
de t
executive cells P with capacity E
4.1. Dividing a subpopulation of new cells PV into a subset = {(x1k, s1k)}
containing cells for which s1k < AV, and a subset P2 = {(x2k, s2k )} containing cells
- J2k >Af
for which
pi v
4.2. Ordering the subset ri by target function, i.e. F() < F(+i)
P0F
4.3. Ordering the set by the sum of the values of all bounding functions, i.e.
s 2 k < s 2 k+1
4.4. L1y of the first cells from an ordered
V L2
set P1 and V the first cells from an ordered set P2V forms a subpopulation of
PE = {( Xi, si )}
executive cells
with capacity
le l1v + l2v , while the first there are
cells from the set P1V
Block 5 - Modification of a subpopulation
N
e
pE
of executive cells r based on mutation
For each j - th cell is performed once as the following operations are performed:
- mutation
r = U (0,1)
Xj =
^ (r < pE л XiJ = 0) v (r > pE л XiJ =i) , ——
E E J ei M
0, (r < pE л xJJ = i) v (r > pE л X tJ = 0)'
where round0 - is the function that rounds the number to the nearest integer.
- calculating the value of the constraint function
Sj = max{0 , g(Xj)}
- replacement by a mutant cell if the condition is met
lf Si < sj or S j = sj A F(X j) < F(x i ),
then Xj Xj, Sj Sj
Block 6 - Calculate the value of the
dynamic tolerance AE for a subpopulation
P
E
Ae= I
L
E k=1
If A e < A m , then ^ e = ^m
Block 7 - Creation of a subpopulation of
memory cells pM with capacity Lm
7.1. Dividing the subpopulation of
de
executive cells P into a subset
PiE ={( xik, sik )}
which
sik < AE
, containing cells for and subset
P2E = x2 s2
w k> kJf, containing cells for
which s2k ~ ^E
7.2. Ordering the subset plE by target
function, i.e. F(x1k) < F(x1k+i)
7.3. Ordering the set P2E by the sum of the values of all bounding functions, i.e.
s2k < s2k+1
7.4. If n = 1, then Lm the first cells from
the ordered union P1 ^p2 form a subpopulation of executive cells
PM ={( xt, Si )}
If n > 1, then lm / 2 the first cells from
piE M P2E
the ordered union are replaced
T / 2
M by the worst (last) cells, a
subpopulation of executive cells P
Block 8 - Modification of a subpopulation
of memory cells pM based on mutation
For each j - th cell is performed Nm , once as the following operations are performed: - mutation
r = U (0,1)
s
k
1, (r < pM A Xj = 0) V (r > pM A Xj =1) 0, (r < pM A Xj =1) V (r > pM A Xj =0)
m
- calculating the value of the constraint function
st =max{0, gz ( xt)}
- replacement by a mutant cell if the condition is met
If < si or s i = s i A F(x i) < F(x i),
then %i %i, Si Si
Block 9 - Ordering the subpopulation of
memory cells p—
Dividing the subpopulation of memory
cells P— into a subset P1— ={(x1k, s1k)}
containing cells for which s1k <A—, and a
subset P2M = {(x2k, J2k)} for which J2k > Am .
containing cells
ni m
9.2. Ordering the subset P1 by target
F(xlk) < F(xlk+1)
function, i.e.
Ty\M
9.3. Ordering the set P2 by the value of the bounding function, i.e. < +1
9.4.
PM =P1M U P2M ={(x, J)}
the subpopulation of new cells Lv, the number of selected new cells taking into
account the limitations L1v , the number of selected new cells without taking into
account the limitations L2v , the number of
mutations of each executive cell ne , the size
of the subpopulation of memory cells L— , the number of mutations of each memory cell
N—, static tolerance A— for a subpopulation of memory cells, the probability of mutation
pe
of executive cells , setting the probability
P—
of mutation of memory cells as ^ .
*
Step 2 - Randomly create the best cell x Step 3 - The creation of a subpopulation
of new cells pV using GPU threads Lvthat are grouped into 1 block. Each thread randomly
x
creates a cell k and calculates the value of
s
the bounding function for this cell k
Step 4 - Computation based on reduction of the dynamic tolerance AV value
cell
Block 10 - Determining of the global best c , ... pv .. .. - a a for the subpopulation P across all cells
|f F(xi) < F(x ), then x* =xi Block 11 - Stop Condition If n < N, then increase the iteration number n by one and go to block 2.
For the proposed method, using the example of optimization of costs arising from insufficient efficiency of placing goods in a warehouse, an algorithm is considered intended for implementation on a GPU using the technology of parallel processing of information CUDA and shown in Fig. 2. This block diagram functions as follows.
Step 1 - Operator's input of the number of iterations N, the cell length M, the size of
using GPU threads Lv , which are grouped into 1 block. If Av < A—, then Av = 01
Step 5 - Dividing the subpopulation of
new cells pV into a subset P1 ={(x1k, s1k)} containing cells for which s1k < Av , and a subset P2V ={(x2k, s2k )} containing cells for which s2k > Av.
Step 6 - Ordering the subset P1V by
target function, i.e. F(x1k) < F(x1k+l)
using
GPU threads I Piv I
1 block
which are grouped into
Step 7 - Ordering the subset P 2 by the sum of the values of all bounding functions,
s2k < s2k+1 using GPU threads I P2^ I
i.e.
which are grouped into 1 block
Step 8 - L1v first cells from the ordered set P1V and L2V first cells from the ordered set P2V form a subpopulation of executive
PE = {(X S )} cells j j with capacity
Le l1v + L 2v , and the first cells from the set P1V
2
4
б
9
i0
ii
i2
1 r
в
1 r
i4
1 r
i5
1 r
i6
1 r
i7
1
is
1 r
i9
1 r
20
i
З
5
7
s
Figure 2 - Block diagram of the algorithm of the proposed immune metaheuristic method
Step 9 - Modification of a subpopulation
r>E
of executive cells p based on mutation using GPU threads Le that are grouped into 1
block. Each thread Ne once mutates a cell Xj and calculates the value of the limiting
function for this cell sj
Step 10 - Reduction computation of the which
X
once mutates a cell j and calculates the
s
value of the limiting function for this cell ' Step 16 - Dividing the subpopulation of
memory cells PM into a subset
pl = {( Xlk, slk )} containing cells for
s1k < A
U ^ M
dynamic tolerance value ae for the
r>E
subpopulation P across all cells using GPU threads Le that are grouped into 1 block. If
AE < AM , then AE = AM
P 2M ={( X 2k, s 2k )} which s2k >Лм.
and a subset containing cells for
Step 17 - Ordering the subset PiM by
Step 11 - Dividing the subpopulation of target function i.e.
F(xik ) < F (xik+i)
T>E
executive cells P into a subset
PiE ={( Xik , sik )},
containing cells for
which sik <ЛE, and a subset
P 2 E ={( x2 k, s2 k )}
containing cells for
which s2k > Ле .
Step 12 - Ordering the subset P1E by
target function i.e. F(x1k) < F(x1k+1) using
I P1E I
GPU threads which are grouped into 1 block
Step 13 - Ordering the set P 2 E by the sum of the values of all bounding functions,
i.e.
s2k < s2
k+1
using GPU threads
I P2e I
which are grouped into 1 block
Step 14 - If n 1, then LM the first cells
p-|E M p?E
from the ordered union form a
subpopulation of executive cells
PM ={( Xi, si )}
I P1M I
using GPU threads which are grouped
into 1 block
Step 18 - Ordering the set P2M by the value of the bounding function, i.e.
s2k < s2k+i using GPU threads I P2M I which are grouped into 1 block
Step 19 - Ordered sets P1V and P2V form a new subpopulation of memory cells
pM , i e. PM=P1M U P2M = {(xi, Si)}
Step 20 - Determining the global best cell
according to the following rule
* *
If F(x1) < F(x ), then x =x1 Step 21 - Stop Condition
If n <N, then increase the iteration number by one and go to step 4.
Step 22 - Writing the obtained global best position to the database.
In the work, the number of iterations N = 100, the size of the subpopulation of new cells
L /2
, otherwise M first cells
L
from the ordered union P1 UP2 are cells taking into account the constraints
v = 100, the number of selected new
L1v
L / 2
replaced M the worst (last) cells, a
M
subpopulation of executive cells p
Step 15 - Modification of a
subpopulation of memory cells pM based on
the mutation using GPU threads LM , which are grouped into 1 block. Each thread
N
= Lv / 4 = 25, the number of selected new cells without taking into account the
constraints L2v == Lv / 4 = 25, the number of
mutations of each executive cell Ne = N = 100, the size of the memory cell
M
subpopulation LM == Lv / 4 = 25, the number
of mutations of each memory cell Nm = N =
100, the static tolerance A m = 0.0001 for the memory cell subpopulation.
For the knapsack problem, the search for a solution was carried out on the standard KNAPSACK_01 databases. For the proposed method, a root-mean-square error of 0.02 was obtained.
The traditional method for optimizing a T-cell model requires:
- setting the probability of mutation, the number of mutations, the number of selected new cells;
- real potential solutions, which makes discrete optimization impossible;
- constant transformations of real potential solutions into intermediate binary ones and vice versa.
The proposed method eliminates these disadvantages.
Conclusions.
1. To minimize losses that do not create consumer value and are the basis of Lean Production technology, an immune
metaheuristic method based on the T-cell model was developed to solve the knapsack problem. The use of this method is aimed at minimizing costs arising from insufficient efficiency of the placement of goods in the warehouse.
2. The proposed metaheuristic method does not require setting the probability of mutation, the number of mutations, the number of selected new cells and allows using only binary potential solutions, which makes discrete optimization possible and reduces computational complexity by preventing constant transformations of real potential solutions into intermediate binary ones and back.
3. There was created an immune metaheuristic algorithm based on the T-cell model, intended for implementation on a GPU using the CUDA parallel processing technology.
4. The proposed optimization method based on immune metaheuristics can be used to intellectualize the Lean Production technology. Prospects for further research are in testing the proposed methods on a wider set of test databases.
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