Actual Aspects of Information Technologies Application at the Problem Decision of the Movement Organisation by a Convoy of Vehicles Oleh Borovyk 1, Yurii Gunchenko 2, Serhii Lienkov 3, Liudmyla Borovyk 4, Oleksii Konovalenko 5 and Iryna Basaraba 6 1, 4, 6 The National Academy of the State Border Guard Service of Ukraine named after Bohdan Khmelnytsky, Shevchenko str., 46, Khmelnytskyi, 29000, Ukraine 2 I.I. Mechnikov National University, Dvorianska Str., 2, Odessa, 65025, Ukraine 3 Military Institute of Taras Shevchenko National University of Kyiv, Lomonosova Str., 81, Kyiv, 03189, Ukraine 5 А 3814, Kyiv, Ukraine Abstract The analysis of the known approaches to solving the problem of organization of transportation by a convoy of vehicles showed that due to the existence of a large number of brands and types of vehicles, from which the convoys are formed, various tactical and technical characteristics of the samples of technology, a branched network of roads, multi-variants the choice of route, the possible development of the traffic situation, they do not solve the problem of efficient organization of traffic, although the article shows the urgency and weight of such a problem. Therefore, the purpose of this study is to substantiate possible approaches to the solution of the problem of organizing transportation by a convoy of vehicles, as well as their formalization. The article analyzes the problems of optimization of the military convoy composition and the choice of the optimal route for its movement from the point of their complex combination to solve the systematic problem of the organization of transportation by the convoy of vehicles. On the basis of the analysis, a multicriteria optimization problem was formulated, including criteria and a system of constraints which included all criteria and limitations of the constituent problems, and substantiation of possible approaches to its solution. The proposed approaches make it possible to: classify the tasks of organizing the march; generate algorithms for solving the problem under study in each of the productions; to evaluate the limited possibilities of the analytical methods available to solve the applied tasks of organizing a march; evaluate possible approaches to forming a mathematical apparatus to solve these problems; to conclude the need to develop information technology that would ensure the solution of the problem of organizing the march in any setting. Keywords 1 Optimization problem, Multicriteria, Mathematical Model, Algorithms, Information technology. 1. Introduction fields of human activity, in particular, when solving various tasks of the logistics sphere. The successful implementation of many relocations is To date, the issue of optimization of highly dependent on the timely arrival of the transportation is extremely important in various ISIT 2021: II International Scientific and Practical Conference «Intellectual Systems and Information Technologies», September 13–19, 2021, Odesa, Ukraine EMAIL: bov_nadpsu@ukr.net (A. 1); bmk1010@ukr.ne (A. 2); lenkov_s@ukr.net (A. 3); blv_nadpsu@ukr.net (A. 4); ssimmplezz@gmail.com (A. 5); irynabasaraba2017@ukr.net (A. 6) ORCID: 0000-0003-3691-662X (A. 1); 0000-0003-4423-8267 (A. 2); 0000-0001-7689-239Х (A. 3); 0000-0003-2949-2187 (A. 4); 0000-0002-2179-5477 (A. 5); 0000-0002-3209-9119 (A. 6) ©️ 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) military convoy at the intended destination. For of cargo transportation from one sender to several effective transportation of various cargoes by land consumers is presented in the transport network. various modern vehicles with wide possibilities However, in the analyzed works [2-4], such are used. Before scheduling transportation, it is requirements for the formation of the optimal possible to optimize the composition of the composition of the convoy of vehicles, such as the convoy of vehicles taking into account a wide level of readiness, the power reserve on range of factors [1]. In the next step, it is necessary motoresource, the number of brands and samples, to solve the problem of determining the optimal the availability of fuel for refueling, etc., were route of movement of the military convoy. A ignored. These requirements were reflected in the sufficiently extensive network of highways author's work [1]. provides a significant number of possible routes The choice of movement routes 8of the that combine the departure point with the military convoy for the efficient movement of destination. Such variance, of course, is observed goods, as well as related problems, was focused in even at the small distances that need to be a number of works, in particular in [5-17]. An overcome. The choice of the optimal route can be approach to choosing the route based on significantly influenced by the dynamics of the "edgelabels" is given in [5]. Its application makes development of the road situation. Due to the it possible to accelerate the search for the shortest influence of the predicted and stochastic factors, path by 500 times compared to Dijkstra's the speed of movement of the convoy on algorithm over a large graph. In [6], an algorithm individual sections of the route can change for selecting optimal routes in a multimodal mode significantly. Failure to adequately account for of a public transport network is presented. changes in traffic conditions can lead to incorrect According to the results of this study, the route selection, which will not ensure timely approach to routing of transit nodes was adapted arrival of the convoy at the destination. Such to plan for relocation by public transport. In the delay may result in the failure of certain tasks. scientific work [7], the method of contraction Therefore, the task of organizing a march is hierarchy was used to find the shortest path. In the relevant, and the presence of multivariance, a study [8], based on the application of the SHARC large number of factors that must be considered in algorithm, the possibilities of finding the shortest its solution, their complex interaction and impact paths for arbitrary means of transportation in a on the result causes a significant computational continental-scale transport network are presented. complexity of the task and the need to use The problem of multimodal route planning has powerful computing tools and the development of been investigated in a scientific paper [9]. In the appropriate information technology for solving work [10] a model for estimating traffic delays of the problem. vehicles is presented, taking into account arbitrary The issue of forming a convoy of vehicles for loads during traffic. The study [11] provides efficient movement of cargo has been given mapping of marshrutes for military ground attention in a number of works, in particular [1-4]. vehicles on the battlefield. In a scientific paper Thus, in [2] the method of tactical calculations for [12], an algorithm for solving the problem of determining the number of vehicles for finding the shortest time paths in urban transportation of goods took into account the commuting networks using the branch and characteristics of cargo, load capacity and speed boundary method was developed. The issues [13- of movement of vehicles, range of movement, 14] investigate the use of geoinformation loading time, unloading, refueling, rest of drivers technologies in solving logistical problems in between flights (if provided), as well as the timing military affairs, based on the use of modern of the movement of goods. The paper [3] reflects ArcGIS information systems [15-17]. In the the issues of predicting the effectiveness of the author's work [18], the problem of choosing the march of military formation on the reliability of optimal route of convoy movement of the border weapons and military equipment, as well as the commanding rapid response technique was taken impact on the march efficiency of the number of into account, taking into account the peculiarities repair units, the technical state of technology in associated with the preliminary establishment and terms of reliability, the level of efficiency of maintenance of the reliability of the initial data repair bodies in carrying out repair work and This based on the use of spline functions [19-21] ; is the cost of repairing weapons and military mathematical models of the studied problem for equipment. In [4], a variant of a cargo three cases (discrete-stochastic, discretely- transportation model for finding the optimal route deterministic and continuous-indefinite) are constructed, which depend on the peculiarities of the number of vehicles in the convoy was realization of the convoy motion; algorithms for minimal ( K2 ); choosing the optimal route of movement of the the number of vehicle brands in the convoy was minimal K 3  ; Rapid Response Command Border Convoy of vehicles for each possible case are proposed. However, despite the sufficient attention that the duration of the march was minimal ( K4 ); was given to the authors, including the tasks of the rate of the readiness factor of each vehicle forming the optimal composition of the military shall not be less than the permitted level ( O1 ); convoy and choosing the route of its movement, the total capacity of vehicles from the the the task of organizing a march that organically combines both one and the other of these tasks has convoy allowed to carry the goods ( O2 ); not been fully explored. This is explained by the the total volume of the body of vehicles from the non-obviousness of approaches to solving such a warehouse allowed to transport the cargo ( O3 ); problem. the total passenger capacity allowed to Given the above urgency and importance of transport personnel ( O4 ); the problem of efficient movement organization, the total fuel consumption of vehicles from the the important and urgent task now is to formalize convoy did not exceed the amount of fuel the task of organizing transportation by a convoy of vehicles. The purpose of this study is to available to march by fuel type ( O5 ,...,O8 ); substantiate possible approaches to the solution of the stock of motorsource was not less than the the specified problem and its formalization in distance of transportation ( O9 ). different formulations taking into account the However, it should be taken into account that criteria and the system of limits of constituent during the movement of the convoy, the motion problems. time along the individual edges can be variable. This condition is determined by the influence on 2. Formulation of the task of the time of movement along a single edge of different conditions, such as climatic (rain, ice, organizing transportation of the fog, etc.), man-made (blockage of the roadway, its military convoy at a meaningful post-damage due to flooding of the terrain, etc.), level and its formalization changes in the period of day (day, night). etc. It should also be noted that the weights of the At the substantive level, the problem under edges can be changed: study looks like this. at times when the convoy is at a certain vertex Given: complex M  x1 ; x2 ;...; xn  vehicles of the graph, and the matrix of weights is updated at these moments. This is a case where the from which the composition of the engineering decision on the further route of traffic is made at convoy may be formed for the carriage of the points of branching of roads taking into personnel and cargo ( xi - symbol of a definite account the situation regarding the condition of individual sections, which changes dynamically specific vehicle, i  1, n ) U 1  ; ____ and the data on which appear periodically; the tactical and technical characteristics of at the times when the convoy is at a certain each vehicle of this group U 2  . vertex of the graph, and for these moments the Also, set up a network of roads that connect the weights matrix that will take place when the departure point (point А) with destination (point convoy enters the vertex are well known in В). The mathematical model of the road network advance. This is a case where a route decision can is a marked graph G , the weight of the edges of be made at the beginning of the traffic, taking into which represents the time of movement of the account the well-known situation regarding the convoy along them U 3  . state of the roads, which will change dynamically, but the data on which can be taken into account in It is necessary to arrange transportation from advance. point A to point B so that: At the physical level, the formulated task of vehicles arrived at point B with maximum organizing a march consists in the complex readiness K1  ; solution of two interrelated problems: problem 1 - choosing the appropriate composition of the convoy of vehicles; problem 2 - choosing the K 1  max, (8) appropriate route of its movement. K 2  min, It should be noted that each of problems 1, 2 is solved separately from each other. The K 3  min, corresponding solutions are given in [1, 18]. K 4  min . The problem 1 is solved as a single-criterion System of restrictions optimization problem of the form: O1 ,...,O9 . (9) Initial data (1) Find , U1 ,U 2 ,U 3 . M o  x1 ; x2 ;...; xr  , (10) Criterion f K1 , K 2 , K3   min (2) Vo  v1 ; v2 ;...; vz  . (11) System of restrictions: In the tasks (7)-(11) M o  x1 ; x2 ;...; xr  - O1 ,...,O9 , (3) appropriate composition of the convoy of O10 . (4) vehicles, аnd Vo  v1 ; v2 ;...; vz  - expedient route In problems (1)-(4), one-criteria is obtained by of its movement. the functional combination of three separate The analysis of task 1 in the form (1) - (4) and criteria K1 , K 2 , K 3 , which appeared in the direct task 2 in the form (5) - (6) leads to the conclusion that the solution of the studied problem in the statement of problem 1, and restriction O10 form (7) - (11) can be following obtained by converting the criterion K4 . M o  x1 ; x2 ;...; xr   M1  x1 ; x2 ;...; xm , аnd The result of solving problem 1 is some set Vo  v1 ; v2 ;...; vz    V2  v1 ; v2 ;...; vs . M1  x1 ; x2 ;...; xm , the elements of which are specific vehicles that are part of the convoy. 3. Foundation of approaches to Herewith, m  n і M1  M . Task 2 is solved as a single-criterion solving the problem of optimization problem of the form: organization of transportation by Initial data a convoy of technique M 1 , U 2 ,U 3 . (5) Criterion Conditions for partial problems of the general K4  min . (6) task of organizing the march, justification of Tasks (5) - (6) take into account the variability approaches to solving the common problem, of the edges of the road network graph, and also algorithms for the implementation of each of the format of such change is how it occurs, at what variants are structured below. moments, at which stage, the dynamic matrixes of Variant 1. the edges are known. Task 1. The result of solving task 2 is the route of Mathematical model: U1 ,U 2 ,U 3 , O1 ,..., O9 , movement of the convoy V2  v1 ; v2 ;...; vs  - the O10 , f K1 , K2 , K3   min . set of vertices through which the route of travel The result of the solution: The composition of must be passed. the convoy is obtained in the form of a plurality Herewith, v1  A , vs  B . M1  x1 ; x2 ;...; xm  . The problem studied in the following notations Problem Solving Technology 1. Problem 1 in can be represented as a multicriteria optimization statement (1) - (4) is solved as an optimization problem of the following form: problem. Initial data Task 2. U1 ,U 2 ,U3 . (7) Mathematical model: M 1 , U 2 ,U 3 , K4  min . Criterion The result of the solution: The route of movement of the convoy in the form of a set is obtained V2  v1 ; v2 ;...; vs  . Problem Solving Technology 2. Problem 2 in statement (5) - (6) is solved. 1 2  be noted that the capacity of the sets M 1 , M 1 , Investigated task. d  The solution to the problem under study is …, M 1 may be different, and the elements of following: M o  M1 , Vo  V2 . these sets may also not coincide. Variant 3. Variant 2. Task 1. Task 1. Mathematical model: U1 ,U 2 ,U 3 , O1 ,..., O9 , Mathematical model: U1 ,U 2 ,U 3 , O1 ,...,O9 , O10 . The result of the solution: The variants of the O10 , O11 , O12 , O13 composition of the convoy in the form of sets are The result of the solution: The variants of the obtained composition of the convoy in the form of sets are M11  x11 ; x21 ;...; xm11  , obtained M11  x11 ; x21 ;...; xm11  , M 12   x12  ; x22  ;...; xm22 ,…, M 12   x12  ; x22  ;...; xm22 ,…, M 1d   x1d  ; x2d  ;...; xmsd   . M 1d   x1d  ; x2d  ;...; xmsd   . Problem Solving Technology 1. Problem 1 in Problem Solving Technology 1. Problem 1 in statement (1), (3), (4) is solved as a combinatorial statement (1), (3), (4) is solved with additional problem. restrictions O11 , O12 , O13 , as a combinatorial task. Task 2. ____ Task 2. i  Mathematical model: M 1 , U 2 ,U 3 i  1, d , i   ____  Mathematical model: M 1 , U 2 ,U 3  i  1, d  , K4  min .   The result of the solution: For each fixed value, K4  min . the path of the convoy motion in the form of a set The result of the solution: For each fixed value is obtained ____ V2  v1 ; v2 ;...; vs 1 ; vs  , 1 1 1 i  1, d the route of movement of the convoy in the form of a set is obtained V22   v1 ; v22  ;...; vs21 ; vs ,…, V21  v1 ; v21 ;...; vs11 ; vs , V2d   v1 ; v2d  ;...; vsd1 ; vs . V22   v1 ; v22  ;...; vs21 ; vs ,…, Problem Solving Technology 2. Task 2 in V2d   v1 ; v2d  ;...; vsd1 ; vs . statement (5) - (6) is solved. Investigated task. Problem Solving Technology 2. Problem 2 in The solution to the problem under study is statement (5) - (6) is solved at each fixed value ____ k  k  k  following: M o  M 1 , Vo  V2 , where M 1 - is i  1, d . k  Investigated task. the composition of the convoy that provides V2 . The solution to the problem under study is Problem Solving Technology. It is established k  1 2  following: that the set V2 of the number of sets V2 , V2 ,…, M o  M 1k  , Vo  V2k  . M o  M1 , V2d  , which corresponds to the minimum time of Vo  V2 . movement of the convoy from point A to point B,   that is min K 4 . For the set M 1 k the appropriate route of  Note to variant 2. movement is determined from the note V2 k , as the In variant 2 one that suits it. M11  x11 ; x21 ;...; xm11  , Note to variant 3. M 12   x12  ; x22  ;...; xm22 , …, In variant 3 restriction O11 obtained by M 1d   x1d  ; x2d  ;...; xmd d   converting the criterion K1 , restriction O12 - - sets that determine possible composition of criterion K2 , restriction O13 - criterion K3 . convoys. The elements of these sets are specific In variant 3 that determines the possible vehicles from among the elements of the set M . composition of the convoys, 1 2  d  So, M1  M , M 1  M , …, M 1  M . should M11  x11 ; x21 ;...; xm11  , obtained M 12   x12  ; x22  ;...; xm22 , …, M11  x11 ; x21 ;...; xm11  , M 1d   x1d  ; x2d  ;...; xmd d  , M 12   x12  ; x22  ;...; xm22 ,…, and also sets that determine possible route of M 1d   x1d  ; x2d  ;...; xmsd   . movement, Problem Solving Technology 1. Task 1 in V21  v1 ; v21 ;...; vs11 ; vs  statement (1), (3), (4) is solved as a combinatorial , search problem. V2  v1 ; v2 ;...; vs1 ; vs  …, 2  2  2  Task 2. , Mathematical model: M 1 , U 2 ,U 3 , K4  min . V2d   v1 ; v2d  ;...; vsd1 ; vs , Result of the solution: For every fixed value not compulsory coincide with corresponding sets ____ of variant 2. i  1, d movement route of the convoy is obtained If among the variants of convoy movement in the form of set V21 , V22  ,…, V2d  are such that provide the same V21  v1 ; v21 ;...; vs11 ; vs , V22   v1 ; v22  ;...; vs21 ; vs ,…, value of the minimum time of movement of the convoy from point A to point B, so that min K 4 , V2d   v1 ; v2d  ;...; vsd1 ; vs . for each of these routes the composition of the corresponding convoys and by criterion are Problem Solving Technology 2. Problem 2 in determined (2) f K1 , K2 , K3   min expedient statement (5) - (6) is solved at each fixed value ____ composition of convoy is determined M 1k  . i  1, d . Variant 4. Investigated task. Investigated task. Solution of the investigated task is following: Mathematical model: U1 ,U 2 ,U 3 , O1 ,..., O9 , M o  M 1k  , Vo  V2k  . k  k  K1  max, K 2  min, K 3  min, K 4  min . The pair is selected M 1 , V2 among the sets Result of solution: The solution to the problem in the note for which the value of the complex under study is following: M o  M1 , Vo  V2 . performance indicator is maximum. Note to variant 5. Here M 1 і V2 are sets, that satisfy all the In Option 5, to solve the problem under study restrictions of the studied problem in the i  i   ____  formulation of variant 4, and under which the for each pair of sets M 1 , V2  i  1, d  the   criterion is fulfilled g K1 , K 2 , K3 , K 4   min . efficiency of transportation is evaluated by Note to variant 4. tactical, technical, economic and comprehensive In such formulation, the studied problem performance index. The materials of the work are should be reduced first to an optimization single- used [22]. criterion problem. For example, this can be done Variant 6. by entering a criterion g K1 , K 2 , K3 , K 4   min . Task 1. The function g should be presented in a Mathematical model: U1 ,U 2 ,U 3 , O1 ,..., O9 , multiplicative form. O10 , O11 , O12 , O13 . Next, it is nessessary to create a dynamic Result of the solution: The variants of the matrix of weights of the edges of the graph for composition of the convoy in the form of sets are each of the possible solutions to the task. o do this, obtained M11  x11 ; x21 ;...; xm11  , the procedure described in [18] should be applied. After that, the studied problem can be solved as a combinatorial optimization problem. M 12   x12  ; x22  ;...; xm22 ,…, Variant 5. M 1d   x1d  ; x2d  ;...; xmsd   . Task 1. Mathematical model: U1 ,U 2 ,U 3 , O1 ,..., O9 , Problem solving technology 1. Problem 1 in O10 . statement (1), (3), (4) is solved with additional Result of the solution: The variants of the restrictions O11 , O12 , O13 , as a combinatorial task. composition of the convoy in the form of sets are Task 2. solving the problem of transportation organization Mathematical model: M 1 , U 2 ,U 3 , K4  min . by a military convoy was carried out. The above Result of the solution: For each fixed value approaches were the result of the analysis of the ____ optimization decisions made by the authors for the i  1, d route of convoy movement is obtained in choice of the appropriate composition of the the form of a set military convoy and the appropriate route of its V21  v1 ; v21 ;...; vs11 ; vs , movement. Some of the approaches are based on the application of methods that have been worked V22   v1 ; v22  ;...; vs21 ; vs ,…, out to solve the specified march organization V2d   v1 ; v2d  ;...; vsd1 ; vs . tasks, and some of them are based on the use of the author's method of assessing the effectiveness Problem solving technology 2. Problem 2 in of the march. In addition, the paper formalizes statement (5) - (6) is solved at each fixed value ____ each of these approaches and outlines the i  1, d . algorithms for solving the problem under study in Investigated task. each statement. The proposed approaches make it Solution of the investigated task is following: possible to: classify the organization of the march; M o  M 1k  , Vo  V2k  . generate algorithms for solving the problem under study in each of the productions; to evaluate the The pair is selected M 1k  , V2k  among the sets limited possibilities of analytical methods in the note for which the value of the complex available to solve the applied tasks of organizing performance indicator is maximum. a march; evaluate possible approaches to the Note to variant 6. formation of a mathematical tools for solving In variant 6, to solve the problem under study these problems; to conclude on the need to develop information technology that would i    ____ i  for each pair of sets M 1 , V2  i  1, d  the provide the solution to the task of organizing the   march in any setting. efficiency of transportation is evaluated by tactical, technical, economic and comprehensive performance index. The materials are used in 5. Acknowledgements paper [22]. General note. The work was performed within the It should be noted that the problem under study framework of joint research of the Department of for each of the productions given in variants 1-6 General Scientific and Engineering Disciplines, should be solved in two productions, depending the Department of Telecommunication and on how the edges are changed. Information Systems and the Department of An analysis of the approaches described in Vehicles and Engineering Support of the State variants 1-6 to solve the problem under study Border Guard of the National Academy of the indicates that each of the options has the right to State Border Guard Service of Ukraine. exist The ability to apply individual approaches to solving application problems depends on the 6. References solution of optimization problems in each case, which, in turn, depends on the search for [1] O. V. Borovyk, R. V. Rachok, L. 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