Begell House Inc.
Journal of Automation and Information Sciences
JAI(S)
1064-2315
52
4
2020
The Transportation Problem under Uncertainty
1-13
10.1615/JAutomatInfScien.v52.i4.10
Alexander A.
Pavlov
National Technical University of Ukraine
"Igor Sikorsky Kiev Polytechnic Institute",
Kiev
Elena G.
Zhdanova
National Technical University of Ukraine
"Igor Sikorsky Kiev Polytechnic Institute",
Kiev
uncertainty
combinatorial optimization
compromise solution
transportation problem
The efficiency of applying the general theoretical positions proposed by A.A. Pavlov to find a compromise solution for one class of combinatorial optimization problems under uncertainty by the example of solving the transportation linear programming problem is studied. The studied class of problems is characterized as follows: 1) the optimization criterion is a weighted linear convolution of arbitrary numerical characteristics of a feasible solution; 2) there exists an efficient algorithm to solve the problem in deterministic formulation that does not allow one to change the constraints structure; 3) by the uncertainty is meant the ambiguity of values of the weight coefficients included in the optimization criterion. We search for compromise solutions according to one of five criteria. A mathematical model of transportation problem is formulated in which uncertainty is caused by the fact that the matrix of transportation costs-per-unit can take one of several possible values at the stage of solution implementation. Practical situations which lead to such a model are described. The method of finding the compromise solution is illustrated by the examples of some individual transportation problems under uncertainty. The research confirmed the efficiency of practical application of the general theoretical principles and allowed us to expand significantly the class of combinatorial optimization problems under uncertainty for which these theoretical results are applicable.
Compromise Decisions. System Approach
14-25
10.1615/JAutomatInfScien.v52.i4.20
Albert N.
Voronin
National Aviation University of Ukraine,
Kiev
compromise
multicriteria optimization
system approach
restrictions
scalar convolution
The problem of the construction of a system for making the compromise solution for subjects with different goals is considered. The problem is solved within the framework of a systemic approach. Procedures of decomposition and composition of partial criteria in multicriteria decision-making problems are described. A compromise solution can be obtained by extremizing the scalar convolution of partial criteria reflecting the degree of attaining goals of subjects. The fundamental role of constraints in optimization problems is shown. We describe types of scalar convolutions used in multicriteria problems. The concept of a nonlinear compromise scheme, based on the principle "away from restrictions" is formulated. Extremization of the objective function leads to the general compromise solution, which moves away to the greatest extent partial criteria from its constraints. Both tasks significant for the general application and the tasks with the main semantic essence of satisfying the individual advantages of the decision making person (DMP) are solved using a common ideological basis. The apparatus of a nonlinear compromise scheme, designed as a formalized tool for studying the system of decision-making and control systems with conflicting criteria enables the solving of multicriteria problems of a wide class. Multicriteria is the implementation of the principle of complementarity in the methodology of the study of complex systems. In general, a simultaneous description of a phenomenon (object) from several sides always gives a qualitatively new, more perfect imagination about the described phenomenon (object) in comparison with any "unilateral" description. So, even two flat images forming a stereo pair form a volumetric image of an object, not to mention potentials of the holography. The multi-criteria approach, giving a "stereoscopic" look at the estimation of the system functioning opens new ways for the perfection of complex control systems and decision making. For the integral perception of a complex system under different conditions of its operation it is necessary to apply the multi-criteria approach.
Variability of Anatomical Features of Leaf Blade in Species of Genus Magnolia L. on the First Ontomorphogenesis Stages
26-37
10.1615/JAutomatInfScien.v52.i4.30
Oxana A.
Futornа
Academician A.V. Fomin Botanical Garden of Kiev National Taras Shevchenko University, Kiev
Vladislava A.
Badanina
Research and Training Center "Institute of
Biology and Medicine" of Kiev National
Taras Shevchenko University, Kiev
Marina N.
Gaidarzhy
Academician A.V. Fomin Botanical Garden
of Kiev National Taras Shevchenko
University, Kiev
Anastasiya V.
Golubenko
Academician A.V. Fomin Botanical Garden
of Kiev National Taras Shevchenko
University, Kiev
Nataliya Yu.
Taran
Research and Training Center "Institute of
Biology and Medicine" of Kiev National
Taras Shevchenko University, Kiev
Magnolia L.
leaf anatomical structure
ontomorphogenesis
adaptation
The quantitative anatomical features of leaves of three species of Magnolia genus: Magnolia kobus Sarg., Magnolia obovata Thunb., Magnolia denudata Desr. growing on the territory of Academician A.V. Fomin Botanical Garden of Kiev Taras Shevchenko National University have been studied. It was found out that on the first stages of ontomorphogenesis M. kobus is characterized by a less specialized type of mesophyll (homogeneous spongy type) unlike M. obovata and M. denudate which are characterized by the dorsoventral type. The number of mesophyll cell layers in the studied species is 4-6. The least variable anatomical feature of the leaf of the studies species is their thickness (CV = 2%). Other anatomical features are characterized by average values of the variation coefficients (15-31%). Based on correlation matrix by the method of "maximum correlation path" this paper has constructed the correlation pleiads of leaf blade anatomical features of the studied plants. Using the results of correlation analysis we have determined groups of features that exhibit the interconnected manifestation in ontogenesis by genetic, physiological and biochemical reasoning. Of the three studied species of Magnolia genus only in M. obovata the vast majority of the studied anatomical features are characterized by high correlation coefficients on the first stages of ontomorphogenesis. The plants M. cobus and M. denudate have stronger consistency between the features of epidermal tissue. We assume that the studied species suffer from a lock of moisture and high temperatures on the first stages of ontomorphogenesis.
Real-Time Algorithm for Calculation of the Distance of the Interrupted Take-off
38-46
10.1615/JAutomatInfScien.v52.i4.40
Alexander A.
Belousov
V.M. Glushkov Institute of Cybernetics of National Academy of Sciences of Ukraine, Kiev
Vladimir V.
Kuleshyn
V.M. Glushkov Institute of Cybernetics of
National Academy of Sciences of Ukraine,
Kiev
Victor I.
Vyshenskiy
V.M. Glushkov Institute of Cybernetics of
National Academy of Sciences of Ukraine,
Kiev
interrupted take-off
length of the braking distance
real-time algorithm
the Riccati equation
An interrupted take-off is the situation when the decision about the airplane take-off cancellation is accepted. When it is necessary for the aircraft crew to decide about the interruption of take-off, they compare the current velocity with the "decision-making velocity". Based on this velocity one can estimate whether the aircraft can safely stop within the available distance of the interrupted flight. These values are taken from the "Aircraft Flight Manual" before the take-off. The analysis of accidents shows that if the current velocity tends to the "decision-making velocity", the real distance of the interrupted flight (the braking distance until the complete aircraft stop) can change from the computed value in advance. The distance of the interrupted take-off can be underestimated, which results in overrun beyond the existing distance. The overestimation of the distance of the interrupted flight prevents the crew from choosing the decision "interrupt take-off" although it is still safe. The proposed real-time algorithm of the determination of the distance of the interrupted flight uses the step-wise interpolation of the thrust. Two intervals of the thrust variation (the thrust decreases from the maximum to zero and then increases to the nominal reversal thrust) can be interpolated by three intervals of the constant thrust (flight thrust, zero thrust, nominal reverse thrust). Using this interpolation, the Riccati equation of the aircraft motion has three different explicit solutions, corresponding to three different constant values of the thrust. These solutions can be used in realtime computations. The algorithm takes into account different aircraft parameters (velocity, thrust, etc.) before the time instant of decision making. As a result, it is possible to estimate the distance of the interrupted take-off more exactly in comparison with the advanced computed value. This is especially important if the aircraft velocity is close to the "decision-making velocity". In this situation, the aircraft crew obtains more accurate information about the distance of the interrupted take-off and avoids the rolling out of the airport boundaries during the interrupted take-off. Thus, the decision about the interrupted take-off will be more reliable and safe.
Conditional Optimization of a Problem with Quadratic Objective Function on a Set of Permutations
47-64
10.1615/JAutomatInfScien.v52.i4.50
Lyudmila N.
Kolechkina
University of Lodz, Lodz (Poland)
Alla N.
Nahirna
National University of "Kyiv-Mohyla
Academy", Kiev
optimization
mathematical model
quadratic function
set of permutations
reference solution
optimal solution
The statement of the optimization problem with the quadratic objective function on the combinatorial set of permutations is formulated. A new method of solving the optimization problem, taking into account the fulfillment of the conditions of the problems formed when considering transpositions of elements of the set of permutations is proposed. The presented method consists of three steps. At the first step, a decision tree is constructed, the branching branches of which are transpositions of the corresponding elements of the set of permutations. At this step, all possible transpositions are compiled in the quantity p that determine the further representation of the set of permutation points in the form of a permutation of the corresponding elements. Subgraphs of the graph G. are constructed from these points and subsets of the set of transpositions are compiled. It should be noted that the graph G is only a part of the polyhedron of
permutations M(Pkn). In the second step, the problems are compiled whose objective functions are quadratic and are presented taking into account the transpositions under consideration. When solving each problem, a set of
transpositions of elements is formed, which consists of Sqop − the subset of points in the graph G subgraph that satisfy the constraints; Sqcon − the subset of
points in a subgraph of the graph G that do not satisfy the constraint; Sqcl − the
subset of the cut-off points of the subgraph of the graph G that do not belong to the two previous subsets. On each subgraph of the graph G , additional constraints (4) of the problem (3)-(5) are checked. In this case, only the increments of the constraints and objective function are calculated using the necessary formulas. The set of reference solutions will consist of the point xextr
at which extr F(xextr) and set of the permutation points Sac , which have not been considered during the transposition of elements, but belong to the polyhedron of the permutations M(Pkn). In the third step, the search for the optimal solution to the problem is carried out by comparing the increments of the quadratic objective function of the point xextr and points of the set Sac. The article gives a numerical example of the implementation of this method. From 120 points of the set of permutations, the optimal solution was found in 18 steps when considering 27 points and 28 cut-off points. Using this method, one can get the optimal solution in a finite number of steps.
The Concept of Information. Part 2. The Functions of a Scientific Theory
65-81
10.1615/JAutomatInfScien.v52.i4.60
Alexander F.
Kurgaev
V.M. Glushkov Institute of Cybernetics of
National Academy of Sciences of Ukraine,
Kiev
functions of scientific theory
communicative functions
descriptive prescriptive functions
argumentative functions
deduction
induction
explanation
prediction
understanding
problem
empirical cognition
theoretical cognition
metalanguage
information computer
Any scientific theory should effectively perform a variety of information processing functions, regardless of the specifics of knowledge and the field of formalization. To achieve the global aim − maximum assistance in solving each of the infinite number of problems of the evolution of society − the information computer should be able to simulate all the functions of scientific theories, which are combined into a conceptually single system of knowledge processing, and due to this the information computer should provide the possibility to use knowledge directly in an explicit form for solving current and new problems. The meaning of communicative, descriptive-prescriptive, and argumentative (deduction, induction, explanation, prediction, understanding) functions of scientific theories is clarified. The models of synthesis of various components of the structure of scientific theories are described. The objects of real-world and the communicative functions of analysis and generation of language messages are enough for the organization of arbitrarily complex dialogue between a subject and the real world. The descriptive-prescriptive functions are the cornerstone for cognition and transformation of reality. All facts of reality are descriptive, whereas the standards, samples, ideals and norms are estimates. The argumentation is a process of reasoning during which the arguments, opinions, and conclusions are generated, that justify the assessment of truth or falsity of a statement or a theory. The self-description of the metalanguage of normal forms of knowledge is presented. The structure of the core of the information computer, which is based on this metalanguage, is presented, comprised of the following: the metaprogram compiler, two interpreters (the metaprogram interpreter and the terminal program interpreter), a glossary of terms and two arrays of data (input array and output array). The process of functioning of a knowledge processing system based on an information computer is described. The information on the implementation of the layout of the information computer in the form of a personal computer supplemented with the knowledge base interpreter made on a prototyping board of Actel corporation using minimum required hardware and software support is given. Giving users the metalanguage for describing application problems and the improved technology of formulating and solving problems, which realize all the features of a scientific theory, will provide extremely high growth of "soft" product reliability and programming efficiency.