Repository at CSBC Browsing by Author "Zabolotnii, Serhii"

Browsing by Author "Zabolotnii, Serhii"

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Application of Statistical Pattern Recognition in a Generating-Element Space for Human Activity Classification Using Smartphone Sensors
(Springer Nature B.V., 2026) Заболотній, Сергій Васильович; Zabolotnii, Serhii; Хотунов, Владислав Ігорович; Khotunov, Vladyslav; Чепинога, Анатолій Володимирович; Chepynoha, Anatolii; Klopotovskyi, Pavlo; Клопотовський, Павло Анатолійович
Human Activity Recognition (HAR) using smartphone sensors has become a key component in health monitoring, context-aware computing, and smart environments. Traditional machine learning approaches often assume a Gaussian distribution of sensor data, which may not hold true in real-world scenarios. This paper presents a novel application of the mathematical framework of decomposition in a space with a generating element to address problems in statistical pattern recognition. This approach, based on Kunchenko’s theory of stochastic polynomials, enables the effective processing of non-Gaussian data by constructing optimal polynomial features based on the minimization of the mean square error of the decomposition. We apply this method to the UCI HAR dataset, which contains accelerometer and gyroscope data from 30 individuals performing six daily activities. Our approach generates polynomial features of various orders that capture higher-order statistical dependencies in the sensor signals. Experimental results demonstrate that augmenting traditional time-domain and frequency-domain features with these polynomial features improves classification accuracy when using a SVM classifier. The method is particularly effective in distinguishing between static activities (such as sitting and standing), which are traditionally challenging to classify. The proposed approach offers a theoretically grounded feature engineering technique that enhances HAR performance while maintaining computational efficiency suitable for real-time applications.
Application of the matrix factor analysis method for determining parameters of the objective function for transport risk minimization
(Lublin University of Technology, 2021) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Mogilei, Sergii; Могілей Сергій Олександрович
The paper regards a common transport problem with a non-classic optimization criterion to minimize transportation risks. It demonstratesthat the risk parameters of the function could be found through the factor analysis method. Besides, considering that the problem contains several pointsof sending and delivering loads, the method is dealt with as a matrix. The research also regards the algorithm of matrix factor analysis applicationfor determining parameters of the objective function for the problem to be solved. The survey results in a new method to construct the objective functionfor the optimization problem with probability parameters. It generally assists in suggesting a formal solution to such problems, foremost due to particular software.
Application of the Polynomial Maximization Method for Estimating Nonlinear Regression Parameters with Non-Gaussian Asymmetric Errors
(Springer Nature, 2024) Заболотній, Сергій Васильович; Zabolotnii, Serhii; Tkachenko, Oleksandr; Nowakowski, Waldemar; Warsza, Zygmunt Lech
In the article, an alternative approach to estimating parameters in nonlinear regression models under asymmetric error distributions is examined. A novel approach for adaptive estimation is proposed, which is based on the use of second-order polynomial functions. This enables a straightforward implementation to account for deviations from Gaussian idealization in the form of moments up to the fourth order. It is demonstrated that the overall problem can algorithmically be reduced to the numerical solution of a system of nonlinear stochastic equations. Analytical expressions are obtained, which facilitate the estimation of parameters and the analysis of their asymptotic variance. Statistical modeling using the Monte Carlo method was conducted, and the results indicate that the accuracy of PMM2 estimates is comparable to SLS estimates and significantly so exceeds the accuracy of OLS estimates.
Application of the Polynomial Maximization Method for Estimation Parameters in the Polynomial Regression with Non-Gaussian Advances in Intelligent Systems and Computing
(Springer Nature B.V., 2021) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Tkachenko, Oleksandr; Ткаченко, Олександр Миколайович; Warsza, Zygmunt Lech
This paper considers the application of the polynomial maximization method to find estimates of the parameters of polynomial regression. It is shown that this method can be effective for the case when the distribution of the random component of the regression models differs significantly from the Gaussian distribution. This approach is adaptive and is based on the analysis of higher-order statistics of regression residuals. Analytical expressions that allow finding estimates and analyzing their uncertainty are obtained. Cases of asymmetry and symmetry of the distribution of regression errors are considered. It is shown that the variance of estimates of the polynomial maximization method can be significantly less than the variance of the estimates of the least squares method, which is a special case. The increase in accuracy depends on the values of the cumulant coefficients of higher orders of random errors of the regression model. The results of statistical modeling by the Monte Carlo method confirm the effectiveness of the proposed approach.
Application of the Polynomial Maximization Method for Estimation Parameters of Autoregressive Models with Asymmetric Innovations
(Springer Nature B.V., 2022) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Tkachenko, Oleksandr; Warsza, Zygmunt Lech
This paper considers the application of the Polynomial Maximization Method to find estimates of the parameters of autoregressive model with non-Gaussian innovation. This approach is adaptive and is based on the analysis of higher-order statistics. Analytical expressions that allow finding estimates and analyzing their uncertainty are obtained. Case of asymmetry of the distribution of autoregressive innovations is considered. It is shown that the variance of estimates of the Polynomial Maximization Method can be significantly less than the variance of the estimates of the linear approach (based on Yule-Walker equation or Ordinary Least Squares). The increase in accuracy depends on the values of the cumulant coefficients of higher orders of innovation residuals. The results of statistical modeling by the Monte Carlo method confirm the effectiveness of the proposed approach.
Applying the Polynomial Maximization Method to Estimate ARIMA Models with Asymmetric Non-Gaussian Innovations
(https://arxiv.org/, 2025) Заболотній, Сергій Васильович; Zabolotnii, Serhii
Classical estimators for ARIMA parameters (MLE, CSS, OLS) assume Gaussian innovations, an assumption frequently violated in financial and economic data exhibiting asymmetric distributions with heavy tails. We develop and validate the second-order polynomial maximization method (PMM2) for estimating ARIMA models with non-Gaussian innovations. PMM2 is a semiparametric technique that exploits higher-order moments and cumulants without requiring full distributional specification. Monte Carlo experiments (128,000 simulations) across sample sizes and four innovation distributions demonstrate that PMM2 substantially outperforms classical methods for asymmetric innovations. For ARIMA(1,1,0) with , relative efficiency reaches 1.58--1.90 for Gamma, lognormal, and innovations (37--47\% variance reduction). Under Gaussian innovations PMM2 matches OLS efficiency, avoiding the precision loss typical of robust estimators. The method delivers major gains for moderate asymmetry () and , with computational costs comparable to MLE. PMM2 provides an effective alternative for time series with asymmetric innovations typical of financial markets, macroeconomic indicators, and industrial measurements. Future extensions include seasonal SARIMA models, GARCH integration, and automatic order selection.
Constructing Reference Plans of Two-Criteria Multimodal Transport Problem
(Transport & Telecommunication Institute, Latvia, 2021) Przystupa, Krzysztof; Qin, Zhang; Zabolotnii, Serhii; Заболотній, Сергій Васильович; Pohrebennyk, Volodymyr; Mogilei, Sergii; Могілей, Сергій Олександрович; Zhongju, Chen; Gil, Leszek
The object of this study is a multicriteria transport problem, being stated for availability of several means of cargo delivery, meaning a multimodal transport problem. The optimization criteria of the multimodal transport problem described above are two objective functions of minimizing total transportation costs and level of transport risks. Three types of transport were selected for research: automobile, rail and river (inland waterway). The results of the study lay the foundation for development of a new valid algorithm for solving multimodal transport problems like multi-criteria optimization ones. The main advantage of such an algorithm lies in its higher potential convergence rate compared to classical numerical optimization methods, which now are predominantly used to solve the problems of this type. This advantage may not be decisive, but it appears to be at least quite an important argument when choosing the method of realization for two-criteria multimodal transport problems earlier considered, especially, in case of a large dimension. Moreover, the algorithm described in the work can be applied to similar problems with any number of types of transport and optimization criteria.
EstemPMM package for estimating parameters of time series and regression model with asymmetric non-gaussian errors
(Sofia: Softrade, 2025) Заболотній, Сергій Васильович; Zabolotnii, Serhii
Thesis of the XXII International Scientific and Technical Seminar “Measurement Uncertainty: Scientific, Normative, Applied and Methodical Aspects” (UM-2025), which was held online on December 10-11, 2025.
Estimating parameters of linear regression with an exponential power distribution of errors by using a polynomial maximization method
(ПП «ТЕХНОЛОГІЧНИЙ ЦЕНТР», Український державний університет залізничного транспорту, 2021) Заболотній, Сергій Васильович; Zabolotnii, Serhii; Хотунов, Владислав Ігорович; Khotunov, Vladyslav; Чепинога, Анатолій Володимирович; Chepynoha, Anatolii; Ткаченко, Олександр Миколайович; Tkachenko, Oleksandr
This paper considers the application of a method for maximizing polynomials in order to find estimates of the parameters of a multifactorial linear regression provided the random errors of the regression model follow an exponential power distribution. The method used is conceptually close to a maximum likelihood method because it is based on the maximization of selective statistics in the neighborhood of the true values of the evaluated parameters. However, in contrast to the classical parametric approach, it employs a partial probabilistic description in the form of a limited number of statistics of higher orders. The adaptive algorithm of statistical estimation has been synthesized, which takes into consideration the properties of regression residues and makes it possible to find refined values for the estimates of the parameters of a linear multifactorial regression using the numerical Newton-Rafson iterative procedure. Based on the apparatus of the quantity of extracted information, the analytical expressions have been derived that make it possible to analyze the theoretical accuracy (asymptotic variances) of estimates for the method of maximizing polynomials depending on the magnitude of the exponential power distribution parameters. Statistical modeling was employed to perform a comparative analysis of the variance of estimates obtained using the method of maximizing polynomials with the accuracy of classical methods: the least squares and maximum likelihood. Regions of the greatest efficiency for each studied method have been constructed, depending on the magnitude of the parameter of the form of exponential power distribution and sample size. It has been shown that estimates from the polynomial maximization method may demonstrate a much lower variance compared to the estimates from a least-square method. And, in some cases (for flat-topped distributions and in the absence of a priori information), may exceed the estimates from the maximum likelihood method in terms of accuracy.
Estimation of Linear Regression Parameters of Symmetric Non-Gaussian Errors by Polynomial Maximization Method
(Springer Nature B.V., 2019) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Warsza, Zygmunt Lech; Tkachenko, Oleksandr; Ткаченко, Олександр Миколайович
In this paper, a new way of estimation of single-factor linear regression parameters of symmetrically distributed non-Gaussian errors is proposed. This new approach is based on the Polynomial Maximization Method (PMM) and uses the description of random variables by higher order statistics (moments and cumulants). Analytic expressions that allow to find estimates and analyze their asymptotic accuracy are obtained for the degree of polynomial S = 3. It is shown that the variance of polynomial estimates can be less than the variance of estimates of the ordinary least squares’ method. The increase of accuracy depends on the values of cumulant coefficients of higher order of the random regression errors. The statistical modeling of the Monte Carlo method has been performed. The results confirm the effectiveness of the proposed approach.
Estimation of Measurand Parameters for Data from Asymmetric Distributions by Polynomial Maximization Method
(Springer Nature B.V., 2018) Warsza, Zygmunt Lech; Zabolotnii, Serhii; Заболотній, Сергій Васильович
In this paper the non-conventional method for evaluating the standard uncertainty of the estimator of measurand value obtained from the non-Gaussian asymmetrically distributed sampled data with a priori partial description (known only few initial moments, unknown PDF distribution of population) is proposed. This method of statistical estimation is based on the apparatus of maximization the stochastic polynomials (PMM method proposed by Kunchenko) and uses the higher-order statistics (moment or cumulant description) of random variables. The analytical expressions for finding estimates and analyzing their accuracy to the degree of the polynomial s = 2 is given. It is shown that for the asymmetric PDF-s the uncertainty estimates for received polynomial are generally smaller than the uncertainty estimates obtained based on the mean (arithmetic average). Reducing the uncertainty of measurement depends on the skewness and kurtosis. On the basis of the Monte Carlo method statistical modelling is carried out, the results confirm the effectiveness of the proposed approach.
Estimation of measurand parameters for data from asymmetric distributions by polynomial maximization method (PMM)
(Industrial Research Institute for Automation and Measurements PIAP, 2018) Warsza, Zygmunt Lech; Zabolotnii, Serhii; Заболотній, Сергій Васильович
Przedstawiono sposób wyznaczania estymatorów wartości i niepewności menzurandu niekonwencjonalną metodą maksymalizacji wielomianu stochastycznego (PMM) dla próbki danych pomiarowych pobranych z populacji modelowanej zmienną losową o rozkładzie niesymetrycznym. W metodzie PMM stosuje się statystykę wyższego rzędu i opis z użyciem momentów lub kumulantów. Wyznaczono wyrażenia analityczne dla estymatorów wartości i niepewności standardowej typu A menzurandu za pomocą wielomianu stopnia r = 2. Niepewność standardowa wartości menzurandu otrzymana metodą PPM zależy od skośności i kurtozy rozkładu. Jest ona mniejsza od średniej arytmetycznej wyznaczanej wg przewodnika GUM i bliższa wartości teoretycznej dla rozkładu populacji danych. Jeśli rozkład ten jest nieznany, to estymatory momentów i kumulantów wyznacza się z danych pomiarowych próbki. Sprawdzono skuteczność metody PMM dla kilku podstawowych rozkładów.
Factor analysis method application for constructing objective functions of optimization in multimodal transport problems
(Lublin University of Technology, 2021) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Honcharov, Artem; Гончаров, Артем Володимирович; Mogilei, Sergii; Могілей, Сергій Олександрович
The paper regards a specific class of optimization criteria that possess features of probability. Therefore, constructing objective function of optimization problem, the importance is attached to probability indices that show the probability of some criterial event or events to occur. Factor analysis has been taken for the main method of constructing objective function. Algorithm for constructing objective function of optimization is donefor criterion of minimization risk level in multimodaltransportations that demanded demonstration data. The application of factor analysis in classical problem solution was shown to givethe problem a more distinct analytical interpretation in solving it.
From Black-Box Confidence to Measurable Trust in Clinical AI: A Framework for Evidence, Supervision, and Staged Autonomy
(https://arxiv.org/, 2026) Заболотній, Сергій Васильович; Zabolotnii, Serhii; Holinko, Viktoriia; Antonenko, Olha
Trust in clinical artificial intelligence (AI) cannot be reduced to model accuracy, fluency of generation, or overall positive user impression. In medicine, trust must be engineered as a measurable system property grounded in evidence, supervision, and operational boundaries of AI autonomy. This article proposes a practical framework for trustworthy clinical AI built around three principles: evidence, supervision, and staged autonomy. Rather than replacing deterministic clinical logic wholesale with end-to-end black-box models, the proposed approach combines a deterministic core, a patient-specific AI assistant for contextual validation, a multi-tier model escalation mechanism, and a human supervision layer for verification, escalation, and risk control. We demonstrate that trust also depends on selective verification of clinically critical findings, bounded clinical context, disciplined prompt architecture, and careful evaluation on realistic cases. Classifier-driven modular prompting is examined as an incremental path to scaling clinical depth without sacrificing prompt performance and without waiting for complete rule-based coverage. To operationalize trust, a set of trust metrics is proposed, built on metrological principles -- measurement uncertainty, calibration, traceability -- enabling quantitative rather than subjective assessment of each architectural layer. In this perspective, trustworthy clinical AI emerges not as a property of an individual model, but as an architectural outcome of a system into which evidence trails, human oversight, tiered escalation, and graduated action rights are embedded from the outset.
FROM STATISTICAL PATTERN RECOGNITION TO EMOTION ANALYSYS: APPLICATION OF THE APPARATUS OF DECOMPOSITION IN SPAСE WITH A GENERATING ELEMENT FOR NLP MODELS
(Інститут кібернетики ім. В.М. Глушкова НАН України, 2026) Заболотній, Сергій Васильович; Zabolotnii, Serhii; Чепинога, Анатолій Володимирович; Chepynoha, Anatolii; Хотунов, Владислав Ігорович; Khotunov, Vladyslav
Розпізнавання емоцій у текстах є важливою задачею сучасного оброблення природної мови, де на сьогодні домінують трансформерні архітектури. Однак їхні внутрішні механізми залишаються «чорною скринькою», а якість класифікації, особливо для складних випадків, має потенціал для покращення. У цій роботі запропоновано новий гібридний підхід, який поєднує потужність сучасних мовних моделей з глибоким аналізом їхніх векторних представлень за допомогою адаптації класичного методу статистичного розпізнавання образів, що ґрунтується на розкладі в просторі з порідним елементом (просторі Кунченка). Метод дає змогу згенерувати новий набір «статистико-геометричних» ознак на основі похибки реконструкції векторного представлення текстових повідомлень відповідних класів. Експерименти на українському (EMOBENCH-UA) та англійському (EmoEvent) наборах даних показали, що запропонований гібридний підхід забезпечує статистично значуще підвищення яккості класифікації. Дослідження також виявило ключові умови ефективності методу: він є потужним «уточнювачем» для моделей, донавчених на цільовій задачі, але неефективний на «сирих», неспеціалізованих векторних представленнях. Встановлено, що вибір базисних функцій для реконструкції є важливим гіперпараметром, що дає можливість адаптувати метод до специфічної геометрії простору даних.
Local-First Clinical Text Structuring with Fine-Tuned MedGemma for Readmission Risk Assessment
(https://zenodo.org, 2026) Заболотній, Сергій Васильович; Zabolotnii, Serhii; Holinko, Viktoriia
Background. Unstructured clinical notes remain a bottleneck for deployable healthcare AI; cloud-dependent pipelines raise privacy and infrastructure barriers. Methods. We present MedGemma StructCore, a local-first two-stage extraction pipeline using compact MedGemma 4B models. Stage 1 applies Schema-Guided Reasoning to summarize notes into structured JSON across nine clinical clusters. Stage 2 projects summaries into canonical KVT4 (Cluster|Keyword|Value|Timestamp) facts via a LoRA-adapted model. Deterministic normalization, a signal-integrity gate, and offline hybrid regeneration audit and reduce silent objective signal-loss between stages. Prompt KV-cache reuse yields +10.6% speedup with bit-exact output [Verified]. Results. On MIMIC-IV (N=50,000; patient-level split; Ntest=9,857), the tabular baseline (A4) achieves AUROC 0.685 (95% CI 0.670–0.699) [Verified]. On the full canonical test split (Ntest=9,857), under a constrained training regime (Ntrain=1,500, Nval=400), A3factlevel achieves AUROC 0.659, AUPRC 0.321, and Brier 0.145. Against a fair tabular refit baseline (LogReg and XGBoost) with the same training split and demographic covariates, A3factlevel improves AUPRC and Brier [Verified], while AUROC uplift is small and not statistically verified [Preliminary]. Notably, XGBoost does not outperform logistic regression on the same feature set, confirming that downstream gains are attributable to KVT4 features rather than estimator choice. As a post-closure continuation branch, direct typed downstream fusion of four high-signal semantic labels improves the current Stage 2 baseline on the same canonical split and yields a verified AUPRC gain over the canonical A4 tabular arm [Verified], while remaining near-parity rather than clearly superior to A3factlevel. KVT4 format validity is 99.74%; a signal-integrity audit (N=4,000) finds 15.55% doc-level objective loss (among admissions with Stage 1 numeric vitals/labs), reduced to 8.48% by offline hybrid regeneration without additional LLM calls. Structured-reference validation now includes a large LABS benchmark on the full canonical test split and a preliminary VITALS benchmark path with chartevents-backed BP/Weight evaluation. A model scaling pilot replacing Stage 1 with GPT4.1-mini confirms that moderate LABS micro-F1 (≈0.52 ceiling) reflects reference-alignment mismatch rather than model capacity [Preliminary, N=200]. Conclusion. The primary contribution is reliable, auditable local-first clinical text structuring infrastructure running on consumer hardware. On the canonical test split, factlevel KVT tokenization improves precision–recall and probabilistic accuracy metrics (AUPRC, Brier) over a tabular refit baseline (Verified); AUROC uplift is small (Preliminary). Direct typed downstream fusion now provides the strongest verified continuation path over the current Stage 2 baseline, suggesting that typed semantic signals are a more promising next optimization target than further free-form Stage 2 generator variants. The current revision package therefore supports a conservative conclusion: notes-derived KVT4 facts add useful predictive signal, but stronger extraction-quality and fairness claims still require further validation.
Method of Verification of Hypothesis about Mean Value on a Basis of Expansion in a Space with Generating Element
(Allerton Press, Inc., 2018) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Martynenko, S. S.; Salypa, S. V.
In this paper it is proposed an original method for verification of statistical hypotheses about mean values of random quantities. This method is based on Kunchenko stochastic polynomials tool and probabilistic description on a basis of higher order statistics (moments and/or cumulants). There are represented analytical expressions allowing to optimize decision rules using certain qualitive criterion and calculate decision-making error. It is shown polynomial decision rule in case of polynomial power S = 1 corresponds to classic linear decision rule which is used for comparative analysis. By means of multiple statistical experiments (Monte–Carlo method) obtained results of Neumann–Pierson criterion show proposed polynomial decision rules are characterized by increased accuracy (decrease of the 2nd genus errors probability) in compare to linear processing. The method efficiency increases with increase of stochastic polynomial order increase of degree of random quantities distribution difference from Gaussian probabilities distribution law.
Modifications of Evans Price Equilibrium Model
(Lublin University of Technology, 2023) Заболотній, Сергій Васильович; Zabolotnii, Serhii; Могілей, Сергій Олександрович; Mogilei, Sergii
The paper regards the classical Evans price equilibrium model in the free product market in the aspect of regarding the opportunitiesfor expanding (modifying) the model given that is aimed at perfecting the accuracy of its mathematical formulating. As an accuracy criterion, we have chosen a summary quadratic deviation of the calculated indices from the given ones. One of the approaches of modifying the basic Evans modelis suggesting there is a linear dependence between price function and time as well as its first and second derivatives. In this case, the model willbe described through differential equation of second order with constant coefficients,revealing some oscillatory process. Besides, it is worth regardinga non-linear (polynomial) dependence between demand, supply and price.The paper proposes mathematical formulating for the modified Evans models that have been approbated for real indices of exchange rates fluctuations. It also proves that increase of the differential and/or polynomial orderof the given model allows its essential accuracy perfection. Besides, the influence of arbitrary restricting circumstances ofthe model onits accuracyis regarded. Each expanded Evans model is accompanied by mathematically formulated price and time dependence.
Ocena niepewności pomiarów o rozkładzie trapezowym metodą maksymalizacji wielomianu
(Wydawnictwo Czasopism i Książek Technicznych SIGMA-NOT Sp. z o.o., 2017) Warsza, Zygmunt Lech; Zabolotnii, Serhii; Заболотній, Сергій Васильович
The types of measurand parameter estimators derived from samples of measured data taken from a sym. trapezoidal population were briefly reviewed (9 refs.). A non-std. approach to find ests. of the non-Gaussian distributions parameters based on the unconventional method for maximizing the stochastic polynomials by using a moment-cumulant description of random variables was proposed. The method was recommended to use for detg. estd. values of the std. deviation and uncertainties of measurand when distribution of the random errors population is a priori unknown and first few cumulants have to be found from the sample data. The method is particularly useful in assessing mixts. and mixing efficiency.
Optimization of the method of constructing reference plans of multimodal transport problem
(ПП «Технологічний центр», Полтавська державна аграрна академія, 2018) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Mogilei, Sergii; Могілей, Сергій Олександрович
Класична транспортна задача полягає у визначенні оптимального плану перевезень вантажів з пунктів відправки до пунктів доставки за критерієм мінімальної собівартості таких перевезень. Така задача враховує лише один вид транспорту, що в недостатній мірі відповідає практичним потребам сучасних логістичних підприємств. Саме тому об’єктом даного дослідження є класична транспортна задача, по-становка якої враховує наявність кількох засобів доставки вантажу, а саме: автомобільного, залізничного та водного. Транспортну задачу такого типу визначено як мультимодальну. Реалізація мультимодальної транспортної задачі передбачає використання різноманітних чисельних методів та виконується за допомогою програмних засобів. Фактично, концептуальний підхід до її розв’я-зання полягає в простому підборі можливих розв’язків. За умови великої розмірності задачі такий підхід може бути надзвичайно громіздким, а тому потребує певного удосконалення. Під час проведення дослідження було оптимізовано метод побудови опорного плану такої задачі на основі критерію мінімізації кількості чисельних ітерацій, обґрунтовано переваги запропонованого підходу у порівнянні з уже відомими. В основу нового підходу було покладено раніше відомий метод мінімального елемента, що використовується при розв’язанні транспортної задачі, а також проведе-но аналогію із задачею Штейнера. Останнє, в свою чергу, дало змогу означити новий підхід як метод Штейнера. Результатом дослідження є розробка загального алгоритму реалізації запропонованого методу Штейнера. В якості апробації даного алгоритму подано модельний приклад, який демонструє ідентичність результатів розв’язання мультимодальної транспортної задачі всіма розглянутими в роботі способами. Розробка нових методів реалізації мультимодальної транспортної задачі дозволить побудувати ефек-тивні алгоритми розв’язання більш комплексних задач транспортної логістики. Критерій зменшення кількості чисельних ітерацій, застосований на всіх етапах реалізації таких задач, значно скоротить час відшукання їхніх розв’язків.

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