<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "https://jats.nlm.nih.gov/publishing/1.3/JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xml:lang="ru">
  <front xmlns:xlink="http://www.w3.org/1999/xlink">
    <journal-meta>
      <journal-title-group>
        <journal-title>π-Economy</journal-title>
        <trans-title-group xml:lang="ru">
          <trans-title>π-Economy</trans-title>
        </trans-title-group>
      </journal-title-group>
      <issn pub-type="epub">2782-6015</issn>
    </journal-meta>
    <article-meta xmlns:xlink="http://www.w3.org/1999/xlink">
      <article-id pub-id-type="publisher-id">11</article-id>
      <article-id pub-id-type="doi">10.18721/JE.19411</article-id>
      <title-group>
        <article-title>Self-learning agent model for adaptive planning of multimodal transportation</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Самообучающаяся агентная модель адаптивного планирования мультимодальных перевозок</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Antonov</surname>
            <given-names>Aleksandr</given-names>
          </name>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Ilyin</surname>
            <given-names>Igor</given-names>
          </name>
          <email>ilyin@fem.spbstu.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Levina</surname>
            <given-names>Anastasia</given-names>
          </name>
          <email>alyovina@gmail.com</email>
        </contrib>
      </contrib-group>
      <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-08-31">
        <day>31</day>
        <month>08</month>
        <year>2026</year>
      </pub-date>
      <volume>19</volume>
      <issue>4</issue>
      <fpage>198</fpage>
      <lpage>213</lpage>
      <self-uri xmlns:xlink="http://www.w3.org/1999/xlink" content-type="pdf" xlink:href="https://economy.spbstu.ru/userfiles/files/articles/2026/4/11_antonov_ilin_lyovina.pdf"/>
      <abstract xml:lang="en">
        <p> Multimodal transportation is characterized by high level of uncertainty, heterogeneity of participants (rail, maritime, road transport), and technological constraints, which make traditional centralized planning methods based on static optimization models insufficiently effective. A contradiction arises between need for global coordination of supply chains and inability to promptly adapt to dynamic changes in environment without loss of flexibility. Additional complexity comes from need to coordinate decisions among independent participants of transport process, each having own objectives and constraints. The aim of the article is to develop a self-learning multi-agent model for adaptive planning of multimodal transportation based on decentralized decision-making and parametric adaptation of agent criteria. Methodological basis combines principles of agent-based modeling, elements of decision theory, and formalization of participant behavior through universal satisfaction function reflecting multi-criteria nature of transport processes. Within study, analysis of existing approaches to multimodal transportation planning, formalization of requirements for mathematical methods, and design of agent structure representing key elements of transport system and their interaction were carried out. As a result, mathematical model is proposed in which each element of transport network is represented as autonomous agent with own criteria (cost, time, resources) and local decision-making mechanism. Interaction of agents is implemented through coordination mechanism that ensures formation of consistent transportation plan without centralized control. Key element is self-learning mechanism: system adapts priorities of agents by comparing expected and actual outcomes of operations, accumulating experience to improve accuracy of subsequent decisions and robustness to external disturbances. Novelty lies in development of formalized model of self-learning multi-agent system that enables adaptation of decision-making parameters based on retrospective analysis and allows consideration of recurring patterns. Practical significance is confirmed by possibility of using developed model in intelligent logistics platforms, as well as by reducing need for complete re-planning when deviations occur and by increasing robustness of transport processes. The results demonstrate potential of multi-agent approach for efficient management of multimodal transportation under conditions of high uncertainty.</p>
      </abstract>
      <kwd-group xml:lang="en">
        <kwd>multimodal transportation</kwd>
        <kwd>multi-agent systems</kwd>
        <kwd>adaptive planning</kwd>
        <kwd>agent satisfaction functions</kwd>
        <kwd>self-learning systems</kwd>
        <kwd>distributed decision-making</kwd>
        <kwd>logistics systems</kwd>
        <kwd>transport management systems</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <back>
    <ref-list>
      <title>References</title>
      <ref id="ref1">
        <mixed-citation publication-type="journal">Dantzig G.B., Ramser J.H. (1959) The Truck Dispatching Problem. Management Science, 6 (1), 80–91. DOI: 10.1287/mnsc.6.1.80</mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation publication-type="journal">Ahuja R.K., Magnanti T.L., Orlin J.B. (1993) Network flows: Theory, algorithms, and applications. Englewood Cliffs, NJ: Prentice Hall.</mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation publication-type="journal">Ferjani A., El Yaagoubi A., Boukachour J., Duvallet C. (2024) An optimization-simulation approach for synchromodal freight transportation. Multimodal Transportation, 3 (3), art. no. 100151. DOI: 10.1016/j.multra.2024.100151</mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation publication-type="journal">SteadieSeifi M., Dellaert N.P., Nuijten W., Van Woensel T., Raoufi R. (2014) Multimodal freight transportation planning: A literature review. European Journal of Operational Research, 233 (1), 1–15. DOI: 10.1016/j.ejor.2013.06.055</mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation publication-type="journal">Demir E., Bektaş T., Laporte G. (2014) A review of recent research on green road freight transpor- tation. European Journal of Operational Research, 237 (3), 775–793. DOI: 10.1016/j.ejor.2013.12.033</mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation publication-type="journal">Pillac V., Gendreau M., Guéret C., Medaglia A.L. (2013) A review of dynamic vehicle routing problems. European Journal of Operational Research, 225 (1), 1–11. DOI: 10.1016/j.ejor.2012.08.015</mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation publication-type="journal">Alaei S., Durán-Micco J., Macharis C. (2024) Synchromodal transport re-planning: an agent-based simulation approach. European Transport Research Review, 16, art. no. 1. DOI: 10.1186/s12544- 023-00624-y</mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation publication-type="journal">Richter N., Martins-Turner K., Nagel K. (2024) Extension of an agent-based simulation for the optimized allocation of freight requests to differently structured supply chains. Procedia Computer Scien- ce, 238, 728–735. DOI: 10.1016/j.procs.2024.06.084</mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation publication-type="journal">Frolov K.V., Babkin A.V., Frolov A.K. (2024) Concept and essence of digitalization and digital transformation based on fundamental and applied aspects of the systems-cybernetic theory. π-Economy, 17 (1), 7–26. DOI: 10.18721/JE.17101</mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation publication-type="journal">Macharis C., Bontekoning Y.M. (2004) Opportunities for OR in intermodal freight transport research: A review. European Journal of Operational Research, 153 (2), 400–416. DOI: 10.1016/S0377- 2217(03)00161-9</mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation publication-type="journal">Bock S. (2010) Real-time control of freight forwarder transportation networks by integrating multimodal transport chains. European Journal of Operational Research, 200 (3), 733–746. DOI: 10.1016/j. ejor.2009.01.046</mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation publication-type="journal">Hrušovský M., Demir E., Jammernegg W., Van Woensel T. (2021) Real-time disruption management approach for intermodal freight transportation. Journal of Cleaner Production, 280 (2), art. no. 124826. DOI: 10.1016/j.jclepro.2020.124826</mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation publication-type="journal">Di Febbraro A., Sacco N., Saeednia M. (2016) An agent-based framework for cooperative planning of intermodal freight transport chains. Transportation Research Part C: Emerging Technologies, 64, 72–85. DOI: 10.1016/j.trc.2015.12.014</mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation publication-type="journal">Davidsson P., Henesey L., Ramstedt L., Törnquist J., Wernstedt F. (2005) An analysis of agent-based approaches to transport logistics. Transportation Research Part C: Emerging Technologies, 13 (4), 255–271. DOI: 10.1016/j.trc.2005.07.002</mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation publication-type="journal">Gambardella L.M., Rizzoli A.E., Funk P. (2002) Agent-based planning and simulation of combined rail/road transport. Simulation, 78 (5), 293–303. DOI: 10.1177/0037549702078005551</mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation publication-type="journal">Dolgui A., Ivanov D., Sokolov B. (2021) Ripple effect in the supply chain: an analysis and recent literature. International Journal of Production Research, 59 (1–2), 414–430. DOI: 10.1080/00207- 543.2017.1387680</mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation publication-type="journal">Zhang T., Cheng J., Zou Y. (2024) Multimodal transportation routing optimization based on multi-objective Q-learning under time uncertainty. Complex &amp; Intelligent Systems, 10 (2), 3133–3152. DOI: 10.1007/s40747-023-01308-9</mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation publication-type="journal">Le T.V., Fan R. (2024) Digital twins for logistics and supply chain systems: Literature review, conceptual framework, research potential, and practical challenges. Computers &amp; Industrial Engineering, 187, art. no. 109768. DOI: 10.1016/j.cie.2023.109768</mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation publication-type="journal">Xu L., Mak S., Schoepf S., Ostroumov M., Brintrup A. (2025) Multi-agent digital twinning for collaborative logistics: Framework and implementation. Journal of Industrial Information Integration, 45, art. no. 100799. DOI: 10.1016/j.jii.2025.100799</mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation publication-type="journal">Tomljenovic V., Merzifonluoglu Y., Spigler G. (2024) Optimizing inland container shipping through reinforcement learning. Annals of Operations Research, 339, 1025–1050. DOI: 10.1007/s10479- 024-05927-4</mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation publication-type="journal">De Bok M., Tavasszy L., Thoen S. (2022) Application of an empirical multi-agent model for urban goods transport to analyze impacts of zero emission zones in The Netherlands. Transport Policy, 124, 119–127. DOI: 10.1016/j.tranpol.2020.07.010</mixed-citation>
      </ref>
      <ref id="ref22">
        <mixed-citation publication-type="journal">Ivanov D., Dolgui A. (2021) OR-methods for coping with the ripple effect in supply chains during COVID-19 pandemic: Managerial insights and research implications. International Journal of Production Economics, 232, art. no. 107921. DOI: 10.1016/j.ijpe.2020.107921</mixed-citation>
      </ref>
      <ref id="ref23">
        <mixed-citation publication-type="journal">Pan S., Ballot E., Fontane F. (2021) The reduction of greenhouse gas emissions from freight transport by pooling supply chains. International Journal of Production Economics, 143 (1), 86–94. DOI: 10.1016/j.ijpe.2010.10.023</mixed-citation>
      </ref>
      <ref id="ref24">
        <mixed-citation publication-type="journal">Antonov A., Levina A., Zhao Z. (2025) Evolution of Digital Systems in the Economy Through the Adoption of Multi-Agent Technologies. In: Digital Systems and Information Technologies in the Energy Sector (eds. I. Ilin, M. Youzhong), Cham: Springer, 187–201. DOI: 10.1007/978-3-031-80710- 7_14</mixed-citation>
      </ref>
      <ref id="ref25">
        <mixed-citation publication-type="journal">Ahmad M.A., Al-Bazi A., Clegg B. (2026) A hybrid multi-agent and system dynamics approach for risk-informed selection of third-party logistics providers in supply chains. Computers in Industry, 176, art. no. 104443. DOI: 10.1016/j.compind.2026.104443</mixed-citation>
      </ref>
      <ref id="ref26">
        <mixed-citation publication-type="journal">Zhang M., Pan C. (2023) Hierarchical optimization scheduling algorithm for logistics transport vehicles based on multi-agent reinforcement learning. IEEE Transactions on Intelligent Transportation Systems, 25 (3), 3108–3117. DOI: 10.1109/TITS.2023.3337334</mixed-citation>
      </ref>
      <ref id="ref27">
        <mixed-citation publication-type="journal">Khussanov A., Kaldybayeva B., Prokhorov O., Khussanov Z., Kenzhebekov D., Yevadilla M., Janabayev D. (2025) Agent-Based Simulation Modeling of Multimodal Transport Flows in Transportation System of Kazakhstan. Logistics, 9 (4), art. no. 172. DOI: 10.3390/logistics9040172</mixed-citation>
      </ref>
      <ref id="ref28">
        <mixed-citation publication-type="journal">Silalahi S.A., Pujawan I.N., Singgih M.L. (2025) Agent-Based Simulation of Digital Interoperability Thresholds in Fragmented Air Cargo Systems: Evidence from a Developing Country. Logistics, 9 (4), art. no. 160. DOI: 10.3390/logistics9040160</mixed-citation>
      </ref>
      <ref id="ref29">
        <mixed-citation publication-type="journal">Kahalimoghadam M., Thompson R.G., Rajabifard A. (2025) An intelligent multi-agent system for last-mile logistics. Transportation Research Part E: Logistics and Transportation Review, 200, art. no. 104191. DOI: 10.1016/j.tre.2025.104191</mixed-citation>
      </ref>
      <ref id="ref30">
        <mixed-citation publication-type="journal">Kalyazina S., Ilin I., Levina A. (2025) A Multi-Agent System in the IT Architecture of Project Portfolio Management of an Energy Company. In: Digital Systems and Information Technologies in the Energy Sector (eds. I. Ilin, M. Youzhong), Cham: Springer, 261–273. DOI: 10.1007/978-3-031-80710-7_19</mixed-citation>
      </ref>
      <ref id="ref31">
        <mixed-citation publication-type="journal">Salas-Peña A., García-Palomares J.C. (2025) Simulating Co-Evolution and Knowledge Transfer in Logistic Clusters Using a Multi-Agent-Based Approach. ISPRS International Journal of Geo-Information, 14 (4), art. no. 179. DOI: 10.3390/ijgi14040179</mixed-citation>
      </ref>
      <ref id="ref32">
        <mixed-citation publication-type="journal"> </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>
