The article considers the mathematical formulation of a multi-criteria transport problem with time constraints. The criteria in it are the cost of transportation, their importance and the time spent on transportation. A feature of this task is the presence of time constraints, such as time windows for customers and the duration of stay of vehicles on the road. As a solution to the multi-criteria problem, the selection of Pareto optimal points is proposed, since this optimization method has a wide range of tasks to apply. The formulation of pareto optimization and the definition of pareto optimality are given. Pareto optimization methods are considered: the lexicographic method and scalarization, the varieties of which are the method of ε-constraints, which is based on the gradation of optimization criteria in descending order of their importance, and the method of linear scalarization, the mechanism of which is based on combining all optimization functions into one. Using the example, we consider the reduction of a formalized multicriteria transport problem to a form suitable for scalarization. The definition of pareto efficiency seems acceptable for the implementation of its mechanisms as part of an adaptive decision support system aimed at solving optimization problems in various fields and operating with heuristic algorithms.
1. Titova E.I., Chaprasova A.V. Razreshimost' transportnoi zadachi po kriteriyu vremeni. Molodoi uchenyi. 2014;(4):36–38. (In Russ.).
2. Gogolin V.A., Nikolaeva Е.A. Transport take with time of supply. Sovremennye naukoemkie tekhnologii = Modern High Technologies. 2017;(7):23–26. (In Russ.).
3. Gvozdev L.R., Medvedeva T.A. Solving the problem of vehicles routing with time windows using the ant colony algorithm. Molodoi issledovatel' Dona = Young Don Researcher. 2022;(3):58–61. (In Russ.).
4. Huang N., Li J., Zhu W., Qin H. The multi-trip vehicle routing problem with time windows and unloading queue at depot. Transportation Research Part E: Logistics and Transportation Review. 2021;152. https://doi.org/10.1016/j.tre.2021.102370
5. Koshkin B.P., Noskov S.I., Olentsevich V.A., Ryazantsev A.I. About multi-criteria transport problem. Fundamental'nye issledovaniya = Fundamental Research. 2017;(7):35–38. (In Russ.).
6. Zolotaryuk A.V. Matematicheskaya model' mnogokriterial'noi optimizatsii transportnykh perevozok. Innovatsionnye tekhnologii v nauke i obrazovanii. 2015;(1):317–320. (In Russ.).
7. Podinovskii V.V., Nogin V.D. Pareto-optimal'nye resheniya mnogokriterial'nykh zadach. Moscow: Fizmatlit; 2007. 256 p. (In Russ.).
8. Nogin V.D. Mnozhestvo i printsip Pareto. Saint Petersburg: Izdatel'sko-poligraficheskaya assotsiatsiya vysshikh uchebnykh zavedenii; 2022. 110 p. (In Russ.).
9. Podinovskii V.V. Mnogokriterial'nye zadachi prinyatiya reshenii: teoriya i metody analiza. Moscow: Publishing URAIT; 2024. 486 p. (In Russ.).
10. Kushnir A.Yu. Mnogokriterial'naya optimizatsiya transportnykh perevozok. In: V Mezhdunarodnyi nauchnyi studencheskii kongress «Razvitie rossiiskoi ekonomiki: problemy i perspektivy»: Razvitie rossiiskoi ekonomiki: problemy i perspektivy: sbornik statei uchastnikov V Mezhdunarodnogo nauchnogo studencheskogo kongressa, 28 February – 18 April 2014, Moscow, Russia. Moscow: Finance University under the Government of the Russian Federation; 2014. P. 826–830. (In Russ.).
11. Zobnina O.V., Du A.I., Babaeva Yu.A. Multi-criteria optimization. StudNet. 2021;4(1):87–93. (In Russ.).
12. Li J.-Y., Zhan Zh.-H., Li Y., Zhang J. Multiple Tasks for Multiple Objectives: A New Multiobjective Optimization Method via Multitask Optimization. IEEE Transactions on Evolutionary Computation. 2023. https://doi.org/10.1109/TEVC.2023.3294307
13. Hwang C.-L., Masud A.S.M. Multiple Objective Decision Making – Methods and Applications: A State-of-the-Art Survey. Berlin, Heidelberg, New York: Springer-Verlag; 1979. 358 p.
14. Brakhman T.R. Mnogokriterial'nost' i vybor al'ternativy v tekhnike. Moscow: Radio i svyaz'; 1984. 288 p. (In Russ.).
15. Belykh M.A., Barabanov V.F., Podvalny S.L., Donskikh A.K. Structure of the intelligent system for supporting evolutionary algorithms. Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta = Bulletin of Voronezh State Technical University. 2021;17(3):7–13. (In Russ.). https://doi.org/10.36622/VSTU.2021.17.3.001
16. Belykh M.A., Barabanov A.V. Skhema raboty vybora evolyutsionnogo algoritma intellektual'noi sistemy. Informatsionnye tekhnologii modelirovaniya i upravleniya. 2022;128(2):114–117. (In Russ.).
Belykh Mikhail Alekseevich
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Voronezh State Technical University
Graduate student
Voronezh, Russia
