TY - JOUR

T1 - Поиск оптимального маршрута в трехмерном пространстве

AU - Аббасов, Меджид Эльхан оглы

AU - Лаврухин, Михаил Юрьевич

AU - Горбунова, Анна Андреевна

PY - 2025/10/15

Y1 - 2025/10/15

N2 - This paper investigates, for the first time, a three-dimensional mathematical model for constructing an optimal trajectory that had previously been studied only in the two-dimensional setting. An integral cost functional of the trajectory is formulated and a necessary condition for its minimum is derived. The resulting integro-differential equation is solved by the Galerkin and collocation methods. A genetic algorithm is also proposed. Classical methods based on necessary extremum conditions are well suited for finding local optima in smooth problems, whereas the genetic algorithm is advantageous when exact methods are unavailable: it can escape local extrema and often produces solutions close to the global optimum. Results of numerical experiments are presented, and future research directions aimed at improving numerical schemes and developing hybrid approaches are outlined.

AB - This paper investigates, for the first time, a three-dimensional mathematical model for constructing an optimal trajectory that had previously been studied only in the two-dimensional setting. An integral cost functional of the trajectory is formulated and a necessary condition for its minimum is derived. The resulting integro-differential equation is solved by the Galerkin and collocation methods. A genetic algorithm is also proposed. Classical methods based on necessary extremum conditions are well suited for finding local optima in smooth problems, whereas the genetic algorithm is advantageous when exact methods are unavailable: it can escape local extrema and often produces solutions close to the global optimum. Results of numerical experiments are presented, and future research directions aimed at improving numerical schemes and developing hybrid approaches are outlined.

KW - Galerkin method

KW - collocation method

KW - genetic algorithm

KW - mathematical modelling

KW - optimal trajectory

KW - projection methods

UR - https://applmathjournal.spbu.ru/issue/view/1049

UR - https://www.mendeley.com/catalogue/d7318004-a373-3887-bd36-b199ebd75403/

U2 - 10.21638/spbu10.2025.301

DO - 10.21638/spbu10.2025.301

M3 - статья

VL - 21

SP - 318

EP - 328

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 3

ER -