Geodesic
On the route construction in changing environments using solutions of the eikonal equation
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 58 (2021), pp. 59-72

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The article deals with the vehicle routing problem in an environment with dynamically changing properties. The problem is relevant in current conditions when the delivery cost has a steady upward trend and is often comparable to the cost of the product itself. A central feature of the study is that the optimality criterion is the minimum delivery time, but not the distance traveled. The optical-geometric approach developed by the authors, based on the analogy between the propagation of light in an optically inhomogeneous medium and the minimization of the integral functional, is used as a research tool. We use exact and approximate solutions of the eikonal equations to describe wave fronts. Two original numerical algorithms for route construction are proposed and implemented as software. A computational experiment is performed that justified the effectiveness of the proposed model-algorithmic tools.
Keywords: vehicle routing problem, optimization, optical-geometric approach, computational algorithm.
Mots-clés : eikonal equation 
@article{IIMI_2021_58_a3,
     author = {A. L. Kazakov and A. A. Lempert},
     title = {On the route construction in changing environments using solutions of the eikonal equation},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {59--72},
     publisher = {mathdoc},
     volume = {58},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2021_58_a3/}
}
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A. L. Kazakov; A. A. Lempert. On the route construction in changing environments using solutions of the eikonal equation. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 58 (2021), pp. 59-72. http://geodesic.mathdoc.fr/item/IIMI_2021_58_a3/