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.
On the route construction in changing environments using solutions of the eikonal equation
