Routing the Networks With Negative Weights of Links in the Matlab Optimization Package

Abstract

The subject of research in the field of unmanned maritime and river navigation vessels is the new technological principles and models of unmanned navigation with high reliability and accuracy in the autonomous regimes on the specified path, with the use of satellite navigation, electronic charts and ground-based radio navigation systems. Non-crew vessels management from the shore requires the implementation of group management by the mobile objects, taking into account the update of the local maps of the shipping situation. When selecting the vessels routes, it is necessary to solve the operational problem of determining the shortest vessel route (Autonomous mobile object) at the specific navigation conditions, which directly defines the energy efficiency of the vessel in the voyage. The solution of the operational problem of selecting the shortest paths (routes) for a group of vessels moving in the direction of the specified targets with known coordinates located in a limited space is presented in the paper. A model and an optimization algorithm allowing, in comparison with existing solutions, to significantly expand the class of tasks by introducing the negative weights of individual sections of the path (graph arcs) and make the transition to solving high-dimensional problems are proposed. The key issue in the problem of automation and formation of the routes is the selection of the mathematical apparatus not only for the calculation of the shortest routes, but also for their recovery. For this purpose, a recursive optimization method based on the integer linear programming is proposed for high-dimensional tasks. The practical implementation of the proposed algorithm is demonstrated by the example of calculating a network model with a complex topology, using an iterative procedure for the program compiled in the MATLAB codes. It is shown that the computer model realized on its basis has properties of convergence of calculations and convenience of practical use. In contrast to the existing ones, the proposed model allows to remove the restrictions associated with the presence of negative weights and cycles at the network, to automate the calculations of the shortest paths in the places of branching by means of digital technologies. The correctness of the obtained solutions is confirmed, which makes it possible to use the model and algorithm as a component of the tasks tool designed to control the transport process.