Abstract

The routing problems with optimization of the starting point: dynamic programming

Highlights

  • Routing problems arise in many applications. These problems arise in investigating sheet cutting on CNC machines

  • Another applied problem related to routing is that of minimization of radiation dose of employees for the work complex under increased radiation; the above-mentioned radiation dose depends on the route selected for work execution

  • These difficulties have both numerical and qualitative nature. These difficulties are related to diverse constraints and complicated cost functions; they are generated by requirements of applied problems

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Summary

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THE ROUTING PROBLEMS WITH OPTIMIZATION OF THE STARTING POINT: DYNAMIC PROGRAMMING. A mathematical model is presented which includes a system of megalopolises (nonempty finite sets) and cost functions depending on the list of tasks. This approach makes it possible to solve the problem of optimizing complexes, which include the initial state (starting point), the method of numbering megalopolises in the order of their visits, and the specific trajectory of the process. For a problem complicated by the dependence of the terminal function on the initial state, a decomposition algorithm is used, which allows, in a substantial part of the procedure, the application of a single (for all initial states) DP scheme.

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