Solvability of pseudobulous conditional optimization problems of the type of many salesmen

Abstract

Formalizing routing problems of many traveling salesman (mTSP) in complex networks leads to NP-complete pseudobulous conditional optimization problems. The subclasses of polynomially solvable problems are distinguished, for which the elements of the distance matrix satisfy the triangle inequality and other special representations of the original data. The polynomially solvable assignment problem can be used to determine the required number of salesmen and to construct their routes. Uses a subclass of tasks in the form of pseudobulous optimization with disjunctive normal shape (\textit{DNS}) constraints to which the task is reduced mTSP. Problems in this form are polynomially solvable and allow to combine knowledge about network structure, requirements to pass routes by agents (search procedures) and efficient algorithms of logical inference on constraints in the form of \textit{DNS}. This approach is the theoretical justification for the development of multi-agent system management leading to a solution mTSP. Within the framework of intellectual planning, using resources and capabilities, and taking into account the constraints for each agent on the selected clusters of the network, the construction of a common solution for the whole complex network is achieved.