Hybrid control systems and the dynamic traveling salesman problem

A new approximate algorithm for solving the dynamic traveling salesman problem (DTSP) is proposed; the traveling salesman starting from the base city visits megapoleis and cities inside megapoleis and comes back to the base city. A specific feature of this variant of DTSP is the movement of cities inside megapoleis in time. To solve this problem, a general solution theory for hybrid (complicated) systems with “combinatorial” and “continuous” path segments is developed. The general theory is based on the sufficient optimality conditions known in the theory of optimal control.