Optimization of Multiple Traveling Salesmen Problem by a Novel Representation Based Genetic Algorithm

The Vehicle Routing Problem (VRP) is a complex combinatorial optimization problem that can be described as follows: given a fleet of vehicles with uniform capacity, a common depot, and several costumer demands; find the set of routes with overall minimum route cost which service all the demands. The multiple traveling salesman problem (mTSP) is a generalization of the well-known traveling salesman problem (TSP), where more than one salesman is allowed to be used in the solution. It is well-known that mTSP-based algorithms can also be utilized in several VRPs by incorporating some additional site constraints. The aim of this chapter is to review how genetic algorithms can be applied to solve these problems and to propose a novel, interpretable representation based algorithm. The elaborated heuristic algorithm is demonstrated by examples considering different round tour types determination of further tasks for optimal operation of the distribution system for instance the modification of the vehicle capacity, and the effects of change of cost elements and data structure.