A Novel Approach to Solve Multiple Traveling Salesmen Problem by Genetic Algorithm

The multiple Traveling Salesman Problem (mTSP) is a complex combinatorial optimization problem, which is a generalization of the well-known Traveling Salesman Problem (TSP), where one or more salesmen can be used in the solution. The optimization task can be described as follows: given a fleet of vehicles, a common depot and several requests by the customers, find the set of routes with overall minimum route cost which service all the demands. Because of the fact that TSP is already a complex, namely an NP-complete problem, heuristic optimization algorithms, like genetic algorithms (GAs) need to take into account. The extension of classical GA tools for mTSP is not a trivial problem, it requires special, interpretable encoding to ensure efficiency. The aim of this paper is to review how genetic algorithms can be applied to solve these problems and propose a novel, easily interpretable representation based GA.