Mathematical modeling of multiple tour multiple traveling salesman problem using evolutionary programming

This study describes a single phase algorithm for the fixed destination multi-depot multiple traveling salesman problem with multiple tours (mdmTSP). This problem widely appears in the field of logistics mostly in connection with maintenance networks. The general model of the technical inspection and maintenance systems is shown in the first part, where the solution of this problem is an important question. A mathematical model of the system’s object expert assignment is proposed with the constraints typical of the system, like experts’ capacity minimum and maximum and constraints on maximum and daily tours of the experts. In the second part, the developed evolutionary programming algorithm is described which solves the assignment, regarding the constraints introducing penalty functions in the algorithm. In the last part of the paper, the convergence of the algorithm and the run times and some examination of the parallelization are presented.