A hybrid estimation of distribution algorithm for solving the multi-objective multiple traveling salesman problem

The multi-objective multiple traveling salesman problem (MmTSP) is a generalization of the classical multi-objective traveling salesman problem. In this paper, a formulation of the MmTSP, which considers the weighted sum of the total traveling costs of all salesmen and the highest traveling cost of any single salesman, is proposed. An estimation of distribution algorithm (EDA) based on restricted Boltzmann machine is used for solving the formulated problem. The EDA is developed in the decomposition framework of multi-objective optimization. Due to the limitation of EDAs in generating a wide range of solutions, the EDA is hybridized with the evolutionary gradient search. Simulation studies are carried out to examine the optimization performances of the proposed algorithm on MmTSP with different number of objective functions, salesmen and problem sizes.