A new estimation of distribution algorithm to solve the multiple traveling salesmen problem with the minimization of total distance

Even though the Estimation of Distribution Algorithms (EDAs) have recently been applied to solve many hard problems, only a few EDAs discussed the in-group optimization problems, such as the multiple traveling salesmen problem (mTSP) studied in this research. These problems include the assignment and sequencing procedures in the same time and to be shown in different forms. As a result, this research proposed an algorithm deal by using the Self-Guided GA together with the Minimum Loading Assignment rule (MLA) to tackle the mTSP. We compare the proposed algorithm against the best direct encoding technique, two-part encoding genetic algorithm, in the experiment on the 33 instances drawn from the well-known TSPLIB. The experimental results show the proposed algorithm is better than the compared algorithm in terms of minimization of the total traveling distance. An interesting result also presents the proposed algorithm would not cause longer traveling distance when we increase the number of salesmen from 3 to 10 persons under the objective of minimization of total traveling distance. This research may suggest the EDAs researcher could employ the MLA rule instead of the direct encoding algorithms.