Competition-based neural network for the multiple travelling salemen problem with minmax objective

In this paper, a new algorithm in competition-based network has been introduced to solve the minmax multiple travelling salesmen problem (MTSP) which needs the maximum distance among all salesmen to be minimum. As in the previous approaches, the generalized 2-opt exchange heuristic algorithms and the elastic net algorithm are reviewed and applied to the minmax MTSP problem solution. Furthermore, a comprehensive empirical study has been provided in order to investigate the performance of the algorithms. The adaptive approach can obtain the superior solution in all instances, compared to the generalized 2-opt exchange heuristic and the elastic net. In additional evaluation, the adaptive algorithm is combined with a simple improvement heuristic and compared with a recently adaptive tabu search. As a result, the adaptive approach can obtain the appropriate solutions 3% in average of the best solution of the adaptive tabu search heuristic accompanied with a higher speed of 31% in average.