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

Abstract

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 the higher speed of 31% in average. Scope and purpose Recently, the neural networks have been one of much interest to OR community; in particular to those dealing with the combinatorial optimization problem such as travelling salesman problem (TSP). Nevertheless, the neural approaches are difficult to apply to more complex problems as additional constraints must be satisfactorily considered. In addition, the comparison between the heuristic approaches and the neural approaches has never been reported before. In this paper, an adaptive neural network approach has been proposed for solving the minmax multiple travelling salesmen problem, which is an extension of the TSP, and it is compares with previous heuristics: elastic net, generalized 2-opt exchange heuristic and adaptive tabu search heuristic.