抄録
The Multiple Traveling Salesmen Problem (MTSP) is extension of the Traveling Salesman Problem (TSP). This problem is widely applied to many real routing and scheduling problems. This paper proposes a gradient ascent learning algorithm of the elastic net approach for the MTSP. The learning model has two phases: an elastic net phase, and a gradient ascent phase. The elastic net phase tries to find the minimum of total distances. This procedure is equivalent to gradient descent of an energy function, and leads to a local minimum of energy that represents a good solution to the problem. Once the elastic net gets stuck in local minima, the gradient ascent phase attempts to fill up the valley by modifying parameters in a gradient ascent direction of the energy function. Thus, these two phases are iterated until the elastic net gets out of local minima. The simulations are conducted on a series of standard data in order to investigate the performance of the proposed algorithm. The proposed algorithm is shown to be capable of escaping from the elastic net local minima and generating superior solution in all instances compared to the original elastic net.
