Mathematical modelling of traveling salesman problem (TSP) by implementing simulated annealing and genetic algorithms

Abstract

Abstract The Traveling Salesman Problem (TSP) is very well known as one of the optimization problems of circuit of Hamiltonian , which will seek for the shortest route that must be passed by a number of city salesmen exactly once and will return to the initial city. Genetic Algorithm (GA) and Simulated Annealing (SA) are one method that can be used in TSP case. Fertilizer distribution at PT. Sahabat Mewah dan Makmur (SMM) in Belitung which is one of the branches of PT. Austindo Nusantara Jaya Group does not yet have an optimal fertilizer distribution schedule, where when fertilizer will be distributed from the starting point of distribution to the location of storage warehouses, it is not determined which location points will receive delivery, shipments are made to warehouse locations that still have enough storage space or stacked in the nearest warehouse. PT.SMM distributes fertilizer from Port of Tanjung Pandan to warehouses in Jangkang, Balok, Ladang Jaya, Sari Bunga, and Aik Ruak. The results show that in the GA of 120 routes, there are 8 routes with a distance of 175 km; In SA, the shortest distance is equal to GA, which is 175 km.