Traveling salesman problem option for the Route solver
The Route solver has the option to generate the optimal sequence of visiting the stop locations. This is the traveling salesman problem, or TSP. The TSP is a combinatorial problem, meaning there is no straightforward way to find the best sequence. Heuristics are used to find good solutions to these types of problems in a short amount of time. The TSP implementation within Network Analyst also handles time windows on the stops; that is, it finds the optimal sequence to visit the stops with a minimum amount of lateness.
The traveling salesman solver starts by generating an origin-destination cost matrix between all the stops to be sequenced and uses a tabu search-based algorithm to find the best sequence of visiting the stops. Tabu search is a metaheuristic algorithm for solving combinatorial problems. It falls in the realm of local search algorithms. The exact implementation of the tabu search is proprietary, but it has been researched and developed extensively in-house at Esri to quickly yield good results.