What is the background to the route planning problem?
Die Route planning plays in various industries a role. The obvious are, of course, the Delivery of parcels, food or groceries, but other areas also work with route planning, such as garbage collection or cities when planning bus schedules.
The goal of tour planning is to optimize the route: It is important to choose the shortest routes in order to save travel costs and time. The latter is particularly important for companies that supply customers with goods.
that Route planning problem It has various names. It has been known since 1832, but it was treated mathematically for the first time 1930. That's what it was first called a messenger problem before it finally Traveling Salesman (or Salesperson) problem, in German: Salesman's problem was baptized. A route planning algorithm was 1959 published. Since then, however, there have been many various solutions.
The navigation system as a graph of nodes and edges
In these, Maps or road networks divided into junctions and edges. Navigation system algorithms therefore model paths or roads as graphs, which results from the connections between the nodes and edges. In relation to a road network, junctions represent the intersections and edges represent the paths in between. Die Knots and edges are given weightsto now calculate which is the fastest route from start to finish. Without the Abstraction as a graph So that wouldn't be possible.
How does the algorithm work?
To do this, the program uses the next node, which over the edges from the start Reached directly can be. If he hits nodes where he has already been, this is classified as a detour and comparedwhether the detour may even be shorter than the main route. This is how the algorithm shimmers through the road network until it reaches its destination. As a reference value, he takes the Air line to help the approximate direction and distance. He also prefers motorways when users are not traveling on foot or by bicycle.
The Output is the best way with the aim of finding the shortest possible tour. This algorithm comes from by Dijkstrasthat he 1959 published. One What other solutions have in common is graph theory, as it abstracts space, which is necessary to calculate the route. Graph theory also forms the groundwork for the Route planning, also Standard problem of route planning or Vehicle Routing Problem called.
The standard problem of route planning
The salesman's problem has been generalized to VRP, the Vehicle Routing Problem or Standard problem of route planning. Die Route planning works with clustering and routing. that Standard problem of route planning So is a Part of trip planning. It is used for the development of optimization process, i.e. to calculate an optimal route. George Dantzig formulated it in 1959 to apply it to the optimization of gas deliveries to gas stations.
An optimal tour makes it possible to Minimize transportation costs, the necessary number at Vehicles and drivers toward minimize, the Travel time And the time for loading to minimize, around the victory ultimately to maximizing. Optimized tours are therefore still a relevant aspect for couriers, parcel services and other delivery services today.
Route planning at a glance
The difference to the Dijkstra algorithm, which involves nodes and edges of a graph as abstract road network works, is that the start and finish points are the same. The result is therefore a round trip with one or more Stopovers. The latter is also the case with the Route planning, where the software on the one hand calculates which orders have been put together for a tour become, and in which order On the other hand, the intermediate stops are served.
The problem of the salesman therefore appears more frequently as a sub-problem because it is primarily aimed at the shortest route from start to finish. At the Route planning But must, for example, also a heterogeneous vehicle fleet are taken into account and priority customers, which in a particular time frame must or want to be supplied. Route planning software helps companies to create routes for Delivery of goods to plan and optimize. Die data base Set road network And the Customer master data as well as vehicular and Driver lists and Order lists Dar.
