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In the instance of the Vehicle Routing Problem (VRP) with Google's OR-Tools that I'm trying to solve, only certain routes (tours) should end at the starting point, i.e. the depot.

I can edit the distances from every location to the depot. Setting them all to 0 will have the effect of setting an arbitrary end location and the routes will look kind of "radial" with a center in the depot. Whereas setting a distance from every location to the depot will make the routes look "circular".

The question is, how to model the problem so that only some of the routes (containing a specific type of node) will be "circular"?

Vital V
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1 Answers1

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Here some examples:
"Radial" (starting from center 0) . e.g.: https://github.com/google/or-tools/raw/stable/ortools/constraint_solver/doc/vrp_starts_ends_solution.svg?sanitize=true src: https://github.com/google/or-tools/blob/stable/ortools/constraint_solver/doc/VRP.md#multiple-starts-ends
note: in this example each vehicle has a different start node and all use the same depot end node aka 0

Loop: (Starting from depot and returning to it).
e.g.: https://github.com/google/or-tools/raw/stable/ortools/constraint_solver/doc/vrp_global_span_solution.svg?sanitize=true src: https://github.com/google/or-tools/blob/stable/ortools/constraint_solver/doc/VRP.md#global-span-constraints

Simply create a dummy node, with distance zero from any nodes like you say BUT also keep your depot.

When building the RoutingIndexManager you can pass a start/end list so in the end list choose between your dummy node or the real depot in order to have the vehicle coming back to depot or not.

And in your "print/display" method you can check the end node index and draw/print accordingly...

note: you can find the python script used to generate these svg in the source tree (ed I didn't run it for months so it may be broken (TODO: add CI jobs on it ^^))

Mizux
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  • Interesting, I didn't know you can set start/end locations when creating RoutingIndexManager. But as far as I understand this, it will match the start/end locations with vehicle indexes. In this problem the "loop" routes are not related with any particular vehicle. It's only routes containing certain nodes that need to end at the depot – Vital V Jan 22 '20 at 10:33
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    seems close to a PickupAndDelivery constraint to me. You can create a dummy depot node for each node which need a "return to depot" constraint – Mizux Jan 22 '20 at 10:41
  • Yes, it is. It actually was my initial idea, but I was trying to avoid more constraints. I'll give it a shot – Vital V Jan 22 '20 at 11:06