# Routing problems with a large amount of points and one constraint

I am currently tackling a routing problem where I have to create daily schedule for workers to repair some installations. There 200,000 installations and a worker can only work 8 hours per fay. The goal is to make optimal routes on a daily basis; therefore optimizing the distance between the different points he has to visit on a daily basis but there is also a constraint on the priority of each installation. Indeed each installation has a priority between 0 and 1 and higher priority points should be given higher weights.

I am just looking for some suggestions as I have tried implementing some solutions (https://developers.google.com/optimization/routing/tsp) but due to the many points I have, this results in too long computation time.

Thank you.

Best regards,

Charles

On

As you know, there is no perfect answer for your issue, but maybe I can guide your research :

• Alpha-Beta pruning : I've been using it to reduce the amount of possibilities for an AI playing Hex game.
• A* pathfinding : I've been using it to simulate a futuristic hyperloop-like capsule-based network, as a complement of Dijkstra algorithm.

You can customize both algorithm according to your needs.

Hoping to be useful !

On

Due to large scale of the described problem it is nearly impossible to achieve the optimal solution for each case. You could try something based on mixed integer programming, especially in TSP or vehicle routing problem but I assume that it won't work in your case.

What you should try, at least in my opinion, are heuristic approaches for solving TSP/VRP: tabu search, simulated annealing, hill climbing. Given enough time and a proper set of constraints one of these methods would produce "good enough" solutions, which are much better than a random guessing. Take a look at something like Google OR-Tools

On

That's a massive sized problem. You will need to cluster it into smaller subproblems before tackling it. We've applied sophisticated fuzzy clustering techniques to experimentally solve a 20,000 location problem. For 200,000 you'll probably need to aggregate by geographic regions (e.g. postcode / zipcode) though before you could attempt to run some kind of clustering to split it up. Alternatively you may just want to try a hard split based on geography first of all.