Fast pathfinding and distance matrix in 2d grid

Context: I’m working on a warehouse simulation that supports different floor designs and simulates one or multiple agents that are tasked with order picking. One order can consist of more than one product. The routing for picking products is solved as a capacitated vehicle routing problem (CVRP). This requires a distance matrix between product locations, for which the A* algorithm is used. Currently, distance matrices are generated per order, just before picking on that order is started. Many simulation runs are desired for accurate measures, so computational efficiency is of high importance. For completeness, I included a screenshot of the simulation below, with product locations (dark), an agent (white), products in the current order (blue), and the products being picked in the current route (green/red). Note that the white lines represent the current picking priority, not the exact paths.

Simulation screenshot

Problem: The size of the distance matrix grows quadratically with the number of products per order. Therefore, the time for computing it with A* quickly becomes unacceptable.

Question: I need a method that makes the computation of distance matrices more efficient. This can be either an exact method or a heuristic, as long as not too much accuracy is sacrificed. I am not looking for implementations or specific code snippets, but for ideas and/or methods that are used for similar problems that I can implement myself.

Attempted methods/ideas: Here are some approaches I’ve considered or tried to implement with no success:

  • Distance matrix for the full warehouse: unfeasible, as the number of product locations is simply too large.
  • Using Euclidean distance: not good enough. This would assume that products on opposite sides of a warehouse row are close together when in reality an agent would have to take a long detour between the two.
  • Using a clustering algorithm to identify areas that are close together and base a distance matrix on clusters instead of individual locations: this would reduce the total matrix size, making it possible to pre-compute it completely. However, this would greatly reduce accuracy and I’ve yet to find a clustering algorithm that reliably works for this problem with different floor layouts.

Layout examples: White pixels indicate floor cells, black pixels indicate product locations. Products within an order are randomly selected from all possible locations. More floor layouts (any floor layout!) should be supported by the chosen method.

Layout 1

Layout 2

Here is a pasteable array for layout 1 if anyone wants to mess around with it:

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Answer

I know link-only answers are usually discouraged, but “what algorithms can make A* faster” is a hugely complicated topic that’s been an active area of research nonstop for the past 50 years. So it’s not really possible to give anything more than a vague summary in a Stackoverflow answer.

For 2D grids like your own, there are two common techniques that give huge speedups:

  • JPS (Jump Point Search) is a variant of A* that exploits the symmetries in 2D grids that contain lots of open space to avoid queuing/dequeuing huge numbers of extraneous nodes.
  • RSR (Rectangular Symmetry Reduction) is a preprocessing algorithm that reduces a map into “rooms” (or in your case, “hallways”) to form a sort of navigation mesh for your map, reducing the size of the graph.

Additionally, since you mentioned it does not need be optimal,

Finally, if your grid changes over time, there is a whole field of incremental algorithms that perform better than A*.