What could be a good state space for dogs locating problem?

Question

Suppose that we have a M*N maze and some and there are K dogs in different cells of this mase looking for their houses (their unique houses are also located in some cell in the maze). in each step, all of the dogs can stay at their location or move to an adjacent cell in the maze (the eligible moves are: up, down, right, left if possible). what could be a good state space for this problem?

Unique houses mean that each dog has its specific house located somewhere on the maze.
Two dogs can stand same cell too.

I personally think that the sum of manhattan distances for each dog from its house could be a good heuristic but I could not define a good state space myself.

Here is a link to a picture of a sample for k=2 and a 5*5 maze: Example

Can the dogs move through each other, or do they need to avoid each other? Do they know where the houses are located? — Nathan S., Feb 27 '20 at 17:26
@NathanS. Yes, they know where their houses are and two dogs can stand on one cell if needed. — K.N, Feb 27 '20 at 18:08

score 0 · Answer 1 · answered Feb 27 '20 at 20:36

Because all of the animals are independent (they don't block each other and they have unique individual goals), you shouldn't model the joint actions between all agents. You are really solving K independent pathfinding problems, where each one can use the manhattan distance heuristic individually, given 4-connected movement. If you solve them jointly you make the problem exponentially larger when it doesn't have to be.

There are lots of ways of building better heuristics or re-using search information, but that's a different question.

What could be a good state space for dogs locating problem?

1 Answers1