In the multi agent path finding problem (MAPF) paths should be found for several agents, each with a different start and goal position such that agents do not collide. Previous optimal solvers applied global A*-based searches. We present a new search algorithm called Conflict Based Search (CBS). CBS is a two-level algorithm. At the high level, a search is performed on a tree based on conflicts between agents. At the low level, a search is performed only for a single agent at a time. In many cases this reformulation enables CBS to examine fewer states than A* while still maintaining optimality. We analyze CBS and show its benefits and drawbacks. Experimental results on various problems shows a speedup of up to a full order of magnitude over previous approaches.

Conflict-based search for optimal multi-agent path finding

https://www.aaai.org/ocs/index.php/AAAI/AAAI12/paper/viewFile/5062/5239

Conflict-based search for optimal multi-agent pathfinding

http://2.3jachtuches.pagesperso-orange.fr/dossiers/IA/taquin/doc/Disjoint.pdf

Disjoint pattern database heuristics

Heuristic search is a leading approach to domain-independent planning. For cost-optimal planning, however, existing admissible heuristics are generally too weak to effectively guide the search. Pattern database heuristics (PDBs), which are based on abstractions of the search space, are currently one of the most promising approaches to developing better admissible heuristics. The informedness of PDB heuristics depends crucially on the selection of appropriate abstractions (patterns). Although PDBs have been applied to many search problems, including planning, there are not many insights into how to select good patterns, even manually. What constitutes a good pattern depends on the problem domain, making the task even more difficult for domain-independent planning, where the process needs to be completely automatic and generaL We present a novel way of constructing good patterns automatically from the specification of planning problem instances. We demonstrate that this allows a domain-independent planner to solve planning problems optimally in some very challenging domains, including a STRIPS formulation of the Sokoban puzzle.

/pdf/domain-independent-construction-of-pattern-database-12ytaatl7j.pdf

Domain-independent construction of pattern database heuristics for cost-optimal planning

We explore a method for computing admissible heuristic evaluation functions for search problems. It utilizes pattern databases (Culberson & Schaeffer, 1998), which are precomputed tables of the exact cost of solving various subproblems of an existing problem. Unlike standard pattern database heuristics, however, we partition our problems into disjoint sub-problems, so that the costs of solving the different subproblems can be added together without overestimating the cost of solving the original problem. Previously (Korf & Felner, 2002) we showed how to statically partition the sliding-tile puzzles into disjoint groups of tiles to compute an admissible heuristic, using the same partition for each state and problem instance. Here we extend the method and show that it applies to other domains as well. We also present another method for additive heuristics which we call dynamically partitioned pattern databases. Here we partition the problem into disjoint subproblems for each state of the search dynamically. We discuss the pros and cons of each of these methods and apply both methods to three different problem domains: the sliding-tile puzzles, the 4-peg Towers of Hanoi problem, and finding an optimal vertex cover of a graph. We find that in some problem domains, static partitioning is most effective. while in others dynamic partitioning is a better choice. In each of these problem domains, either statically partitioned or dynamically partitioned pattern database heuristics are the best known heuristics for the problem.

/pdf/additive-pattern-database-heuristics-4t6dxdpenc.pdf

Michael Reid

Papers

Time complexity of iterative-deepening-A