43 research outputs found
Multi-agent Path Finding with Continuous Time Viewed Through Satisfiability Modulo Theories (SMT)
This paper addresses a variant of multi-agent path finding (MAPF) in
continuous space and time. We present a new solving approach based on
satisfiability modulo theories (SMT) to obtain makespan optimal solutions. The
standard MAPF is a task of navigating agents in an undirected graph from given
starting vertices to given goal vertices so that agents do not collide with
each other in vertices of the graph. In the continuous version
(MAPF) agents move in an -dimensional Euclidean space along
straight lines that interconnect predefined positions. For simplicity, we work
with circular omni-directional agents having constant velocities in the 2D
plane. As agents can have different sizes and move smoothly along lines, a
non-colliding movement along certain lines with small agents can result in a
collision if the same movement is performed with larger agents. Our SMT-based
approach for MAPF called SMT-CBS reformulates the
Conflict-based Search (CBS) algorithm in terms of SMT concepts. We suggest lazy
generation of decision variables and constraints. Each time a new conflict is
discovered, the underlying encoding is extended with new variables and
constraints to eliminate the conflict. We compared SMT-CBS and
adaptations of CBS for the continuous variant of MAPF experimentally
Lazy Modeling of Variants of Token Swapping Problem and Multi-agent Path Finding through Combination of Satisfiability Modulo Theories and Conflict-based Search
We address item relocation problems in graphs in this paper. We assume items
placed in vertices of an undirected graph with at most one item per vertex.
Items can be moved across edges while various constraints depending on the type
of relocation problem must be satisfied. We introduce a general problem
formulation that encompasses known types of item relocation problems such as
multi-agent path finding (MAPF) and token swapping (TSWAP). In this formulation
we express two new types of relocation problems derived from token swapping
that we call token rotation (TROT) and token permutation (TPERM). Our solving
approach for item relocation combines satisfiability modulo theory (SMT) with
conflict-based search (CBS). We interpret CBS in the SMT framework where we
start with the basic model and refine the model with a collision resolution
constraint whenever a collision between items occurs in the current solution.
The key difference between the standard CBS and our SMT-based modification of
CBS (SMT-CBS) is that the standard CBS branches the search to resolve the
collision while in SMT-CBS we iteratively add a single disjunctive collision
resolution constraint. Experimental evaluation on several benchmarks shows that
the SMT-CBS algorithm significantly outperforms the standard CBS. We also
compared SMT-CBS with a modification of the SAT-based MDD-SAT solver that uses
an eager modeling of item relocation in which all potential collisions are
eliminated by constrains in advance. Experiments show that lazy approach in
SMT-CBS produce fewer constraint than MDD-SAT and also achieves faster solving
run-times
Feasibility Study: Moving Non-Homogeneous Teams in Congested Video Game Environments
Multi-agent path finding (MAPF) is a well-studied problem in artificial
intelligence, where one needs to find collision-free paths for agents with
given start and goal locations. In video games, agents of different types often
form teams. In this paper, we demonstrate the usefulness of MAPF algorithms
from artificial intelligence for moving such non-homogeneous teams in congested
video game environments.Comment: To appear in AIIDE 1
Multi-Agent Path Finding with Deadlines: Preliminary Results
We formalize the problem of multi-agent path finding with deadlines
(MAPF-DL). The objective is to maximize the number of agents that can reach
their given goal vertices from their given start vertices within a given
deadline, without colliding with each other. We first show that the MAPF-DL
problem is NP-hard to solve optimally. We then present an optimal MAPF-DL
algorithm based on a reduction of the MAPF-DL problem to a flow problem and a
subsequent compact integer linear programming formulation of the resulting
reduced abstracted multi-commodity flow network.Comment: AAMAS 2018, to appea
Justifying and Improving Meta-Agent Conflict-Based Search
The Meta-Agent Conflict-Based Search~(MA-CBS) is a recently proposed
algorithm for the multi-agent path finding problem. The algorithm is an
extension of Conflict-Based Search~(CBS), which automatically merges
conflicting agents into meta-agents if the number of conflicts exceeds a
certain threshold. However, the decision to merge agents is made according to
an empirically chosen fixed threshold on the number of conflicts. The best
threshold depends both on the domain and on the number of agents, and the
nature of the dependence is not clearly understood.
We suggest a justification for the use of a fixed threshold on the number of
conflicts based on the analysis of a model problem. Following the suggested
justification, we introduce new decision policies for the MA-CBS algorithm,
which considerably improve the algorithm's performance. The improved variants
of the algorithm are evaluated on several sets of problems, chosen to underline
different aspects of the algorithms.Comment: 7 page
Multi-Agent Pathfinding with Continuous Time
Multi-Agent Pathfinding (MAPF) is the problem of finding paths for multiple
agents such that every agent reaches its goal and the agents do not collide.
Most prior work on MAPF was on grids, assumed agents' actions have uniform
duration, and that time is discretized into timesteps. We propose a MAPF
algorithm that does not rely on these assumptions, is complete, and provides
provably optimal solutions. This algorithm is based on a novel adaptation of
Safe interval path planning (SIPP), a continuous time single-agent planning
algorithm, and a modified version of Conflict-based search (CBS), a state of
the art multi-agent pathfinding algorithm. We analyze this algorithm, discuss
its pros and cons, and evaluate it experimentally on several standard
benchmarks.Comment: Camera-ready version of the paper as to appear in IJCAI'19
proceeding
Area Protection in Adversarial Path-Finding Scenarios with Multiple Mobile Agents on Graphs: a theoretical and experimental study of target-allocation strategies for defense coordination
We address a problem of area protection in graph-based scenarios with
multiple agents. The problem consists of two adversarial teams of agents that
move in an undirected graph shared by both teams. Agents are placed in vertices
of the graph; at most one agent can occupy a vertex; and they can move into
adjacent vertices in a conflict free way. Teams have asymmetric goals: the aim
of one team - attackers - is to invade into given area while the aim of the
opponent team - defenders - is to protect the area from being entered by
attackers by occupying selected vertices. We study strategies for allocating
vertices to be occupied by the team of defenders to block attacking agents. We
show that the decision version of the problem of area protection is PSPACE-hard
under the assumption that agents can allocate their target vertices multiple
times. Further we develop various on-line vertex-allocation strategies for the
defender team in a simplified variant of the problem with single stage vertex
allocation and evaluated their performance in multiple benchmarks. The success
of a strategy is heavily dependent on the type of the instance, and so one of
the contributions of this work is that we identify suitable vertex-allocation
strategies for diverse instance types. In particular, we introduce a
simulation-based method that identifies and tries to capture bottlenecks in the
graph, that are frequently used by the attackers. Our experimental evaluation
suggests that this method often allows a successful defense even in instances
where the attackers significantly outnumber the defenders
Finding Optimal Solutions to Token Swapping by Conflict-based Search and Reduction to SAT
We study practical approaches to solving the token swapping (TSWAP) problem
optimally in this short paper. In TSWAP, we are given an undirected graph with
colored vertices. A colored token is placed in each vertex. A pair of tokens
can be swapped between adjacent vertices. The goal is to perform a sequence of
swaps so that token and vertex colors agree across the graph. The minimum
number of swaps is required in the optimization variant of the problem. We
observed similarities between the TSWAP problem and multi-agent path finding
(MAPF) where instead of tokens we have multiple agents that need to be moved
from their current vertices to given unique target vertices. The difference
between both problems consists in local conditions that state transitions
(swaps/moves) must satisfy. We developed two algorithms for solving TSWAP
optimally by adapting two different approaches to MAPF - CBS and MDD- SAT. This
constitutes the first attempt to design optimal solving algorithms for TSWAP.
Experimental evaluation on various types of graphs shows that the reduction to
SAT scales better than CBS in optimal TSWAP solving
On the Tour Towards DPLL(MAPF) and Beyond
We discuss milestones on the tour towards DPLL(MAPF), a multi-agent path
finding (MAPF) solver fully integrated with the Davis-Putnam-Logemann-Loveland
(DPLL) propositional satisfiability testing algorithm through satisfiability
modulo theories (SMT). The task in MAPF is to navigate agents in an undirected
graph in a non-colliding way so that each agent eventually reaches its unique
goal vertex. At most one agent can reside in a vertex at a time. Agents can
move instantaneously by traversing edges provided the movement does not result
in a collision. Recently attempts to solve MAPF optimally w.r.t. the
sum-of-costs or the makespan based on the reduction of MAPF to propositional
satisfiability (SAT) have appeared. The most successful methods rely on
building the propositional encoding for the given MAPF instance lazily by a
process inspired in the SMT paradigm. The integration of satisfiability testing
by the SAT solver and the high-level construction of the encoding is however
relatively loose in existing methods. Therefore the ultimate goal of research
in this direction is to build the DPLL(MAPF) algorithm, a MAPF solver where the
construction of the encoding is fully integrated with the underlying SAT
solver. We discuss the current state-of-the-art in MAPF solving and what steps
need to be done to get DPLL(MAPF). The advantages of DPLL(MAPF) in terms of its
potential to be alternatively parametrized with MAPF, a theory of
continuous MAPF with geometric agents, are also discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1809.0595
Lifelong Multi-Agent Path Finding for Online Pickup and Delivery Tasks
The multi-agent path-finding (MAPF) problem has recently received a lot of
attention. However, it does not capture important characteristics of many
real-world domains, such as automated warehouses, where agents are constantly
engaged with new tasks. In this paper, we therefore study a lifelong version of
the MAPF problem, called the multi-agent pickup and delivery (MAPD) problem. In
the MAPD problem, agents have to attend to a stream of delivery tasks in an
online setting. One agent has to be assigned to each delivery task. This agent
has to first move to a given pickup location and then to a given delivery
location while avoiding collisions with other agents. We present two decoupled
MAPD algorithms, Token Passing (TP) and Token Passing with Task Swaps (TPTS).
Theoretically, we show that they solve all well-formed MAPD instances, a
realistic subclass of MAPD instances. Experimentally, we compare them against a
centralized strawman MAPD algorithm without this guarantee in a simulated
warehouse system. TP can easily be extended to a fully distributed MAPD
algorithm and is the best choice when real-time computation is of primary
concern since it remains efficient for MAPD instances with hundreds of agents
and tasks. TPTS requires limited communication among agents and balances well
between TP and the centralized MAPD algorithm.Comment: In AAMAS 201