136 research outputs found
Multi-Goal Multi-Agent Path Finding via Decoupled and Integrated Goal Vertex Ordering
We introduce multi-goal multi agent path finding (MAPF) which
generalizes the standard discrete multi-agent path finding (MAPF) problem.
While the task in MAPF is to navigate agents in an undirected graph from their
starting vertices to one individual goal vertex per agent, MAPF assigns
each agent multiple goal vertices and the task is to visit each of them at
least once. Solving MAPF not only requires finding collision free paths
for individual agents but also determining the order of visiting agent's goal
vertices so that common objectives like the sum-of-costs are optimized. We
suggest two novel algorithms using different paradigms to address MAPF:
a heuristic search-based search algorithm called Hamiltonian-CBS (HCBS) and a
compilation-based algorithm built using the SMT paradigm, called
SMT-Hamiltonian-CBS (SMT-HCBS). Experimental comparison suggests limitations of
compilation-based approach
Multi-Agent Path Finding with Continuous Time Using SAT Modulo Linear Real Arithmetic
This paper introduces a new approach to solving a continuous-time version of
the multi-agent path finding problem. The algorithm translates the problem into
an extension of the classical Boolean satisfiability problem, satisfiability
modulo theories (SMT), that can be solved by off-the-shelf solvers. This
enables the exploitation of conflict generalization techniques that such
solvers can handle. Computational experiments show that the new approach scales
better with respect to the available computation time than state-of-the art
approaches and is usually able to avoid their exponential behavior on a class
of benchmark problems modeling a typical bottleneck situation.Comment: Full version of the pape
Counterexample Guided Abstraction Refinement with Non-Refined Abstractions for Multi-Agent Path Finding
Counterexample guided abstraction refinement (CEGAR) represents a powerful
symbolic technique for various tasks such as model checking and reachability
analysis. Recently, CEGAR combined with Boolean satisfiability (SAT) has been
applied for multi-agent path finding (MAPF), a problem where the task is to
navigate agents from their start positions to given individual goal positions
so that the agents do not collide with each other.
The recent CEGAR approach used the initial abstraction of the MAPF problem
where collisions between agents were omitted and were eliminated in subsequent
abstraction refinements. We propose in this work a novel CEGAR-style solver for
MAPF based on SAT in which some abstractions are deliberately left non-refined.
This adds the necessity to post-process the answers obtained from the
underlying SAT solver as these answers slightly differ from the correct MAPF
solutions. Non-refining however yields order-of-magnitude smaller SAT encodings
than those of the previous approach and speeds up the overall solving process
making the SAT-based solver for MAPF competitive again in relevant benchmarks
Solving Satisfiability Modulo Counting for Symbolic and Statistical AI Integration With Provable Guarantees
Satisfiability Modulo Counting (SMC) encompasses problems that require both
symbolic decision-making and statistical reasoning. Its general formulation
captures many real-world problems at the intersection of symbolic and
statistical Artificial Intelligence. SMC searches for policy interventions to
control probabilistic outcomes. Solving SMC is challenging because of its
highly intractable nature(-complete), incorporating
statistical inference and symbolic reasoning. Previous research on SMC solving
lacks provable guarantees and/or suffers from sub-optimal empirical
performance, especially when combinatorial constraints are present. We propose
XOR-SMC, a polynomial algorithm with access to NP-oracles, to solve highly
intractable SMC problems with constant approximation guarantees. XOR-SMC
transforms the highly intractable SMC into satisfiability problems, by
replacing the model counting in SMC with SAT formulae subject to randomized XOR
constraints. Experiments on solving important SMC problems in AI for social
good demonstrate that XOR-SMC finds solutions close to the true optimum,
outperforming several baselines which struggle to find good approximations for
the intractable model counting in SMC
Two Decades of Maude
This paper is a tribute to JosĂ© Meseguer, from the rest of us in the Maude team, reviewing the past, the present, and the future of the language and system with which we have been working for around two decades under his leadership. After reviewing the origins and the language's main features, we present the latest additions to the language and some features currently under development. This paper is not an introduction to Maude, and some familiarity with it and with rewriting logic are indeed assumed.Universidad de Málaga. Campus de Excelencia Internacional AndalucĂa Tech
- …