On the Tour Towards DPLL(MAPF) and Beyond

arXiv.org Artificial Intelligence

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$^R$, a theory of continuous MAPF with geometric agents, are also discussed.

Combining Inference and Search for the Propositional Satisfiability Problem

AAAI Conferences

The most effective complete method for testing propositional satisfiability (SAT) is backtracking search. Recent research suggests that adding more inference to SAT search procedures can improve their performance. This paper presents two ways to combine neighbour resolution (one such inference technique) with search.

Satisfiability Modulo Constraint Handling Rules (Extended Abstract)

AAAI Conferences

Satisfiability Modulo Constraint Handling Rules (SMCHR) is the integration of the Constraint Handling Rules (CHRs) solver programming language into a Satisfiability Modulo Theories (SMT) solver framework.  Constraint solvers are implemented in CHR as a set of high-level rules that specify the simplification (rewriting) and constraint propagation behavior.  The traditional CHR execution algorithm manipulates a global store representing a flat conjunction of constraints.  This paper introduces SMCHR: a tight integration of CHR with a modern Boolean Satisfiability (SAT) solver.  Unlike CHR, SMCHR can handle (quantifier-free) formulae with an arbitrary propositional structure.  SMCHR is essentially a Satisfiability Modulo Theories (SMT) solver where the theory T is implemented in CHR.

Optimal Cooperative Path-Finding with Generalized Goals in Difficult Cases

AAAI Conferences

We suggest to employ propositional satisfiability techniques in solving a problem of cooperative multi-robot path-finding optimally. Several propositional encodings of path-finding problems have been suggested recently. In this paper we evaluate how efficient these encodings are in solving certain cases of cooperative path-findings problems optimally. Particularly, a case where robots have multiple optional locations as their targets is considered in this paper.

Solving the Round Robin Problem Using Propositional Logic

AAAI Conferences

In this paper we present a new and extremely competitive approach to solving a notoriously hard problem from the sports scheduling domain, the round robin problem. By combining local search satisfiability algorithms and an appropriate problem encoding based on classical propositional logic, we are able to find feasible schedules many times faster than using the best existing approaches to the round robin problem. Moreover, using this scheduling as satisfiability approach we are able to solve a previously unsolved instance, the round robin problem for 20 teams.