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Routing and Scheduling in Answer Set Programming applied to Multi-Agent Path Finding: Preliminary Report

Roland Kaminski, Torsten Schaub, Tran Cao Son, Jiří Švancara, Philipp Wanko

TL;DR

This work formally elaborate upon the idea to capture the flow of time in terms of partial orders rather than time steps attached to actions and fluents, and presents several resulting ASP encodings that demonstrate their effectiveness via an empirical analysis.

Abstract

We present alternative approaches to routing and scheduling in Answer Set Programming (ASP), and explore them in the context of Multi-agent Path Finding. The idea is to capture the flow of time in terms of partial orders rather than time steps attached to actions and fluents. This also abolishes the need for fixed upper bounds on the length of plans. The trade-off for this avoidance is that (parts of) temporal trajectories must be acyclic, since multiple occurrences of the same action or fluent cannot be distinguished anymore. While this approach provides an interesting alternative for modeling routing, it is without alternative for scheduling since fine-grained timings cannot be represented in ASP in a feasible way. This is different for partial orders that can be efficiently handled by external means such as acyclicity and difference constraints. We formally elaborate upon this idea and present several resulting ASP encodings. Finally, we demonstrate their effectiveness via an empirical analysis.

Routing and Scheduling in Answer Set Programming applied to Multi-Agent Path Finding: Preliminary Report

TL;DR

This work formally elaborate upon the idea to capture the flow of time in terms of partial orders rather than time steps attached to actions and fluents, and presents several resulting ASP encodings that demonstrate their effectiveness via an empirical analysis.

Abstract

We present alternative approaches to routing and scheduling in Answer Set Programming (ASP), and explore them in the context of Multi-agent Path Finding. The idea is to capture the flow of time in terms of partial orders rather than time steps attached to actions and fluents. This also abolishes the need for fixed upper bounds on the length of plans. The trade-off for this avoidance is that (parts of) temporal trajectories must be acyclic, since multiple occurrences of the same action or fluent cannot be distinguished anymore. While this approach provides an interesting alternative for modeling routing, it is without alternative for scheduling since fine-grained timings cannot be represented in ASP in a feasible way. This is different for partial orders that can be efficiently handled by external means such as acyclicity and difference constraints. We formally elaborate upon this idea and present several resulting ASP encodings. Finally, we demonstrate their effectiveness via an empirical analysis.
Paper Structure (14 sections, 14 theorems, 13 equations, 9 figures, 2 tables)

This paper contains 14 sections, 14 theorems, 13 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Routing
  4. Event orderings
  5. Fact format
  6. Vanilla Encoding for MAPF
  7. Ordering Encoding for MAPF
  8. Routing and scheduling
  9. Event mappings
  10. Fact format
  11. Vanilla Encoding for Weighted MAPF
  12. Sequence Encoding for Weighted MAPF
  13. Experiments
  14. Discussion

Key Result

Proposition 1

For each conflict-free path-based ordered event set for a MAPF problem, there is a unique minimally compatible conflict-free path-based ordered event set for the problem.

Figures (9)

  • Figure 1: Example MAPF problem together with stroll candidates
  • Figure 2: Plan $\{\pi_a^5,\pi_b^5\}$ from \ref{['eq:path:b:fiv']} without vertex and swap conflicts but with a follow-conflict
  • Figure 3: Plan $\{\pi_a^6,\pi_b^6\}$ from \ref{['eq:path:b:six']} without vertex, swap, and follow conflicts
  • Figure 4: A weighted graph and its corresponding unweighted graph
  • Figure 5: Two strolls having a vertex conflict at index 2
  • ...and 4 more figures

Theorems & Definitions (27)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Proposition 1
  • Proposition 2
  • Proposition 3: Soundness
  • Proposition 4: Completeness
  • Definition 6
  • ...and 17 more