# Multi-Agent Path Finding with Capacity Constraints

## TL;DR

This paper extends multi-agent path finding (MAPF) to allow multiple agents per vertex by modeling capacity constraints in SAT-based formulations, evaluating their performance and proposing new models.

## Contribution

It introduces SAT-based models for MAPF with capacity constraints, extending existing formulations to handle multiple agents per vertex.

## Key findings

- Extended SAT models for MAPF with capacity constraints.
- Performance evaluation of new SAT-based formulations.
- Comparison of eager and lazy modeling approaches.

## Abstract

In multi-agent path finding (MAPF) the task is to navigate agents from their starting positions to given individual goals. The problem takes place in an undirected graph whose vertices represent positions and edges define the topology. Agents can move to neighbor vertices across edges. In the standard MAPF, space occupation by agents is modeled by a capacity constraint that permits at most one agent per vertex. We suggest an extension of MAPF in this paper that permits more than one agent per vertex. Propositional satisfiability (SAT) models for these extensions of MAPF are studied. We focus on modeling capacity constraints in SAT-based formulations of MAPF and evaluation of performance of these models. We extend two existing SAT-based formulations with vertex capacity constraints: MDD-SAT and SMT-CBS where the former is an approach that builds the model in an eager way while the latter relies on lazy construction of the model.