# An Optimal Algorithm to Solve the Combined Task Allocation and Path Finding Problem

## TL;DR

This paper introduces an optimal algorithm, TCBS, for combined task allocation and multi-agent path planning in collision-avoidance scenarios, serving as a baseline for evaluating sub-optimal methods despite NP-hardness.

## Contribution

The paper presents the first optimal algorithm for the combined task allocation and path planning problem, providing a benchmark for sub-optimal solutions.

## Key findings

- TCBS finds optimal solutions for the combined problem.
- Experimental results compare sub-optimal methods against TCBS.
- TCBS serves as a baseline for evaluating sub-optimal algorithms.

## Abstract

We consider multi-agent transport task problems where, e.g. in a factory setting, items have to be delivered from a given start to a goal pose while the delivering robots need to avoid collisions with each other on the floor. We introduce a Task Conflict-Based Search (TCBS) Algorithm to solve the combined delivery task allocation and multi-agent path planning problem optimally. The problem is known to be NP-hard and the optimal solver cannot scale. However, we introduce it as a baseline to evaluate the sub-optimality of other approaches. We show experimental results that compare our solver with different sub-optimal ones in terms of regret.