Multi-Agent Route Planning as a QUBO Problem

TL;DR

This paper formalizes multi-agent route planning as a QUBO problem, demonstrating its NP-hardness, and evaluates classical and quantum solvers on large city instances to find efficient coverage solutions.

Contribution

It introduces a QUBO formulation for multi-agent route planning, enabling the use of quantum and classical solvers, and analyzes the coverage-overlap trade-off in large-scale instances.

Findings

Pareto-optimal solutions mainly in the hard-penalty regime

D-Wave hybrid and Gurobi achieve similar objective values

Coverage-overlap knee observed in experimental results

Abstract

Multi-Agent Route Planning considers selecting vehicles, each associated with a single predefined route, such that the spatial coverage of a road network is increased while redundant overlaps are limited. This paper gives a formal problem definition, proves NP-hardness by reduction from the Weighted Set Packing problem, and derives a Quadratic Unconstrained Binary Optimization formulation whose coefficients directly encode unique coverage rewards and pairwise overlap penalties. A single penalty parameter controls the coverage-overlap trade-off. We distinguish between a soft regime, which supports multi-objective exploration, and a hard regime, in which the penalty is strong enough to effectively enforce near-disjoint routes. We describe a practical pipeline for generating city instances, constructing candidate routes, building the QUBO matrix, and solving it with an exact mixed-integer solver (Gurobi), simulated annealing, and D-Wave hybrid quantum annealing. Experiments on Barcelona instances with up to 10 000 vehicles reveal a clear coverage-overlap knee and show that Pareto-optimal solutions are mainly obtained under the hard-penalty regime, while D-Wave hybrid solvers and Gurobi achieve essentially identical objective values with only minor differences in runtime as problem size grows.