A Hybrid Quantum-assisted Column Generation Algorithm for the Fleet Conversion Problem

The problem of Fleet Conversion aims to reduce the carbon emissions and cost of operating a fleet of vehicles for a given set of tours. It can be modelled as a column generation scheme with the Maximum Weighted Independent Set (MWIS) problem as the slave. Quantum variational algorithms have gained significant interest in the past several years. Recently, a method to represent Quadratic Unconstrained Binary Optimization (QUBO) problems using logarithmically fewer qubits was proposed. Here we use this method to solve the MWIS Slaves and demonstrate how quantum and classical solvers can be used together to approach an industrial-sized use-case (up to 64 tours).