The Optimization of feed-in prices for the Vehicle-To-Grid approach is difficult. It presents a challenge to common classical solver and could be a use case for Quantum Computers.
Run times of the OSQP optimizer for varying scenario sizes (hours). Instabilities in the optimization lead to outliers.
In some cases the classical OSQP (Operator-Splitting Quadratic Program) solver can fail, e.g. when the problem turns out to be non-convex.
Quantum-inspired optimization (e.g. population annealing) gives a result, where OSQP fails. The calculated profit gain through feed-in is 28 million euro for one day.
CMA-ES (Covariance Matrix Adaptation Evolution Strategy) optimization algorithm is a specific solver for non-convex problems. The result differs only slightly from the QIO result, for similar run-times. The profit gain amounts to 30 million euro.
As a solver for more general (non-convex) optimization problems, CMA-ES has a significantly larger run-time than OSQP (seconds vs. micro-seconds).
Profit gain of different solvers for varying timeouts compared to the OSQP classical solver.
With a clever encoding, one can map the V2G QUBO problem to a densest subgraph problem.
By using Gaussian Boson Sampling, the densest subgraph problem can be solved on a photonic quantum computer and mapped back to the V2G Problem.
The V2G QUBO problem can be mapped to a Maximum Weighted Independent Set (MWIS) problem on a Unit Disk Graph (UDG). These problems can be naturally encoded and solved on neutral atom quantum computers. (Image taken from Fig. 1 in 2209.03965)
A 6-bit QUBO problem mapped to a 128-node UDG MWIS problem.
The transformed Problem can be solved with a quantum computer (e.g. QuEra's Bloqade simulator) and mapped back to a solution of the V2G problem.