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This paper proposes a parameter-initialization strategy for QAOA applied to the Vehicle Routing Problem, plus a way to encode subtour constraints without extra qubits. The claim of exact solutions in polynomial time with high probability is a prospective hope, not a demonstrated result, and the abstract gives no benchmark against classical solvers. Readers should watch whether the initialization approach holds up on larger instances and on hardware with realistic noise.
Quantum Vehicle Routing Problem: a smart initialization strategy for ill-conditioned optimization landscapes
arXiv:2610.41120v1 Announce Type: new Abstract: With the expansion of complex transport infrastructure, new paths for linking different destinations have emerged, allowing the definition of multiple routes. The introduction of new roads may also lead to disruptions in traffic flow. This problem can be generalized into a special case of VRP, which aims to find the optimal route for a fleet of vehicles within a network of destinations. Finding solutions to this problem requires an exponential number of operations, hindering the ability of exact solvers to deal with large instances, which must therefore be tackled using heuristics, often leading to suboptimal results. Quantum-based algorithms may allow us to find exact solutions in polynomial time with high probability, offering a potential future alternative to classical solvers and in this work, we focus on the QAOA. Our novel contributions are a parameter-initialization strategy that improves the convergence probability and the integration of the subtour constraints directly into the optimization without using additional qubits by employing an approximation of exponential equality constraints. We believe that our results pave the way for effectively solving instances of VRP using quantum-based solutions, leveraging the space-efficient problem encoding and our initialization strategy, which limits the effect of barren-plateau under random parameter initialization.
Abstract:With the expansion of complex transport infrastructure, new paths for linking different destinations have emerged, allowing the definition of multiple routes. The introduction of new roads may also lead to disruptions in traffic flow. This problem can be generalized into a special case of VRP, which aims to find the optimal route for a fleet of vehicles within a network of destinations. Finding solutions to this problem requires an exponential number of operations, hindering the ability of exact solvers to deal with large instances, which must therefore be tackled using heuristics, often leading to suboptimal results. Quantum-based algorithms may allow us to find exact solutions in polynomial time with high probability, offering a potential future alternative to classical solvers and in this work, we focus on the QAOA. Our novel contributions are a parameter-initialization strategy that improves the convergence probability and the integration of the subtour constraints directly into the optimization without using additional qubits by employing an approximation of exponential equality constraints. We believe that our results pave the way for effectively solving instances of VRP using quantum-based solutions, leveraging the space-efficient problem encoding and our initialization strategy, which limits the effect of barren-plateau under random parameter initialization.
Quantum Physics (quant-ph); Emerging Technologies (cs.ET); Combinatorics (math.CO); Optimization and Control (math.OC)
G.2.2; G.2.1; F.2.2
arXiv:2610.41120 [quant-ph]
(or arXiv:2610.41120v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.41120 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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