Abstract
This work focuses on expressing the TSP with Time Windows (TSPTW for short) as a quadratic unconstrained binary optimization (QUBO) problem. The time windows impose time constraints that a feasible solution must satisfy. These take the form of inequality constraints, which are known to be particularly difficult to articulate within the QUBO framework. This is, we believe, the first time this major obstacle is overcome and the TSPTW is cast in the QUBO formulation. We have every reason to anticipate that this development will lead to the actual execution of small scale TSPTW instances on the D-Wave platform.
Highlights
Quantum computing promotes the exploit of quantum-mechanical principles for computation purposes
TSP with Time Windows (TSPTW) has been investigated in its classical form, no work is known to us that studies this problem within the quadratic unconstrained binary optimization (QUBO) framework, using the D-Wave platform, or even quantum annealing in general
In the case of the TSPTW, we have discovered it to be more advantageous to use binary variables parameterized by three integers: u, v and i
Summary
Quantum computing promotes the exploit of quantum-mechanical principles for computation purposes. The open-source software qbsolv that D-Wave introduced in is aimed at tackling QUBO problems of higher scale than previous attempts, by utilizing a more complex graph structure with higher connectivity among QPUs, by partitioning the input into parts that are independently solved. This process is repeated using a Tabu-based search until no further improvement is found [20,34]. TSPTW has been investigated in its classical form, no work is known to us that studies this problem within the QUBO framework, using the D-Wave platform, or even quantum annealing in general.
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