  Quantum-inspired optimization (QIO) algorithms are computational techniques
that emulate certain quantum mechanical effects on a classical hardware to
tackle a class of optimization tasks. QIO methods have so far been employed to
solve various binary optimization problems and a significant (polynomial)
computational speedup over traditional techniques has also been reported. In
this work, we develop an algorithmic framework, called Perm-QIO, to tailor QIO
tools to directly solve an arbitrary optimization problem, where the domain of
the underlying cost function is defined over a permutation group. Such problems
are not naturally recastable to a binary optimization and, therefore, are not
necessarily within the scope of direct implementation of traditional QIO tools.
We demonstrate the efficacy of Perm-QIO in leveraging the structure of
cost-landscape to find high-quality solutions for a class of vehicle routing
problems that belong to the category of non-trivial combinatorial optimization
over the space of permutations.
