  Combinatorial optimization is of general interest for both theoretical study
and real-world applications. Fast-developing quantum algorithms provide a
different perspective on solving combinatorial optimization problems. In this
paper, we propose a quantum-inspired tensor-network-based algorithm for general
locally constrained combinatorial optimization problems. Our algorithm
constructs a Hamiltonian for the problem of interest, effectively mapping it to
a quantum problem, then encodes the constraints directly into a tensor network
state and solves the optimal solution by evolving the system to the ground
state of the Hamiltonian. We demonstrate our algorithm with the open-pit mining
problem, which results in a quadratic asymptotic time complexity. Our numerical
results show the effectiveness of this construction and potential applications
in further studies for general combinatorial optimization problems.
