  This paper proposes a space-division multiplexed spatial-photonic Ising
machine (SDM-SPIM) that physically calculates the weighted sum of the Ising
Hamiltonians for individual components in a multi-component model.
Space-division multiplexing enables tuning a set of weight coefficients as an
optical parameter and obtaining the desired Ising Hamiltonian at a time. We
solved knapsack problems to verify the system's validity, demonstrating that
optical parameters impact the search property. We also investigated a new
dynamic coefficient search algorithm to enhance search performance. The
SDM-SPIM would physically calculate the Hamiltonian and a part of the
optimization with an electronics process.
