Efficient Traveling Salesman Problem Solvers using the Ising Model with Simulated Bifurcation

An Ising model-based solver has shown efficiency in obtaining suboptimal solutions for combinatorial optimization problems. As an NP-hard problem, the traveling salesman problem (TSP) plays an important role in various routing and scheduling applications. However, the execution speed and solution quality significantly deteriorate using a solver with simulated annealing (SA) due to the quadratically increasing number of spins and strong constraints placed on the spins. The ballistic simulated bifurcation (bSB) algorithm utilizes the signs of Kerr-nonlinear parametric oscillators' positions as the spins' states. It can update the states in parallel to alleviate the time explosion problem. In this paper, we propose an efficient method for solving TSPs by using the Ising model with bSB. Firstly, the TSP is mapped to an Ising model without external magnetic fields by introducing a redundant spin. Secondly, various evolution strategies for the introduced position and different dynamic configurations of the time step are considered to improve the efficiency in solving TSPs. The effectiveness is specifically discussed and evaluated by comparing the solution quality to SA. Experiments on benchmark datasets show that the proposed bSB-based TSP solvers offer superior performance in solution quality and achieve a significant speed up in runtime than recent SA-based ones.