A Flip-count-based Dynamic Temperature Control Method for Constrained Combinatorial Optimization by Parallel Annealing Algorithms

Annealing machines use an Ising model to represent combinatorial optimization problems (COPs) and minimize the energy of the model with spin-flip sequences. Pseudo temperature is a key hyperparameter to control the search performance of annealing machines. In general, the temperature is statically scheduled such that it is gradually decreased from a sufficiently high to a sufficiently low values. However, the search process during high and low temperatures in solving constrained COPs does not improve the solution quality as expected, which requires repeated preliminary annealing for pre-tuning. This paper proposes a flip-count-based dynamic temperature control (FDTC) method to make the preliminary annealing unnecessary. FDTC checks whether the current temperature is effective by evaluating the average number of flipped spins in a series of steps. The simulation results for traveling salesman problems and quadratic assignment problems demonstrate that FDTC can obtain comparable or higher solution quality than the static temperature scheduling pre-tuned for every COP.