Mapping Constrained Slot-Placement Problems to Ising Models and its Evaluations by an Ising Machine

Abstract

Ising machines have attracted attention, which is expected to obtain better solutions of various combinatorial optimization problems at high speed by mapping the problems to natural phenomena. A slot-placement problem is one of the combinatorial optimization problems, regarded as a quadratic assignment problem, which relates to the optimal logic-block placement in a digital circuit as well as optimal delivery planning. Here, we propose a mapping to the Ising model for solving a slot-placement problem with additional constraints, called a constrained slot-placement problem, where several item pairs must be placed within a given distance. Since the behavior of Ising machines is stochastic, the obtained solution does not always satisfy the slot-placement constraint, which is different from the conventional methods such as the conventional simulated annealing. To resolve the problem, we propose an interpretation method in which a feasible solution is generated by post-processing procedures. Using an Ising machine computer, feasible solutions could be obtained up to 50 times faster than the conventional simulated annealing without degrading accuracy for constrained slot-placement problems with 6 x 6 slots and 27 items at the maximum.