Optimizing Heat Treatment Schedules via QUBO Formulation

Quadratic Unconstrained Binary Optimization (QUBO) is the problem of finding binary variable assignments that minimize a given quadratic objective function. Many combinatorial optimization problems can be transformed into equivalent QUBO formulations, and significant research efforts have been devoted to developing efficient QUBO solvers. This paper presents a method for converting a real-world, industrial-scale scheduling problem arising in the heat treatment process of metal parts into an equivalent QUBO formulation. In current operations, two experienced operators manually spend about two hours each day to create a 24 h schedule for two furnaces, considering various constraints and processing priorities. We have developed a C++-based scheduling system that automatically converts this problem into a QUBO instance and solves it using QUBO++, a high-performance toolkit we have recently developed and released. The experimental results on actual scheduling instances show that QUBO++ consistently produces high-quality solutions in a short time, leveraging the computational merits of the QUBO formulation. The system reduces the labor equivalent to two hours of expert work per day, indicating that automated scheduling via QUBO++ is a promising approach for improving efficiency and accuracy in factory operations.