An adaptive sampling-estimation of distribution algorithm for robust scheduling in the steelmaking-continuous casting process

Uncertainty is an important feature of industrial systems, and it extensively exists in the steelmaking industry. This paper focuses on the uncertain scheduling problem arising from the steelmaking-continuous casting (SCC) process. Based on the Benders decomposition strategy, the SCC scheduling problem (SCCSP) is decomposed into two sub-problems: the machine allocation problem (MAP) and the timetabling problem (TTP). To solve the uncertain SCCSP with interval processing times, an estimation of distribution algorithm (EDA) combined with robust optimization (RO) is proposed. First, a novel EDA with multiple probabilistic models and adaptive sampling policy is developed to solve the MAP. Second, the RO approach with ellipsoidal sets is embedded in the EDA and used to solve the TTP. To verify the proposed algorithm, a number of instances are generated from real-world industrial data. The final simulation results show that the proposed algorithm is efficient and effective to solve the uncertain SCCSP with interval processing times.