A Two-Phase Soft Optimization Method for the Uncertain Scheduling Problem in the Steelmaking Industry

In this paper, an uncertain scheduling problem arising from the steelmaking-continuous casting (SCC) production system is investigated. For the practical SCC production system, it is difficult to obtain a schedule with better performance using traditional deterministic scheduling methods since there exists uncertainty in processing times. According to the analysis on characteristics of the uncertain SCC scheduling problem (SCCSP), we construct a soft-form schedule which includes slack ratios as characteristic indexes and the job sequence at the casting stage as key decision variables to cope with the uncertainty in processing times, and propose a two-phase soft optimization method to solve the uncertain SCCSP with the just-in-time and the waiting time objectives under the break probability. In the first phase, the continuous estimation distribution algorithm (EDA) with the ordinal optimization policy is proposed to optimize slack ratios under the chance constraint, in which the optimal computing budget allocation with constrained optimization is applied to reduce the computational burden. In the second phase, based on the above optimized characteristic indexes, the discrete EDA with a local search procedure is proposed to optimize the job sequence at the casting stage. Finally, computational experiments with various scales and noise levels are performed to validate the effectiveness of the proposed algorithm.