An enhanced cross-entropy algorithm for the green scheduling problem of steelmaking and continuous casting with uncertain processing time

Abstract

Under the mainstream trend of global carbon emission reduction, this paper studies an important steelmaking-continuous casting scheduling problem (SCCSP) considering the practical technological requirements in uncertain production environment. This problem can be modeled as the green SCCSP with uncertain processing time (GSCCSP_UPTHP), whose criteria are to minimize the maximum completion time, the average waiting time, and the carbon emissions simultaneously. An enhanced cross-entropy algorithm (ECEA) is proposed for addressing it. In terms of ECEA’s coding and decoding, a two-segment coding strategy and an adaptive decoding strategy are devised according to the problem’s characteristics. In ECEA’s global search, ECEA adopts two probability models with their own self-adjustment mechanisms to collaboratively learn the valuable information from excellent individuals and quickly guide the search to the promising regions. Moreover, the novel competition and assimilation mechanisms are devised to avoid ECEA falling into local optima early. In ECEA’s local search, a problem-dependent local search based on the key points (PDLS_KP) is proposed to sequentially execute the small neighborhood search (SNS) and the large neighborhood search (LNS) starting from the promising region of each selected key point. Meanwhile, a speed-up scanning method is developed to accelerate the search process of the LNS. Extensive experiments based on both the simulation and the real-world instances from an SCC process are constructed to show the effectiveness of TSOA in solving the GSCCSP_UPTHP.