A soft encoding-based evolutionary algorithm for the steelmaking scheduling problem and its extension under energy thresholds

Steelmaking and continuous casting scheduling problem (SCCSP) is a classic optimization problem increasingly incorporating more constraints, such as energy-related ones. However, classic evolutionary algorithms with “rigid” encoding schemes face challenges in finding optimal solutions for heavily constrained SCCSPs. Motivated by this gap, this paper first extends the mathematical model of the classic SCCSP to its variant under energy thresholds (ET-SCCSP) from both single- and multi-objective optimization perspectives, and derives several problem-specific properties. Next, this paper develops a solving algorithm named the soft encoding-based evolutionary algorithm (SoEA), which uses a real-valued vector to encode a feasible solution for SCCSPs. Furthermore, SoEA introduces the following components: (1) a peak-cutting backward list scheduling (PC-BLS) procedure to decode a real-valued vector into a feasible solution, and (2) a local search procedure to enhance the algorithm’s performance. Comparative results in the computational experiment demonstrate that the SoEA with the propose encoding/decoding scheme: (1) achieves better performance than exact solver for small-scale instances under energy thresholds, (2) obtains promising results for medium-scale instances compared to other schemes, and (3) can be intensified by the tailored local search procedure. The proposed SoEA can also serve as a benchmark or tutorial for the development and evaluation of high-efficiency algorithms for other SCCSPs with heavy constraints. The source code is available on the GitHub repository: https://github.com/janason/Soft-Scheduling/tree/master/SoEA.