A knowledge-based NSGA-II algorithm for multi-objective hot rolling production scheduling under flexible time-of-use electricity pricing

With the increasing demand and shortage of energy, the iron and steel industry has focused on achieving low-carbon and smart manufacturing. This study investigates an energy-oriented scheduling problem arising from hot rolling production under flexible time-of-use (TOU) electricity tariffs, where the electric power comes from both the enterprise-owned power plant and the state-owned power grid. First, we model the studied scheduling problem as a multi-objective prize-collecting vehicle routing problem with special constraints. This model selects slabs from the order pool and sequences them to form rolling units, aiming to simultaneously minimize the transition costs in specifications, penalty costs, and electricity costs. Next, we develop a knowledge-based NSGA-II algorithm (KB-NSGA-II) by introducing a self-adaptive recombination procedure and a shortest path search (SPS)-based local intensification procedure. Furthermore, the comparative experimental results indicate that the KB-NSGA-II outperforms other competing algorithms in terms of the following indicators: (1) the hypervolume indicator is improved by approximately 57%; (2) the Spacing indicator is decreased by approximately 40%; and (3) the success ratio indicator of KB-NSGA-II is at least 60% higher than that of other competing algorithms. Finally, we apply a multi-criteria decision-making method named VIKOR to a case study under flexible TOU pricing strategies. These comparison results and the case study confirm that the KB-NSGA-II algorithm obtained better computational performance than the other competing algorithms and provided more flexible solutions under TOU pricing.