An Online Learning-Based mACO Approach for Hot Rolling Scheduling Problems Involving Dynamic Order Arrivals

The hot rolling scheduling problem involving dynamic order arrivals (HRSP-DOA) is pivotal in promoting Industry 4.0 initiatives in steel companies. This paper introduces a novel multi-objective ant colony optimization (mACO) algorithm enhanced with online learning strategies to address the HRSP-DOA. The problem is formulated as a variant of the prize-collecting dynamic vehicle routing problem (PC-DVRP). Its primary mission is to select high-reward orders to form a set of rolling rounds and sequence them within each rolling round to satisfy various technical constraints, thereby minimizing penalty costs and maximizing collected prizes. As new orders arrive, the problem’ s decision and objective spaces undergo unexpected changes, requiring the algorithm to make a quick response. To address these challenges, we propose an mACO with multiple heuristic matrices to search for the Pareto optimal set (POS) for the HRSP-DOA. Furthermore, we introduce the following online learning strategies to enhance mACO’s performance: 1) the upper confidence bound (UCB1) algorithm for selecting the most promising heuristic matrix, which is analogous to a multi-armed bandit problem; and 2) the K-means clustering method for transferring pheromone knowledge from the current event time to the following one. The well-designed comparative tests demonstrate that the proposed approach outperforms state-of-the-art algorithms on all synthetic instances. Component analysis further validates the effectiveness of the proposed online learning mechanisms. Finally, we present a real-world case study from an iron and steel company to verify its applicability. Note to Practitioners—In the context of Industry 4.0, the hot rolling scheduling problem involving dynamic order arrivals (HRSP-DOA) is pivotal for smart steel manufacturing, and it is formulated as a variant of the prize-collecting dynamic vehicle routing problem (PC-DVRP). By leveraging problem-specific properties, this paper develops a multi-objective ant colony optimization (mACO) algorithm with multiple heuristic matrices to address the challenges posed by changes in both decision-making and objective spaces caused by dynamic order arrivals. We also introduce two online learning strategies to enhance search efficiency: 1) the upper confidence bound (UCB1) algorithm for selecting the most promising heuristic matrix; and 2) the K-means clustering method for transferring pheromone knowledge in dynamic environments. The effectiveness of the proposed approach is validated through computational experiments. Furthermore, our dynamic multi-objective optimization algorithm can be implemented in real-world decision support systems and applied to other variants of the DVRP.