A Knowledge-Guided Co-Evolutionary Algorithm for Energy-Efficient Distributed Assembly Welding Shop Scheduling Problem

The growing trend toward decentralization within factories has brought attention to distributed welding shop scheduling problem (DWSP) among both practitioners and researchers. However, despite the prevalence of job-to-product assembly process in industrial fields, the investigation of distributed assembly welding shop scheduling problem (DAWSP) remains unexplored. Meanwhile, given the energy-intensive characteristic of welding operations, addressing energy consumption in welding shop is crucial for achieving environmental sustainability. Thus, this study investigates the energy-efficient DAWSP (EDAWSP), focusing on minimizing total energy consumption (TEC) and makespan. The proposed approaches include a mixed integer linear programming (MILP) model and a knowledge-guided co-evolutionary algorithm (KCEA). In KCEA, a knowledge coefficient is defined to build a bridge that connects the welding part and assembly part. By incorporating knowledge coefficient and weight-sum approach, an effective initialization strategy is proposed for producing a superior initial population. To effectively complete evolutionary process, a co-evolutionary operator is devised based on bi-population strategy. To improve KCEA’s exploitation capability, a local search is developed within the variable neighborhood search (VNS) framework, utilizing six critical-path-based neighborhood structures. Besides, an energy-saving strategy is presented to further minimize TEC without increasing makespan. Finally, a series of comparison experiments are executed. The experimental results illustrate that all improved components of KCEA contribute to its performance, and KCEA outperforms other six optimization algorithms in solving EDAWSP.