Sustainable Scheduling of Distributed Flow Shop Group: A Collaborative Multi-Objective Evolutionary Algorithm Driven by Indicators

Sustainable scheduling within the manufacturing field has garnered substantial attention from both academia and industry. The escalating market demands have heightened requirements on the flexibility of production modes, multizone, and multiobjective. In this context, our study explores the intricacies of the multiobjective distributed flow shop group scheduling problem with sequence-dependent setup times, aiming to concurrently optimize makespan and total energy consumption $(\text {DF}_{m}| \mathrm {group},\text {sd}_{\mathrm {st}} |\#(C_{\max },\mathrm {TEC}))$ . First, a mathematical model is constructed to analyze problem characteristics. Subsequently, we introduce a collaborative multiobjective evolutionary algorithm driven by indicators (CMOEA/I). In CMOEA/I, an indicator-driven approach is proposed for solution selection, which approximates the Pareto front based on the convergence indicator, while screening potential solutions based on the spread indicator. Furthermore, a collaborative model and local search are developed by incorporating the intrinsic linkages of factories, groups, and jobs. Additionally, to further explore the potential nondominated solutions, a speed variation strategy is devised based on the pivots of decreasing speed to save energy and increasing speed to reduce makespan. An extensive set of simulation experiments is conducted on a diverse range of test instances. Through meticulous statistical analysis, the outcomes demonstrate that the CMOEA/I exhibits efficacy when contrasted with other advanced algorithms.