A Hybrid Multiobjective Memetic Algorithm for Energy-Efficient Scheduling of Distributed Heterogeneous Flow Shop With Economic Benefit Problem

Amid growing societal and technological demands, manufacturing enterprises face mounting challenges in balancing competitiveness with sustainability, where product quality has become a pivotal efficiency metric. This study addresses these challenges by formulating an original energy-efficient distributed heterogeneous flow shop scheduling problem with economic benefits (EDHFS-EB), which simultaneously optimizes makespan, total energy consumption (TEC), and job quality. To solve this complex problem, we propose a hybrid multiobjective memetic algorithm (HMOMA) that combines evolutionary search with problem-specific heuristics. The key contributions include the following. First, pioneering the distributed heterogeneous flow shop framework that integrates diverse permutation flow shops (PFSs) and hybrid flow shops (HFSs). Second, introducing the total quality rate (TQR) as an innovative economic indicator with dedicated optimization operators. Third, developing an image knowledge-based initialization heuristic to ensure solution diversity and quality. Finally, creating a decomposition-recombination strategy within an extended order crossover (EOX) framework to concurrently optimize factory assignment and job sequencing. Extensive experiments demonstrate HMOMA’s superior performance over existing methods, providing manufacturers with an effective tool for sustainable production planning.