Machine learning-embedded energy cost optimization for hybrid flow shop scheduling toward low-carbon industrial energy systems

Reducing energy consumption in industrial scheduling has become a critical concern for sustainable manufacturing. This paper addresses energy-aware scheduling in a multi-stage hybrid flow shop (HFS) system by proposing a novel framework that integrates bio-inspired metaheuristics with machine learning. Unlike traditional models that use static energy estimates, we train a supervised regression model (Random Forest) on real-world industrial data to dynamically predict job-machine energy consumption according to load assignment. This prediction is embedded into the cost evaluation phase under Algeria's realistic time-of-use block tariff structure. Three Metaheuristics are applied in optimization : Interior Search Algorithm (ISA), Slime Mould Algorithm (SMA), and Particle Swarm Optimization (PSO). Comparative experiments were conducted on benchmark-inspired instances, integrated with a Random Forest energy model trained on real-world steel industry data (R 2 about 0.944). Compared to a sample of serial-processing baseline, numerical results demonstrate that the proposed ML-enhanced algorithms significantly outperform schedules, achieving a monthly cost reduction of up to 80.14% on simulated 30 jobs two stage hybrid flow shop and a physical energy reduction of 28.8% using the Slime Mould Algorithm (SMA). This work highlights the potential of bio-inspired algorithms for green hybrid flow shop scheduling within electrical networks, contributing to enhanced operational efficiency, sustainability, and energy conservation in modern manufacturing environments. • Develops a hybrid optimization framework that embeds a machine learning-based energy predictor directly into metaheuristic scheduling for green hybrid flow shops. • Introduces tariff-aware scheduling under a realistic multi-block time-of-use electricity pricing structure, enabling economically optimal load shifting strategies. • Demonstrates that intelligent tariff exploitation yields significantly greater financial savings than pure physical energy reduction in industrial systems. • Provides a comprehensive comparative evaluation of ISA, PSO, and SMA, revealing distinct performance trade-offs between energy cost, makespan, and computational efficiency. • Establishes a decision-support methodology for low-carbon industrial production planning that bridges machine learning, bio-inspired optimization, and energy economics.