Multi-objective optimization for energy-aware job scheduling in industry 4.0

Energy-aware flexible job-shop scheduling is a key optimization problem in Industry 4.0 manufacturing, where machine assignment and operation sequencing jointly influence production efficiency, energy consumption, and resource utilization. This paper addresses a multi-objective flexible job-shop scheduling problem with heterogeneous machines, machine-operation compatibility, precedence constraints, non-preemptive processing, and machine-capacity limitations. A mixed-integer linear programming (MILP) model is developed to simultaneously minimize makespan, processing-related energy consumption, and machine workload imbalance. Workload imbalance is conceptually characterized by the standard deviation of machine utilization, while a linear absolute-deviation surrogate is used in the MILP to preserve model tractability. To efficiently solve large-scale instances, a two-phase hybrid optimization framework is proposed. In the first phase, an adaptive hyper-heuristic dynamically selects constructive, improvement, and perturbation heuristics while maintaining a non-dominated solution archive. In the second phase, selected archive solutions are refined using a normalized weighted-sum MILP formulation with warm-start initialization to improve solution quality and provide optimality-gap information. The warm-start solutions are provided as incumbent solutions rather than fixed decision variables, allowing the MILP to modify machine assignments, operation sequencing, and start times during refinement. The proposed framework is evaluated using industrial and synthetic flexible job-shop scheduling instances and compared with NSGA-II, MOEA/D, dispatching-rule heuristics, a standalone adaptive hyper-heuristic, and a single-objective MILP baseline. All methods are evaluated using the same objective definitions and final non-dominated filtering procedure. For the multi-objective methods, the final external archives are additionally evaluated using hypervolume (HV), inverted generational distance (IGD), and spacing. Experimental results demonstrate consistent improvements in both objective values and Pareto-front quality. Compared with NSGA-II, the proposed method reduces makespan by 4.3%, energy consumption by 8.1%, and workload imbalance by 8.0%, while improving hypervolume by 18.1% and reducing inverted generational distance by 63.4%. Relative to the best single-phase baseline, improvements reach 6.5%, 21.6%, and 13.4% for makespan, energy consumption, and workload imbalance, respectively. The Pareto-quality results further indicate improved convergence, coverage, and distribution of the obtained non-dominated solutions. Statistical analysis confirms that these improvements are significant. The proposed hybrid framework provides an effective and reproducible approach for balancing productivity, energy efficiency, and resource utilization in sustainable Industry 4.0 manufacturing systems.