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Wet-process phosphoric acid production is energy-intensive, with tightly coupled reaction, filtration, and concentration stages linked through material-flow continuity and limited buffering. These dependencies make scheduling decisions directly affect throughput, inter-stage stability, and electricity use. This paper studies this setting as a hard discrete-time control and optimization problem, proposing a tri-objective scheduling framework that minimizes makespan, cumulative positive inter-stage waiting time, and total electricity consumption, treating productivity, energy use, and synchronization as coupled decision objectives rather than separate performance indicators. The solution strategy combines process-systems insight with an adaptive hybrid metaheuristic. A physics-informed Heuristic Priority Dynamic (HPD) rule produces feasibility- and balance-oriented initial sequences, improved through NSGA-II and an Adaptive Population-Based Search (APBS) scheme with cooperative subpopulations and adaptive diversification–intensification control. An exact MILP baseline on small instances and a DOE-based sensitivity analysis strengthen benchmarking and reproducibility. The framework is evaluated on a representative three-stage configuration with dedicated equipment and on seven designed instance classes capturing variability, heterogeneity, and bottlenecked loading. Results indicate that APBS delivers the most stable performance across challenging scenarios while maintaining superior synchronization and consistently low energy deviations, remaining effective as problem size grows where MILP becomes impractical. Although focused on phosphate processing, the formulation and algorithms extend to other energy-intensive manufacturing systems where synchronization losses and load-dependent energy behavior are central to safe and sustainable operation.
Mlaouah et al. (Thu,) studied this question.