Imitation Learning-Guided Evolution for Energy-Aware Flexible Job Shop Scheduling Problem with AGVs

Research on flexible job-shop scheduling has often followed the same path: define the machines, specify the jobs, and let the models decide how tasks should be sequenced. That formula worked reasonably well when material handling was either manual or so abundant that transport delays could be ignored. The reality inside contemporary factories is very different. Many production lines now rely on a limited number of automated guided vehicles (AGVs) whose behavior—whether they are carrying loads, waiting idly, or racing between stations—introduces a second layer of decisions that interacts tightly with machine scheduling. At the same time, concerns about energy consumption have shifted from being a peripheral consideration to a core operational objective, especially as manufacturing systems operate under stricter environmental targets and rising electricity costs. These overlapping concerns create a scheduling problem where makespan and total energy consumption are structurally intertwined rather than parallel objectives.

Indeed, the flexible job-shop scheduling problem with AGVs (FJSP-AGV) has gained considerable attention, however, most existing approaches still emphasize throughput or treat energy in simplified ways. Many classical meta-heuristic algorithms, while powerful in principle, do not cope well with the immense combinatorial space generated when each operation may choose among several machines and each movement depends on AGV availability. Reinforcement-learning-based methods have begun to appear, yet common techniques such as Q-learning or deep Q-networks tend to struggle in this domain. Their learning processes are often too slow or too unstable when confronted with high-dimensional scheduling states, making them difficult to deploy in settings that require fast, reliable decision-making. To this end, new research paper published in IEEE Transactions on Evolutionary Computation and conducted by Weiyao Cheng, Associate Professor Leilei Meng, Associate Professor Biao Zhang, Assistant Professor Kaizhou Gao & Professor Hongyan Song from the Liaocheng University, the researchers developed a mixed-integer linear programming model that captures the full interaction between machine processing, AGV transport, and energy consumption, enabling the computation of exact Pareto-optimal schedules for smaller systems. They also introduced an imitation-learning-assisted multi-population evolutionary algorithm that learns from expert-like state–action pairs to refine its search behavior. This algorithm integrates specialized populations for makespan, energy, and fused knowledge, allowing it to navigate large scheduling spaces more effectively.

The research team evaluated the new methods with two parallel objectives: to confirm that the mixed-integer linear programming formulation yields reliable Pareto-optimal schedules and to determine whether the proposed imitation-learning-assisted evolutionary algorithm can outperform established heuristics and its own ablated variants. Their experimental design reflects this dual focus. For the exact model, they employed a series of benchmark instances drawn from the traditional flexible job-shop literature and augmented them with appropriate energy parameters for machines and AGVs. By gradually adjusting the upper bound of the makespan through an epsilon-constraint strategy, they generated a collection of schedules that map out the core trade-off between production speed and energy consumption. The authors found the resulting solutions behaved in a manner one would expect from a well-posed multi-objective optimization framework: tighter makespan requirements tend to force more hurried machine assignments and more frequent AGV dispatching, leading to larger idle and transportation energy usage, whereas a relaxed makespan threshold permits more controlled, energy-efficient sequencing. The consistency of these patterns across instances gave strong evidence that the model captures the essential structure of the energy-aware scheduling problem.

Moreover, the evaluation of the imitation-learning-assisted evolutionary algorithm required a broader set of comparisons. The authors confronted it with three simplified variants—each missing one of the population components—as well as conventional methods frequently used for multi-objective scheduling. These comparisons were carried out over a suite of twenty benchmark problems, chosen to reflect a range of job counts, machine configurations, and transport complexities. In every case, the algorithms were run under identical stopping conditions to prevent any unfair advantage.

The team observed that in the multi-population framework, even before the imitation learning component is added, already displays stronger exploratory capacity than its reduced versions. The three populations, oriented toward makespan, energy, and fused knowledge respectively, appear to complement one another: one tends to push the search toward rapid scheduling, another toward energy conservation, and the third toward combinations that balance both. When imitation learning is introduced, the behavior of the algorithm changes noticeably. Instead of relying solely on evolutionary variation, the algorithm starts to apply search operators in a manner influenced by previously learned patterns. These operators guide the refinement of promising solutions more deliberately, often enabling the method to recover high-quality trade-offs that other heuristics overlook. Over many runs, the algorithm consistently produced more complete and better-shaped Pareto fronts, indicating that the learned policies successfully enhance the algorithm’s ability to navigate complex scheduling landscapes.

In conclusion, Liaocheng University scientists successfully developed new methods that offer both theoretical precision and practical scalability for energy-efficient AGV-based job-shop scheduling. The significance of this work lies in how it reframes a long-standing scheduling problem through the lens of energy-aware manufacturing and intelligent algorithmic design. Flexible job-shop systems with AGV-based transport have become increasingly common, yet the tools available to schedule them still tend to emphasize either throughput or machine utilization. The authors argue, and convincingly demonstrate, that this perspective is no longer adequate. In settings where every idle interval consumes measurable energy and each loaded AGV trip carries distinct power costs, schedules must be built with a more nuanced view of operational trade-offs. Their exact model provides a way to articulate these trade-offs with mathematical clarity, allowing researchers and practitioners to see how production speed and energy use move in opposite directions as constraints change. This alone is valuable, as few existing models offer such transparency.

The broader contribution, however, emerges from the imitation-learning-assisted evolutionary algorithm. It embodies a shift toward optimization methods that do not explore solution spaces but internalize behavioral regularities found in expert-like decisions. Rather than forcing the learning mechanism to discover good behavior through extended trial-and-error interactions with an environment, the imitation-learning strategy allows the algorithm to absorb meaningful search patterns at the outset. Once trained, the model intervenes during the cooperative search phase, recommending operators likely to produce constructive modifications. This mechanism enriches the search with a form of learned intuition—an ability to recognize when a solution resembles earlier ones and to act accordingly. There are many implications for the study. For instance: manufacturing systems evolve, new machines replace old ones, and AGV fleets change in size or capability. A purely hand-crafted heuristic can struggle to adapt to these shifts, whereas a learning-guided evolutionary algorithm can be retrained or updated with relative ease. Moreover, the multi-population structure offers a natural framework for incorporating additional objectives, such as maintenance costs or real-time disturbance handling, without dismantling the core algorithmic design. The method could also influence the development of hybrid human–machine scheduling systems in which operators collaborate with algorithms that have absorbed expert decision patterns. In essence, the study demonstrates that the intersection of imitation learning and evolutionary search is a promising direction for optimization in complex industrial environments. The authors provided both the concept and application tool for addressing energy-efficient scheduling in AGV-driven production systems by blending exact modeling with adaptive heuristic intelligence.