Integrated Spatial–Temporal Scheduling for Aerospace Composite Autoclave Molding

Aerospace composite manufacturing involves several connected production stages, including material preparation, lay-up, curing, demolding, and finishing. During autoclave molding, several composite parts are cured together under controlled temperature and pressure. As production demand grows, limited autoclave capacity can become a bottleneck and delay production. Scheduling involves more than deciding the order of jobs. It also requires determining which parts should be grouped in the same batch, when each batch should start, and whether the parts can physically fit inside the autoclave. Autoclave molding can be treated as a batch-processing scheduling problem. A single curing cycle may contain several non-identical jobs, and its duration is determined by the longest processing time among the jobs assigned to it. Scheduling is also harder because the parts have different shapes and sizes. Traditional models often treat machine capacity as one-dimensional, but both the autoclave and the parts take up two-dimensional space.  Jobs assigned to the same batch must remain within the platform boundaries, cannot overlap, and may need to be rotated to obtain a feasible arrangement. Batch scheduling must consider both which parts are grouped together and how they are placed inside the autoclave. Production timing is also important. Each job becomes available only after the previous manufacturing step is finished, and it must enter the autoclave within a set time. If it waits too long, the material may be wasted. The schedule must consider when each job is ready, how long it can wait, and which jobs can be processed together. Earlier models considered two-dimensional packing, but usually did not combine it with job release dates and time windows. Combining these requirements makes scheduling harder because changing one job can affect the entire batch and the batches that follow.

In a recently published research paper in Engineering Optimization, Dr. Huifen Xu and Professor Naiming Xie from Nanjing University of Aeronautics and Astronautics addressed this coupled scheduling problem by developing an SBPM-RDTW model and a corresponding extended whale optimization algorithm, EWOA-BFIP. The new model treats the autoclave platform and each job as rectangles. Jobs are grouped into batches and arranged so that they fit inside the autoclave without overlapping; each job can also be rotated by 90°. The batches are then processed one after another without interruption. A batch takes as long as the slowest job in it, and it must start at a time that satisfies the release dates and latest allowed start times of all included jobs. The goal is to minimize the time needed to complete all batches.

EWOA-BFIP uses an improved best-fit method to create feasible starting solutions. Jobs are ordered by their release dates and, when they share the same release date, by their latest allowed start times. A skyline-based packing method then places the jobs into available spaces, allowing rotation when needed. This gives the algorithm starting schedules that already account for both timing and two-dimensional space. For larger problems with strict time limits, this method generated feasible starting populations more reliably than random initialization. Lévy-flight steps are used in the shrinking-encircling and prey-search stages to improve exploration of the solution space. Their combination of short steps and occasional longer jumps helps the algorithm search more widely. An annealing search is also applied to the highest-ranked 10% of solutions to improve local refinement. In this way, Lévy flight supports broader exploration, while annealing helps improve the most promising solutions.

Dr. Huifen Xu and Professor Naiming Xie evaluated algorithm across eight problem types and 32 benchmark instances, with comparisons against genetic algorithm, particle swarm optimization, biogeography-based optimization, and conventional whale optimization variants using the same best-fit initialization. Additional tests isolated the contributions of Lévy flight and annealing. Both modifications improved WOA-BFIP, and their combination produced the strongest solution quality across the tested variants. Across the broader benchmark set, EWOA-BFIP achieved the best average values in 28 of 32 instances and the best optimal values in 19. Statistical comparisons also supported the performance difference, with EWOA-BFIP receiving the lowest Friedman average rank and producing wins or draws against every baseline in the pairwise tests. A case supplied by an aerospace composite manufacturer provided a production-oriented assessment. It involved 115 jobs scheduled on a 12 m × 20 m autoclave. EWOA-BFIP achieved an average makespan of 116.66 compared with 122.16 for the next-best baseline result, and its best schedule reached 112. Its average relative percentage deviation was 4.16%, and autoclave space utilization reached 79.41%, the highest among the algorithms examined.

The scheduling approach is well suited to aerospace composite manufacturing facilities where limited autoclave capacity can restrict production. It allows production planners to consider batch composition, use of autoclave space, and processing time together. In this way, physical loading requirements can be coordinated with the allowed processing time for each part. Planning curing operations becomes more challenging when parts become available from the lay-up stage at different times. The schedule identifies which jobs are ready and which must wait before entering the autoclave. It can also give priority to jobs that are close to their latest allowed start time. This helps planners form batches that make good use of autoclave space while still meeting the timing requirements of each part.

The new method can also assist with autoclave capacity planning. The sensitivity analysis indicates that enlarging the available loading area improves scheduling performance only up to a certain machine-size threshold for a fixed job set; beyond that point, additional capacity provides little further reduction in makespan. Such behaviour gives manufacturing engineers a quantitative basis for examining whether greater autoclave capacity is likely to produce meaningful scheduling gains before considering larger equipment or changes in available loading space. The analysis also suggests that it can be useful to wait until enough jobs are available before starting a batch, rather than processing the first jobs immediately. This can help planners group compatible jobs more effectively and reduce the total time the autoclave is in use. Finally, the industrial case demonstrates how the approach can be applied to a substantial production order using actual part dimensions, processing times, release dates, and time windows. In that setting, the scheduling strategy produced shorter schedules together with higher utilization of the available autoclave area, supporting its use as a decision-support method for production sequencing and autoclave loading in aerospace composite manufacturing.