Efficient Random-Keys PSO for Industrial Inspection Scheduling with Shared Robot Constraints

In practical inspection lines, throughput is often constrained by the interaction between test stations and a shared robot rather than by station processing times alone. The line considered in this paper contains two parallel detection benches for tray jobs and a two-stage rotary line for rotary-part jobs. In addition, the released task list begins with an urgent block that must stay unchanged, so only the remaining suffix is available for resequencing. To handle this setting, we combine an event-driven simulator with particle swarm optimization (PSO). The simulator tracks robot send, transfer, and return actions explicitly, and it keeps Rotary 2 occupied until the corresponding return action is finished. The PSO search is carried out on a random-keys encoding of the non-urgent suffix, which preserves the urgentprefix rule by construction. On the studied instance, the best schedule produced by the proposed method reduces makespan from 80,211.99 s under FIFO to 41,775.83 s, i.e., by 47.92%, while also increasing robot utilization and lowering average waiting time. The results show that a lightweight simulation-based PSO can produce effective schedules for inspection lines with coupled robot and blocking constraints.