Finite Potential Game Heuristic Algorithm for Workload Allocation in Dual-Gantry Placement Machines

Dual-gantry surface mount optimization effectively improves the productivity of printed circuit board assembly (PCBA), but also brings new challenges. Optimizing workload allocation to balance the front and rear gantry placement completion time is a significant challenge for improving PCBA productivity. This study proposes a finite potential game heuristic algorithm (FPGHA) to solve the workload allocation problem. The algorithm generates game agents by analyzing the feeding characteristics of the dual-gantry placement machine and using an improved bisection K-means clustering method. Agent utility is calculated based on metrics affecting productivity of the pick-and-place process, including the number of simultaneous pickups, nozzle changes, cycles, and mounting points. Nash equilibrium of FPGHA is obtained by a best-response dynamics and heuristic algorithm. Then, the effectiveness of FPGHA in solving the workload allocation problem is first demonstrated in simulated experiments with different nozzle and feeder configurations. Finally, FPGHA is compared with the hierarchical restricted balance algorithm, adaptive clustering algorithm, and the popular industrial optimizer software in actual placement experiments using real-world industrial printed circuit boards. The effectiveness and accuracy of FPGHA are verified by analyzing the correlation between three variables: The FPGHA estimated value, the actual assembly value, and the PCB assembly time.