Simulation-Based Hierarchical Heuristic for Printed Circuit Board Assembly Optimization in a Spin-Head Surface Mounter ^†

Abstract

This article proposes a simulation-based hierarchical heuristic (SHH) method to optimize nozzle assignment, feeder assignment, and component sequencing in a single spin-head gantry type surface mounter. Spin-head surface mounters are widely used in assembling printed circuit boards (PCBs) for consumer electronics but present a challenging non-deterministic polynomial-time hard (NP-hard) problem. The SHH method introduces multiple heuristics for the three sub-problems and evaluates their combinations in the FlexSim simulation environment. Through case studies using industrial and artificial PCB samples, the optimal combination scheme is identified, demonstrating significant improvements in the operational efficiency. This research not only provides a novel solution for optimizing spin-head surface mounters but also contributes to operations research by addressing complex NP-hard problems.

1. Introduction

The production efficiency of surface mounters is crucial to the electronics manufacturing industry. Spin-head surface mounters, equipped with multiple nozzles working in coordination significantly enhance production speed and precision. Optimizing these machines involves the following three interdependent sub-problems: nozzle assignment, feeder assignment, and component sequencing, with each solution relying on the others [1]. However, a comprehensive approach to the optimization of spin-head surface mounters, addressing all three sub-problems simultaneously, remains a challenge. Spin-head surface mounters are widely used in assembling PCBs for consumer electronics, but their complex operations and the NP-hard nature of the problem make it difficult to achieve optimal efficiency [2]. Considering the significant impact on production speed and precision, it is crucial to develop effective optimization methods that can address the interdependencies of nozzle assignment, feeder assignment, and component sequencing.

Several studies have addressed various aspects of this optimization challenge. Seth et al. introduced a novel vehicle-routing algorithm to optimize component sequencing on collect-and-place machines [3]. Li et al. proposed the average Chebyshev linkage directed search for optimizing nozzle and feeder assignments in spin-head surface mounters (SSMs) [4]. Gao et al. presented a hierarchical multiobjective heuristic for optimizing printed circuit board assembly (PCBA) in single beam-head surface mounters [5]. Additionally, Hsu proposed a two-stage framework for hybrid approaches addressing component sequencing, feeder assignment, and nozzle assignment problems, highlighting the complexity and interdependence of these sub-problems [6].

This research introduces a simulation-based hierarchical heuristic (SHH) method aimed at addressing this challenge by incorporating multiple heuristics for nozzle assignment, feeder assignment, and component sequencing. The FlexSim simulation platform plays a crucial role in this study by providing a dynamic and detailed environment to model and test various heuristic combinations [7]. FlexSim enables the visualization and analysis of complex interactions within the surface mounter operations, facilitating the identification of the most effective strategies [8]. By validating different heuristic combinations across three stages on the FlexSim simulation platform, this study aims to identify the optimal heuristic combination to maximize efficiency. The effectiveness of the proposed SHH method is validated through extensive case studies involving both industrial and artificial PCB samples, showcasing significant improvements in the operational performance. This work not only provides a novel solution for optimizing spin-head surface mounters but also contributes to the broader field of operations research by addressing complex NP-hard problems.

2. Problem Formulation

Once the PCB is positioned, the pick-and-place (PAP) process begins [9]. The schematic diagram of the spin-head surface mounter studied in this paper is shown in Figure 1. The spindle is equipped with six vacuum nozzles, which can be replaced via an automatic nozzle changer (ANC). The spin-head picks components from the feeder, moves them to the camera, and then places them on the PCB, repeating this process until all the components are placed. Feeders are supplied by feeder slots, and components can only be picked and placed by the corresponding type of nozzle.

Assuming a high-volume production environment where only one type of PCB is assembled, all experiments are conducted in a consistent simulation environment with identical machine speed, acceleration, deceleration, and other parameters. This setup ensures a controlled environment for optimizing the pick-and-place process, focusing on the efficient assignment and sequencing of nozzles and feeders to minimize the total assembly time. The goal is to minimize the total processing. The assumptions for this study include the following:

• Each placement operation by the nozzle head is successful on the first attempt.
• The time required for picking and placing components is constant.
• Each component type requires only one feeder, which is assigned to a single feeder slot.

2.1. Flow of the SHH Algorithm

The SHH algorithm is designed to optimize the operations of a single spin-head gantry type surface mounter through the following structured, three-stage process: nozzle assignment heuristic, feeder assignment heuristic, and component sequencing heuristic. Within the FlexSim simulation environment, various heuristic combinations are rigorously tested until all the combinations have been evaluated, leading to the identification of the optimal solution. The detailed flow of the algorithm is illustrated in Figure 2. The comprehensive SHH algorithm operates as follows:

• Nozzle Assignment: The nozzle types for each PAP cycle are determined using the selected nozzle assignment heuristic.
• Feeder Assignment: Feeders for the various components are assigned to specific feeder slots using the selected feeder assignment heuristic.
• Component Sequencing: The placement sequence for components is established based on the determined nozzle types and the selected component sequencing heuristic.

Through the systematic testing and evaluation of different heuristic combinations within the FlexSim simulation environment, the SHH algorithm is capable of identifying the optimal combination that minimizes total assembly time. This structured approach not only enhances the efficiency and effectiveness of the pick-and-place process but also contributes significantly to the broader field of operations research by addressing complex NP-hard problems.

2.2. Internal Logic Description of the FlexSim Model

The internal logic of the FlexSim model initiates with the generation of components based on order specifications. Each component is tagged with detailed information as follows: index, type, assembly X-coordinate, assembly Y-coordinate, and assembly status. Additionally, the model initializes a PCB of specified sizes to prepare for the assembly process.

The model employs three selected heuristic rules for nozzle assignment, feeder assignment, and component sequencing, which guide the creation of three critical distribution tables:

• Nozzle Assignment Table: Documents the nozzle types for each PAP cycle.
• Feeder Assignment Table: Allocates feeder slots for each component type.
• Component Assignment Table: Specifies components to be picked and placed in each PAP cycle.

Components are dispatched to their designated feeder slots according to the feeder assignment table, and a PCB is sent to the conveyor belt at specified positions. For each PAP cycle, the system evaluates the need for nozzle changes based on the nozzle assignment table. If nozzle changes are required, the head moves to the automatic nozzle changer (ANC) to replace the necessary nozzles, with the time calculated based on the number of nozzles changed. Following this, the head retrieves components from the feeder slots as per the component assignment table, moves to the fixed camera for visual positioning and inspection, and places the components on the PCB. This cycle repeats until all the components are placed, continuing until all PCBs are fully assembled. The internal logic flowchart of the FlexSim model is shown in Figure 3.

The primary goal is to minimize the total assembly time, facilitated by maintaining consistent machine speed, acceleration, and deceleration in the simulation environment. This detailed flow ensures efficient and precise component placement, optimizing the entire process through the selected heuristic rules.

2.3. Nozzle Assignment Heuristic

The reasonable assignment of nozzles is crucial for maximizing the efficiency of the PAP process. Although the ANC can automatically change nozzles, this process is time-consuming. Therefore, optimizing nozzle allocation is essential. This paper proposes two heuristics for nozzle assignment based on component demand frequency and nozzle versatility, as shown in Figure 4.

1. Excess Workload Priority Heuristic (EWPH): Arrange the workloads of different types of nozzles in descending order and calculate the minimum PAP cycle count. Allocate portions that exceed the minimum PAP cycle count and nozzle count, prioritizing larger volumes and addressing greater shortages first.

2. Ascending Workload Balance Heuristic (AWBH): Arrange the workloads of different types of nozzles in ascending order. Start from the left and select the largest possible overall workload, then move to the next column and choose a workload equal to the previous column. If the demand for the current cycle is not met by the last column, balance the shortage starting from the last column. After allocation, swap blocks within the same row to maximize the number of identical tasks in the same column.

2.4. Feeder Assignment Heuristic

In the production process of the placement machine, optimizing the allocation of feeders is crucial for improving overall production efficiency. The feeder allocation needs to be based on workload and placement position to ensure that components are delivered accurately and quickly. This paper proposes three feeder assignment heuristics, as shown in Figure 5.

1. Camera Proximity by Workload Heuristic (CPWH): Arrange the feeders in descending order of workload, then allocate them to positions close to the fixed camera. By arranging feeders with the highest workload closest to the fixed camera, the heuristic ensures that components requiring frequent placement are positioned nearest to the inspection point, thereby reducing the time spent on non-productive movements.

2. PCB Proximity by Workload Heuristic (PPWH): Feeders are organized in descending order of workload and then allocated starting from the centerline of the PCB and expanding outwards to both sides. PPWH aims to reduce the head’s travel distance after the components are placed and there is more space available for placing components.

3. Mean X-Coordinate Sorting Heuristic (MXSH): Calculate the average X coordinate value for each type of component, reorder the feeder slots based on these averages, and allocate them starting from the leftmost feeder slot. The MXSH heuristic focuses on spatial efficiency by aligning feeders based on the average X-coordinates of the components they hold.

2.5. Component Sequencing Heuristic

Optimizing the component placement sequence is crucial for improving production efficiency in the placement process of the placement machine. This paper proposes two component sequencing heuristic, as shown in Figure 6.

1. Chebyshev Proximity Heuristic (CPH): Among the components matching the nozzle type, the first nozzle selects the unassigned component with the smallest Chebyshev distance from the bottom left corner for placement. The second nozzle uses the coordinates of the first nozzle’s selection as a reference and selects the component with the smallest Chebyshev distance from that point. This process ensures that each subsequent selection is the closest possible component, thereby minimizing head travel distance.

2. Leftmost Unallocated Component Heuristic (LUCH): Among the components matching the nozzle type, the unassigned component with the smallest x-coordinate is selected for placement. Since the fixed camera is located in the bottom left corner, choosing the leftmost component minimizes the distance to the PCB, resulting in a more efficient component processing sequence.

Each heuristic targets specific aspects of the component placement process. CPH focuses on minimizing the travel distance of the placement head by selecting components based on Chebyshev proximity, while LUCH aims at reducing the distance to the PCB by selecting the leftmost component. These heuristics contribute to a high-speed, precise assembly process, significantly improving the operational performance of the placement machine.

3. Numerical Example and Analysis

3.1. Parameters Setting

The machine parameters include a head movement speed of 100 mm/s and a component placement time of 0.1 s. The PCB parameters include the number of components n, the number of component types t, the size of the PCB s, and the number of PCB m. For the small, medium, and large scales, 10 random instances are generated. Each set of experiments involves processing m identical PCBs, and the total processing time is recorded. The problem instances and the range of experimental parameters are shown in

Table 1. Experimental problem scale and parameter range.

Size	n	t	s	m
Small	50	20	100 mm × 100 mm	300
Medium	100	30	150 mm × 150 mm	600
Large	150	40	200 mm × 200 mm	900

. All simulations are conducted on a PC, 8 GB of RAM, and a 3.2 GHz processor, using FlexSim 2020.

3.2. Computational Experiments and Discussion

The results of the computational experiments are summarized in

Table 2. The performance of combination experiment.

Size	1-1-1	1-1-2	1-2-1	1-2-2	1-3-1	1-3-2	2-1-1	2-1-2	2-2-1	2-2-2	2-3-1	2-3-2
Small	3732.44	3942.51	3617.64	3683.86	4161.92	4059.87	3631.43	3893.89	3511.14	3568.18	4220.43	3941.98
Medium	15,078.91	15,903.61	14,394.14	14,603.26	16,715.27	16,312.09	14,439.79	15,577.78	13,782.33	14,460.59	16,630.09	15,841.61
Large	33,730.38	35,421.56	31,716.34	32,808.15	37,629.19	36,472.18	32,367.56	34,734.36	31,278.73	32,212.12	37,520.78	35,739.41

. Each combination experiment is denoted by a three-part identifier, where the numbers represent the selected heuristic index according to the order of introduction for each stage in this paper. From the data, it is evident that the 2-2-1 combination (Ascending Workload Balance Heuristic—PCB Proximity by Workload Heuristic—Chebyshev Proximity Heuristic) consistently outperforms other combinations across all scales. This combination demonstrates high adaptability and stability, making it the most effective for minimizing total processing time. Conversely, the 2-3-1 combination (Ascending Workload Balance Heuristic—Mean X-Coordinate Sorting Heuristic—Chebyshev Proximity Heuristic) showed the poorest performance, highlighting its inefficiency in comparison.

The superior performance of the 2-2-1 combination can be attributed to its balanced approach to workload distribution and efficient component placement strategy, which minimizes the distance traveled and optimizes processing sequences. This makes the 2-2-1 combination particularly suitable for practical applications where maximizing efficiency is critical. Therefore, it is recommended to prioritize the 2-2-1 heuristic combination in practical applications to achieve optimal results in the PCB assembly processes.

4. Conclusions

In this study, we proposed a simulation-based hierarchical heuristic (SHH) method to optimize the operations of a single spin-head gantry type surface mounter. The experimental results demonstrated that the SHH method effectively identifies optimal combinations, leading to enhanced operational efficiency. This research not only introduces a novel optimization approach for spin-head surface mounters but also provides valuable insights applicable to similar complex manufacturing systems. Future work could explore using these heuristic rules as actions in multi-agent deep reinforcement learning frameworks, further refining and enhancing optimization strategies.