印刷電路板（Printed Circuit Board, PCB）被稱為「電子工業之母」，在電子
產品中扮演不可或缺的角色。隨著上游的先進半導體技術的迅速發展，PCB 的種
類變得更加多樣，並逐漸趨向於客製化。隨著市場對客製化需求和聰明生產的不
斷增長，PCB 製造商正面臨著轉向少量多樣生產模式的挑戰，這帶來了高製造成
本和低生產效率的嚴峻問題。為了提高製造效率和靈活性，製造商需要長期不斷
地優化生產規劃和控制，以確保長期的盈利能力。
在繁瑣且複雜的製造流程中，鐳射鑽孔是關鍵的一環。這種製程需要使用高
價位的設備，並且需要大量的機台來配合生產。因此鐳射鑽孔機台對公司的資本
支出有著顯著的影響。這就突顯了鐳射加工的重要性。若能提高鐳射加工的效率，
就可以在更短的時間內完成更多的工作，從而減少對鐳射設備的需求，並降低資
本支出。鐳射加工是一種非接觸式的物質移除過程，利用高能量的鐳射束加熱融
化並最終移除材料，以形成預定的形狀或結構。由於其高精度和高重現性，使其
成為製作精密和複雜設計的 PCB 理想選擇。鐳射加工的效率和其選擇的加工路
徑有密切的關係。鐳射加工路徑是指鐳射在切割或鑽孔過程中的移動路徑，路徑
的選擇會直接影響加工時間、工件質量以及鐳射的磨耗。因此，本研究的目標為
優化鐳射加工路徑，透過研究和開發更有效的路徑選擇策略，提高加工效率，提
升產品質量，並減少鐳射的磨耗。此外這種路徑優化不僅可以提高生產效率，而
且還可以降低製造成本，進一步在產能規劃中降低對鐳射機台的需求。本研究以
台灣某著名 PCB 製造商為實證對象，驗證本研究之效度及效益。

Printed circuit boards (PCBs) plays an indispensable role in electronic industry.With the rapid development of advanced semiconductor technologies, the variety of PCB products has increasingly diverse, moving towards increasing customization. As
the market demand for customization continues to grow, PCB manufacturers are facing the challenge of shifting towards a production model that involves smaller quantities but greater diversity, leading to significant issues such as high manufacturing costs and low production efficiency. To enhance manufacturing efficiency and flexibility, manufacturers must continually optimize long-term production planning and control decisions to ensure sustainable profitability.
In the intricate and complex manufacturing process, laser drilling plays a pivotal role. This process requires the use of high-cost equipment and a substantial number of machines to support production, thereby significantly impacting the company's capital expenditure. This highlights the importance of laser drilling. Improving the efficiency of laser processing can result in accomplishing more tasks in a shorter time, reducing the demand for laser equipment, and lowering capital expenditures. Laser processing is a non-contact material removal process that utilizes a high-energy laser beam to heat and ultimately remove material to form predetermined shapes or structures. Due to its high precision and reproducibility, it is an ideal choice for fabricating precise and complex PCB designs. However, the efficiency and output of this process are still influenced by the laser processing path. The laser processing path refers to the movement path of the laser during cutting or drilling, and the choice of path directly affects processing time, workpiece quality, and laser wear. Therefore, the objective of this research is to optimize the laser processing path. Through the study and development of more effective path selection strategies, the study aims to enhance processing efficiency, improve product quality, and reduce laser wear. Additionally, this path optimization not only improves energy efficiency but also reduces the amount of purchasing laser machine, and further reduces manufacturing costs. This study uses a well-known PCB manufacturer in Taiwan as a case study to validate the effectiveness and benefits of the algorithm.

Table of Contents
Table of Contents i
Chapter 1 Introduction 1
1.1 Background 1
1.2 Motivation 1
1.3 Research Objectives 2
1.4 Thesis Organization 2
Chapter 2 Literature Review 3
2.1 Laser cutting problem 3
2.2 Traveling salesman problem 3
2.3 Application of TSP in laser drilling and cutting problem 4
Chapter 3 Research Framework 6
3.1 Research flow chart 6
3.2 Mathematical Model 6
3.3 2-opt Based Algorithm 8
3.3.1 Revised Kruskal's algorithm 9
3.3.2 2-Opt 9
3.4 Result 9
Chapter 4 Empirical Study 11
4.1 Experiment of small cases 11
4.2 Experiment of pratical cases 11
Chapter 5 Conclusion 14
5.1 Summary and contribution 14
5.2 Future research 14
References 15

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