Skip to main content
SpringerLink
Log in

A Route Optimization Problem in Electrical PCB Inspections: Pickup and Delivery TSP-Based Formulation

  • Conference paper
  • First Online:
Transactions on Engineering Technologies

  • 509 Accesses

Abstract

This paper discusses a new route optimization for inspecting printed circuit boards (PCBs). In inspections of PCBs, a number of PCBs arrayed on a plane are tested by a probe in some order or sequence. Since the length of an inspection route depends on the order or sequence that the probe visits and tests each of PCBs, the finding of best visiting order or sequence is quite important in order to reduce the PCB inspection time. Recently, due to the miniaturization of PCBs, the procedure of “alignment” has become necessary before the electrical test, which means that there is a precedence constraint between alignment and test. This paper models a PCB inspection route optimization problem with alignment operations as a class of pickup and delivery traveling salesman problem (PDTSP) which is a mixed 0–1 integer programming problem. An efficient heuristic algorithm is proposed to solve the problem with a practical computational time. The proposed algorithm is installed into real PCB inspection machines that have been widely used in the world. Cost reduction effects for PCB inspection factories are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Altinkemer K, Kazaz B, Koksalan M, Moskowitz H (2000) Optimization of printed circuit board manufacturing: integrated modeling and algorithms. Eur J Oper Res 124(2):409–421

    Article  MATH  Google Scholar 

  2. Ancău M (2008) The optimization of printed circuit board manufacturing by improving the drilling process productivity. Comput Ind Eng 55(2):279–294

    Google Scholar 

  3. Crama Y, van de Klundertb J, Spieksmab FCR (2002) Production planning problems in printed circuit board assembly. Discrete Appl Math 123(1–3):339–361

    Google Scholar 

  4. Croes GA (1958) A method for solving traveling salesman problems. Oper Res 6(6):791–812

    Article  MathSciNet  Google Scholar 

  5. Dumitrescu I, Ropke S, Cordeau J-F, Laporte G (2010) The traveling salesman problem with pickup and delivery: polyhedral results and a branch-and-cut algorithm. Math Program 121(2):269–305

    Google Scholar 

  6. Helsgaun K (2000) An effective implementation of the Lin-Kernighan traveling salesman heuristic. Euro J Oper Res 126(1):106–130

    Google Scholar 

  7. Kahng AB, Robins G, Walkup EA (1995) Optimal algorithms for substrate testing in multi-chip modules. Int J High Speed Electron Syst 6(4):595–612

    Google Scholar 

  8. Katagiri H, Guo Q, Wu H, Hamori H, Kato K (2015) Path optimization for electrically inspecting printed circuit boards with alignment marks. Lecture notes in engineering and computer science: proceedings of the international multiconference of engineering and computer scientist 2015, pp 979–984

    Google Scholar 

  9. Katagiria H, Qingqiang G, Bin W, Muranakaa T, Hamori H, Kato K (2015) Path optimization for electrical PCB inspections with alignment operations using multiple cameras. Procedia Comput Sci 60:1051–1060

    Article  Google Scholar 

  10. Kumar R, Li H (1995) Integer programming approach to printed circuit board assembly time optimization. IEEE Trans Compon Packag Manuf Technol Part B: Adv Packag 18(4):720–727

    Google Scholar 

  11. Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling-salesman program. Oper Res 21(2):498–516

    Google Scholar 

  12. Murakami K (2013) Formulation and heuristic algorithms for multi-chip module substrate testing. Comput Electr Eng 39(4):1049–1060

    Article  Google Scholar 

  13. OR I (1976) Traveling salesman-type combinatorial problems and their relation to the logistics of regional blood banking. Ph.D. Thesis, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL

    Google Scholar 

  14. Psaraftis HN (1983) k-interchange procedures for local search in a precedence-constrained routing problem. Euro J Oper Res 13(4):391–402

    Google Scholar 

  15. Renaud J, Boctor FF, Laporte G (2002) Perturbation heuristics for the pickup and delivery traveling salesman problem. Comput Oper Res 29(9):1129–1141

    Article  MATH  Google Scholar 

  16. Sarin SC, Sherali HD, Bhootra A (2005) New tighter polynomial length formulations for the asymmetric traveling salesman problem with and without precedence constraints. Oper Res Lett 33(1):62–70

    Article  MathSciNet  MATH  Google Scholar 

  17. Sherali HD, Sarin SC, Tsai P-F (2006) A class of lifted path and flow-based formulation for the asymmetric traveling salesman problem with and without precedence constraints. Discrete Optim 3(1):20–32

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Engineering, Hiroshima University, Hiroshima, Japan

    Hideki Katagiri & Hongwei Wu

  2. Ericsson, Beijing, China

    Qingqiang Guo

  3. OHT Inc., Fukuyama, Japan

    Hiroshi Hamori

  4. Hiroshima Institute of Technology, Hiroshima, Japan

    Kosuke Kato

Authors
  1. Hideki Katagiri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qingqiang Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongwei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hiroshi Hamori
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Kosuke Kato
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hideki Katagiri .

Editor information

Editors and Affiliations

  1. Multimedia Engineering, Mokpo National University, Mokpo, Cholla-namdo, Korea (Republic of)

    Gi-Chul Yang

  2. Unit 1, 1F, International Association of Engineers, Hong Kong, Hong Kong

    Sio-Iong Ao

  3. University of Canberra, Canberra, Aust Capital Terr, Australia

    Xu Huang

  4. Calzada Tecnologico s/n, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media Singapore

About this paper

Cite this paper

Katagiri, H., Guo, Q., Wu, H., Hamori, H., Kato, K. (2016). A Route Optimization Problem in Electrical PCB Inspections: Pickup and Delivery TSP-Based Formulation. In: Yang, GC., Ao, SI., Huang, X., Castillo, O. (eds) Transactions on Engineering Technologies. Springer, Singapore. https://doi.org/10.1007/978-981-10-0551-0_15

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-0551-0_15

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-0550-3

  • Online ISBN: 978-981-10-0551-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation