Applying some polynomially solvable cases of the traveling salesman problem to the vehicle routing problem

2008 Fiscal Year Final Research Report

• Project/Area Number: 18740058
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Keio University
• Principal Investigator: ODA Yoshiaki Keio University, 理工学部, 講師 (90325043)
• Project Period (FY): 2006 – 2008
• Keywords: 組合せ論 / 離散数学 / アルゴリズム論 / 巡回セールスマン問題 / 計算量理論

Research Abstract

巡回セールスマン問題は与えられた複数の都市をすべて1回ずつ通り、出発点に戻ってくるような最短経路を見つける問題である。この問題は板の穴あけなど実社会の問題にも直結する有名な最適化問題の1つである。しかし、都市数が増えるにつれ、コンピュータを利用しても計算にかる時間が指数的に増大する。そこで、問題がどのような条件をみたしていれば、実用的な時間で解が得られるかという研究がなされてきた。研究では、この効率よく解ける状況を考察するとともに、巡回セールスマン問題におけるこれらの条件を車両配送問題に適用した場合に、最適がもつ構造を明らかにした。

Research Products

• [Journal Article] 3-trees with few vertices of degree 3 in circuit graphs (2009)
  • Author(s): Atsuhiro Nakamoto, Yoshiaki Oda, Katsuhiro Ota
  • Journal Title: Discrete Mathematics 309 Pages: 666-672
  • Peer Reviewed
• [Journal Article] The number of flips required to obtain non-crossing convex cycles (2008)
  • Author(s): Yoshiaki Oda, Mamoru Watanabe
  • Journal Title: Lecture Notes in Computer Science 4535 Pages: 155-165
  • Peer Reviewed
• [Journal Article] K6-minors in triangulations on the double torus (2007)
  • Author(s): Atsuhiro Nakamoto, Yoshiaki Oda, Katsuhiro Ota
  • Journal Title: Congressus Numerantium 188 Pages: 150-160
  • Peer Reviewed
• [Presentation] Demidenko conditions and the vehicle routing problem (2009)
  • Author(s): 小田芳彰
  • Organizer: 日本数学会2009年度年会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-27
• [Presentation] Demidenko conditions and the vehicle routing problem (2009)
  • Author(s): Yoshiaki Oda
  • Organizer: The 40th Southeastern International Conference on Combinatorics, Graph Theory and Computing
  • Place of Presentation: Florida Atlantic University, USA
  • Year and Date: 2009-03-05
• [Presentation] Polynomial time solvable classes of the vehicle routing problem (2008)
  • Author(s): 小田芳彰
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2008-12-15
• [Presentation] Partial constructions of Voronoi diagrams (2007)
  • Author(s): Yoshiaki Oda
  • Organizer: The 32nd Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
  • Place of Presentation: University of Otago, New Zealand
  • Year and Date: 2007-12-04
• [Presentation] Special cases of the vehicle routing problem (2007)
  • Author(s): Yoshiaki Oda
  • Organizer: The 38th Southeastern International Conference on Combinatorics, Graph Theory and Computing
  • Place of Presentation: Florida Atlantic University, USA
  • Year and Date: 2007-03-08
• [Presentation] 車両配送問題の多項式時間で解けるクラス (2006)
  • Author(s): 小田芳彰
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学
  • Year and Date: 2006-12-22