Algorithms and their generalizations for vehicle routing problems of minimizing regrets

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K00004
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: Tohoku University
• Principal Investigator: ITO Takehiro 東北大学, 情報科学研究科, 准教授 (40431548)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: アルゴリズム / グラフ理論 / 近似

Outline of Final Research Achievements

We studied a recently proposed variant of vehicle routing problems which takes the customers’ regrets as the objective function. We developed algorithms for the problem using structures of input graphs, and also proved some computational hardness and inapproximability. In addition, we introduced some generalized variant, and examined an extension of our algorithms in order to put our developed methods in place. Our approximation method for trees is best possible from the viewpoint of approximation ratio, because one can choose an arbitrarily better ratio.

Free Research Field

理論計算機科学

Academic Significance and Societal Importance of the Research Achievements

運搬経路問題は長年盛んに研究されてきたが，既存研究ではサービス提供側のコストを評価対象とすることが多かった．それに対し本問題は，サービス受給側の不満度を評価対象とする比較的新しい設定の問題である．本研究の成果により，入力グラフのどのような構造が本問題を計算困難にしているのか詳細な解析が与えられた．また，効率のよい近似手法を開発することで，入力グラフは限定されるものの，理論保証された精度の近似解を得られるようになった．