Approximation algoirithms for route optimization problems : exploiting geometric structures and application to large scale problems
Project/Area Number  10205225 
Research Category 
GrantinAid for Scientific Research on Priority Areas (B).

Research Institution  Meiji University 
Principal Investigator 
TAMAKI Hisao School of Science and Technology, Department of Computer Science, Meiji University Professor, 理工学部, 教授 (20111354)

Project Fiscal Year 
1998 – 2000

Project Status 
Completed(Fiscal Year 2001)

Budget Amount *help 
¥9,000,000 (Direct Cost : ¥9,000,000)
Fiscal Year 2000 : ¥1,400,000 (Direct Cost : ¥1,400,000)
Fiscal Year 1999 : ¥3,500,000 (Direct Cost : ¥3,500,000)
Fiscal Year 1998 : ¥4,100,000 (Direct Cost : ¥4,100,000)

Keywords  route optimization / traveling salesman problem / approximation algorithms / heuristics / LinKernighan heuristic / alternating cycles contribution / dynamic programming / Catalanian decompositoin / 経路最適化 / 巡回セールスマン問題 / 近似アルゴリズム / 発見的解法 / LinKernighan法 / 交代閉路寄与法 / 動的計画法 / カタラン分割 / 平面巡回セールスマン問題 / 多項式時間近似スキーム / 局所探索 / 幾何的距離 / ヒューリスティックス / 近似解 
Research Abstract 
Starting from the polynomial time approximation scheme of Arora for the traveling salesman problem in the plane, we aimed at applying this theoretical result to practical solution methods and investigated a number of approaches. Main achievements are summarized as follows. (1) Efficient implementation of Arora's dynamic programming : based on the observation that each subproblem in his dynamic programming formulation can be compactly represented by a binary string based on the onetoone correspondence between subproblems and wellformed parenthesis, we developed a fast scheme that maps a subproblem to its child subproblems. Using this scheme, we achieved two orders of magnitude speed up over a naive implementation. This enabled us to experiment on various uses of Aroras scheme. (2) Introducing the concept of Catalan decomposition and developing a dynamic programming scheme based on it : We replaced the rectangular decomposition of Arora by a topological decomposition of a graph and applied the implementation scheme of (1). (3) Development of alternating cycles contribution method : Given a tour to be improved (principal tour) and other tours for references (contributing tours), we extract the difference between the principal tour and each contributing tour in the form of a set of alternating cycles. We than select some of these alternating cycles, merge them with the principal tour and obtain the optimal tour in the resulting graph, hoping to get an improvement over the principal tour. The selection of alternating cycles is based on the flip gain of each cycle and the tractability of the resulting graph when all the selected cycles are added to the principal tour. (4) Development of boosted chained LinKernihan heuristic : We applied the methods of (2) and (3) to the chained LinKernighan heuristic and obtained a significant performance improvement.

Report
(5results)
Research Output
(24results)