2005 Fiscal Year Final Research Report Summary
Research on Speeding Up Techniques for General Mixed Integer Programming Problem Solvers
| Project/Area Number |
16510105
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Social systems engineering/Safety system
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| Research Institution | National University Corporation Tokyo University of Agriculture and Technology |
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Principal Investigator |
SHINANO Yuji National University Corporation Tokyo University of Agriculture and Technology, Institute of Symbiotic Science and Technology, Associate Prof., 大学院共生科学技術研究部, 助教授 (00297623)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIE Tetsuya School of Business Administration University of Hyogo, Associate Prof., 経営学部, 助教授 (40305678)
NAMIKI Mitaro National University Corporation Tokyo University of Agriculture and Technology, Institute of Symbiotic Science and Technology, Associate Prof., 大学院共生科学技術研究部, 助教授 (10208077)
IKEDA Satoshi Miyazaki University, Dept. of Computer Science and Systems Engineering, Associate Prof., 工学部, 助教授 (70282796)
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| Project Period (FY) |
2004 – 2005
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| Keywords | Mixed integer linear programming problem / Parallel processing / Mathematical programming / Integral Basis Method |
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| Research Abstract |
Our research project, which aim is to develop efficient techniques for MIP solvers, is mainly composed of three parts of subprojects.
1. Research on speed up MIP solvers by mathematical programming approach
As the first step of this research project, we validated the effectiveness of the IBM (Integral Basis Method) which was recently proposed as an exact algorithm of MIP (Mixed Integer programming Problem). Generally, the most of computation time of MIP solvers to solve hard instances is used to prove the optimality of incumbent feasible solutions. The IBM has a possibility to prove the optimality faster than the traditional methods. Before our project only an implementation of IBM existed. We implemented IBM for the QAP (Quadratic Assignment Problem) and the general IP (Integer programming Problem). We proposed some classes of valid inequalities to IBM for the QAP and also proposed several techniques using continuous relaxation problem methods and effective variable selection rules. We are searching for effective methods of applying our proposals to IBM-based MIP solvers.
2. Research on speed up MIP solvers by parallel processing approach
We implemented a parallel algorithm to compute the diameter of pancake graphs using the Condor/MW system. The implemented algorithm has the same structure with the branch and bound algorithm used in common MIPs. Therefore, the techniques used for solving the diameter of pancake graphs would be contributed for the parallelization of general MIP solvers.
3. Designing a MIP Solver Portal
This research project is still a design phrase. We will continue to develop a MIP Solver Portal after this project.
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