2005 Fiscal Year Final Research Report Summary
Improvement and application of target approach for solving nonlinear knapsack type optimization problem
| Project/Area Number |
14580397
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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 |
計算機科学
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| Research Institution | Kansai University |
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Principal Investigator |
NAKAGAWA Yuji Kansai University, Informatics, Professor, 総合情報学部, 教授 (60141925)
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| Co-Investigator(Kenkyū-buntansha) |
ISADA Yuriko Tezukayama University, Business Administration, Associate Professor, 経営情報学部, 助教授 (00351867)
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| Project Period (FY) |
2002 – 2005
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| Keywords | discrete optimization / multi-objective optimization / nonlinear knapsack problem / surrogate constraints method / financial engineering / exact method / near-optimization method / parallel computation |
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| Research Abstract |
1) Application of the improved surrogate constraint method to non-separable nonconvex portfolio optimization problem
The Improved Surrogate Constraint method (ISC) was developed, which cane solve exactly and efficiently large-scale multi-constraints separable discrete optimization problems. We apply the ISC to the index optimization problem that 50 brands are selected from 1440 brands of Tokyo Stock Exchange 1st section listed (TOPIX) and track the market index. This means that an extremely large-scale problem of a practical scale was able to be solved about the index fund problem. Moreover, it succeeded in making the index-plus-alpha portfolio. This result appeared in the Nikkan Kogyo Shimbun article Friday, November 18, 2005.
2) Exact method for solving multi-constraints separable discrete optimization problems
In order to apply the ISC method to a larger-scale problem, we tried to use average information (entropy) and to divide an original problem into small subproblems. The test problem of Chu and Beasley are used to show the effectiveness of the present method. The method is compared with business high speed software CPLEX V.9.0 by using 30 0-1 knapsack problems, which are well known as difficult problems. with 500 variables. The computational results show that the ISC using the Problem Partition is nine times as fast as CPLEX on the average and succeeds in economizing the memory.
3) Multi-objective optimization and parallel computation
We developed a new solution algorithm based on the ISC for solving multi-objective discrete optimization problems. It is scheduled to apply the present algorithm to practical multi-objective problems that the existing methods are quite difficult to solve. Moreover, a estimation technique of the difficulty degree of the problem that used entropy was newly developed. This technology is scheduled to be applied to the problem partition method for the parallel computation.
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