| Project/Area Number |
07680447
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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 |
社会システム工学
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| Research Institution | University of Tsukuba |
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Principal Investigator |
KUNO Takahito University of Tsukuba, Institute of Information Sciences and Electronics, Associate Professor, 電子・情報工学系, 助教授 (00205113)
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| Project Period (FY) |
1995 – 1996
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| Project Status |
Completed (Fiscal Year 1996)
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| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1996: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1995: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Mathematical programming / Optimization algorithm / Network programming / Nonconvex programming / Global optimization |
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| Research Abstract |
In this research, we studied certain classes of nonconvex cost network flow problems and proposed efficient algorithms for generating globally optimal solutions. A few of the results are listed below :
1 In the usual two-terminal network, we proposed a method for minimizing the total transportation cost and for simultaneously maximizing the total flow. To accomplish it, we optimized the product of these two values and showed that a successive shortest path algorithm yields a globally optimal solution in pseudo-polynomial time and an epsilon-optimal solution in polynomial time.
2 We developed pseudo-polynomial algorithm to solve a production-transportation problem equivalent to the capacitated minimum concave cost flow problems with at most three nonlinear variables. The algorithm consists of two phases : the first phase generates a feasible solution ; starting from it, the second phase searches for a globally optimal solution in the same way as solving a minimum linear-cost flow problem
3 We extended the idea used to solve the problem in 2 and solved a maximum flow problem with an additional reverse convex constraint in pseudo-polynomial time. We first applied a binary search procedure to generate a candidate for an optimal solution, and then checked its globally optimality using the algorithm similar to the one in 2.
All the above mentioned algorithms were designed by exploiting low-rank (quasi) concavity possessed by the problems, and were shown to be efficient in both practical and theoretical senses. We generalized this special problem structure and obtained the following result :
4 We showed that a multiple convex objective program can be reduced to a single nonconvex objective program, and developed an outer approximation algorithm for generating a globally optimal solution. Computational experiments indicated that the algorithm is practically efficient when the number of objectives is less than five.
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