1998 Fiscal Year Final Research Report Summary
A study on efficient algorithms for multiple objective optimization prob-lems
| Project/Area Number |
09680413
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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 Infor-mation Sciences and Electronics, Associate Professor, 電子・情報工学系, 助教授 (00205113)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Mathematical programming / Optimization algorithm / Multiple objective decision making / Nonconvex programming / Global optimization |
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| Research Abstract |
In this research. we formulated some classes of multiple objective optimization problems into single objective nonconvex optimization problems and proposed efficient algorithms for generating globally optimal solutions to the resulting problems. A few of the results are listed below :
1 We studied a problem constraining the product of two objectives to be less than or equal to a given constant. We developed an algorithm for generating a globally optimal solution within a finite time. The computational results on a workstation indicated that the algorithm is reasonably practical as long as the number of constraints containing the product is less than five.
2 We developed a branch-and-bound algorithm to resolve a multi-objective optimization with a 0-1 knapsack constraint. We incorporated a Lagrangian relaxation into the bounding procedure ; but the time taken for bounding is only a lower-order polynomial in the problem size. The algorithm succeeded in solving problems of 20 objectives and
… More
120 variables within 20 seconds.
3 We investigated the relationship between the multi-objective optimization with a 0-1 knapsack constraint and a production-transportation problem with concave production costs. We then extended the algorithm for the former to the latter network problem. The computational time needed by the algorithm was a few hundreds times less than those by the existing algorithms.
4 We studied a bi-objective shortest path problem and developed two strongly polynomial algo- rithms. One is for the case that the utility function of the decision maker is quasi-concave ; and the other is for the case that the utility function is quasi-convex. We showed that both algorithms are directly applicable to in-car navigation systems and so forth.
All the above mentioned problems have highly nonconvex but low-rank structures. We showed that, even though the problems belong to a well-known hard class, it is possible to design efficient algorithms both in theoretical and practical senses, by exploiting their special structures. Less
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