A study on efficient algorithms for multiple objective optimization problems
Project/Area Number  09680413 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
社会システム工学

Research Institution  University of Tsukuba 
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)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1998 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1997 : ¥1,500,000 (Direct Cost : ¥1,500,000)

Keywords  Mathematical programming / Optimization algorithm / Multiple objective decision making / Nonconvex programming / Global optimization / 数理計画法 / 最適化アルゴリズム / 多目的意思決定 / 非凸計画法 / 大域的最適化 / 多目的最適化 / 非凸計画 
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 branchandbound algorithm to resolve a multiobjective optimization with a 01 knapsack constraint. We incorporated a Lagrangian relaxation into the bounding procedure ; but the time taken for bounding is only a lowerorder 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 multiobjective optimization with a 01 knapsack constraint and a productiontransportation 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 biobjective shortest path problem and developed two strongly polynomial algo rithms. One is for the case that the utility function of the decision maker is quasiconcave ; and the other is for the case that the utility function is quasiconvex. We showed that both algorithms are directly applicable to incar navigation systems and so forth. All the above mentioned problems have highly nonconvex but lowrank structures. We showed that, even though the problems belong to a wellknown hard class, it is possible to design efficient algorithms both in theoretical and practical senses, by exploiting their special structures. Less

Report
(4results)
Research Output
(17results)