2001 Fiscal Year Final Research Report Summary
Studies on Approximation Algorithm for Multi-objective Discrete Optimization Problems
| Project/Area Number |
10205216
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas (B)
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| Allocation Type | Single-year Grants |
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| Research Institution | Osaka University |
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Principal Investigator |
ISHII Hiroaki Osaka University, Graduate School of Engineering, Professor, 工学研究科, 教授 (90107136)
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| Co-Investigator(Kenkyū-buntansha) |
KOIDE Takeshi University of marketing and Distribution Sciences, Assistant Professor, 商学部, 講師 (50330486)
SHIODE Shogo KOBE Gakuin University, Department of Economics, Professor, 経済学部, 教授 (40154174)
SAITO Seiji Osaka University, Graduate School of Engineering, Associate Professor, 工学研究科, 助教授 (90225714)
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| Project Period (FY) |
1998 – 2000
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| Keywords | multi-objective optimization / network design problem / multi-objective scheduling problem / nonlinear functional analysis / multi-objective location problem / beam search method / fuzzy differential equation / fuzzy optimzation |
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| Research Abstract |
In our research we studied multi-objective discrete optimization which include multi-objective scheduling problems, network design problems and multi-objective facility location problems and so on as well as we advanced approximation methods for the optimization. Moreover we studied fuzzy differential equations and fuzzy optimization problems for foundation of the optimization by applying the methods of nonlinear functional analysis. In analyzing multi-objective scheduling problems not only we introduced a new model of scheduling problems with fuzziness and adaptability but also we schemed an algorithm for non-dominated solutions and some algorithms based on the beam-search method by developing calculation of a new lower bound. Numerical experiment illustrates utility of our algorithms to multi-objective flow shop problems. Moreover we gave theoretical results on multi-objective scheduling problems concerning parallel and multi-functional machines. In studying multi-objective network optimization problems we considered the total reliability of stochastic network problems. There are two characteristics. One is to give a utilized method for effective lower bounds of the total reliability and a fruitful solution-method of two-objective optimization with maximizing the total reliability and minimizing costs of construction of networks. We got results on optimal design of tele-communication networks, which can be applicable in many fields of network problems. In facility location analysis we investigated competitive problems and obtained practical optimal solutions with considering situations between firms and residents. Furthermore in order to apply optimization and modeling as new methods we studied fuzzy differential equations and fuzzy optimization problems.
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