2004 Fiscal Year Final Research Report Summary
A study on global/heuristic algorithm for nonlinear nonconvex programming problems
| Project/Area Number |
15560048
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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 |
Engineering fundamentals
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| Research Institution | University of Tsukuba |
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Principal Investigator |
KUNO Takahito University of Tsukuba, Graduate School of Systems and Information Engineering, Associate Professor, 大学院・システム情報工学研究科, 助教授 (00205113)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHISE Akiko University of Tsukuba, Graduate School of Systems and Information Engineering, Associate Professor, 大学院・システム情報工学研究科, 助教授 (50234472)
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| Project Period (FY) |
2003 – 2004
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| Keywords | Global optimization / non convex progam / branch-and-bound method / mathematica programming / algorithm |
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| Research Abstract |
As a prototype of the global/heuristic hybrid algorithm for solving nonconvex programs, we first developed a branch-and-bound algorithm in which upper bounds were tightened by local search. Our aim was to make the quality of the incumbent as high as those of existing heuristics at any forced termination. However, it turned out to take more computational time than algorithms without local search before convergence ; and besides the quality of the incumbent was not so good as we expected. We then dropped the local search procedure and instead designed another procedure for tightening lower bounds in two phases. We further customized it for the following and ran the resulting algorithms on them :
(a)linear sum-of-ratios problems,
(b)concave minimization problems with low-rank nonconvexities,
(c)production-transportation problems with concave production costs, and
(d)twice-differentiable nonconvex programs needed for designing chemical processes.
Computational results indicated that the incumbent becomes equal to a globally optimal solution at an early stage of each algorithm for (a) and (b). This implies that our algorithms serve high-quality heuristics. We also found that as global optimization algorithms those are much more efficient than existing ones in computational time. As for (c) and (d), though there was still room for improvement in efficiency by exploiting their special structures, we could recognize potential of our algorithms for practical use. In addition, we studied the application of interior-point methods to relaxed problems solved repeatedly in our algorithms, and obtained some results favorable from the theoretical points of view.
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