Optimization methods for nonconvex mathematical programming
Project/Area Number  10680419 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
社会システム工学

Research Institution  University of Tsukuba 
Principal Investigator 
YAMAMOTO Yoshitsugu Institute of Policy and Planning Scineces, University of Tsukuba Professor, 社会工学系, 教授 (00119033)

Project Period (FY) 
1998 – 2000

Project Status 
Completed(Fiscal Year 2000)

Budget Amount *help 
¥2,900,000 (Direct Cost : ¥2,900,000)
Fiscal Year 2000 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1999 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1998 : ¥1,900,000 (Direct Cost : ¥1,900,000)

Keywords  Golbal optimization / Nonconvex programming / Linear multiplicative function / Pareto solution / Multicriteria program / Maximal flow / Maximum flow problem / Economic equilibrium / 数理計画 / 非凸計画 / 線形乗法計画 
Research Abstract 
The researh results are three folds. 1.Exact algorithm and heuristic method for linear multiplicative programming : The linear multiplicative programming problem was investigated from the view points of theory and algorithm. The problem is known to be very hard to solve when the number p of linear functions is large. Firstly, we proposed an algorithm for finding an exact globally optimal solution within a fininte number of iterations for the problem with p=2. The computational experiments supports the superiority of the algorithm over the existing algorithms including heuristic methods. Secondly, we proposed two improvements about (1) the way of finding an initial solution, and (2) the way of generating Pareto efficient faces. The computational experiment shows the accuracy of the solutions obtained is 95%. 2.The continuum of equilibria : We showed that the solution set of a certain system of equations arising from the economic equilibrium problem is connected. This implies the continuity
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of the economic equilibira as the parameter of the market varies. 3.Maximum network flow problem under restricted controllability : The minimum flow value of maximal flows is important in the situation where the controllability is restricted. The value shows "how inefficiently the network can be utilized." The problem is formulated as an optimization problem over the efficient set of a multicriteria program. We reviewed the existing algorithms for the problem and summarized them in a survey paper. Most of the existing algorithms assume that the number of criteria is much smaller than the number of variables of the problem, which is not the case for the minimum maximal flow problem, and hence are not likely to solve the problem efficiently. Then we proposed to combine the adjacent vertex search procedure with the nonadjacent vertex search procedure to make a finite convergent algorithm.We carried out the computational experiment and succeeded in solving problem instances up to 76 variables. Less

Report
(4results)
Research Output
(18results)