A study on efficient algorithms for nonlinear nonconvex network programming problems
Project/Area Number  07680447 
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 
1995 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥1,600,000 (Direct Cost : ¥1,600,000)
Fiscal Year 1996 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1995 : ¥800,000 (Direct Cost : ¥800,000)

Keywords  Mathematical programming / Optimization algorithm / Network programming / Nonconvex programming / Global optimization / 数理計画法 / 最適化アルゴリズム / ネットワーク計画 / 非凸計画 / 大域的最適化 
Research Abstract 
In this research, we studied certain classes of nonconvex cost network flow problems and proposed efficient algorithms for generating globally optimal solutions. A few of the results are listed below : 1 In the usual twoterminal network, we proposed a method for minimizing the total transportation cost and for simultaneously maximizing the total flow. To accomplish it, we optimized the product of these two values and showed that a successive shortest path algorithm yields a globally optimal solution in pseudopolynomial time and an epsilonoptimal solution in polynomial time. 2 We developed pseudopolynomial algorithm to solve a productiontransportation problem equivalent to the capacitated minimum concave cost flow problems with at most three nonlinear variables. The algorithm consists of two phases : the first phase generates a feasible solution ; starting from it, the second phase searches for a globally optimal solution in the same way as solving a minimum linearcost flow problem 3 We extended the idea used to solve the problem in 2 and solved a maximum flow problem with an additional reverse convex constraint in pseudopolynomial time. We first applied a binary search procedure to generate a candidate for an optimal solution, and then checked its globally optimality using the algorithm similar to the one in 2. All the above mentioned algorithms were designed by exploiting lowrank (quasi) concavity possessed by the problems, and were shown to be efficient in both practical and theoretical senses. We generalized this special problem structure and obtained the following result : 4 We showed that a multiple convex objective program can be reduced to a single nonconvex objective program, and developed an outer approximation algorithm for generating a globally optimal solution. Computational experiments indicated that the algorithm is practically efficient when the number of objectives is less than five.

Report
(4results)
Research Output
(18results)