Research on Global Optimization Problems in Engineering Systems

工程系统全局优化问题研究

• 批准号: 06452141
• 负责人: KONNO Hiroshi
• 金额: $ 4.61万
• 依托单位: TOKYO INSTITUTE OF TECHNOLOGY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06452141/
• 关键词: global optimization; low rank nonconvex problems; outer approximation; nonlinear programming; cutting plane; nonconvex minimization; Pareto optimal surface; multi-objective optimization; 大域的最適化法; 多目的最適化問題; 凸乗法計画問題; 凹型生産コスト・輸送問題; 計算幾何学; パラメトリッ

Main reuslts of this research project are the following.(1)We proposed a type of lexicographic ordering method to prevent possible convergence of the outer-approximation method to a point x^<**> epsilon^P where P is the set of Pareto optimal solution associated with a minimization of a convex function on P.We are now able to obtain a solution on P without fail by using this new method.(2)We developed an outer approximation method for a concave cost production-transportation network and demonstrated its efficiency for low rank problems, namely, problems containing relatively few concave cost arcs.(3)We developed an efficint algorithm for solving low rank concave quadratic programming problems by using Rosen's cutting plane and Tuy's cutting plane method. This method is very efficient and we may be able to obtain an even more efficient method by combining it with a heuristic such as tabusearch approach.(4)Konno wrote a survey article on low rank global optimization problems, which was published in Joho-Shori.(5)Completed a monograph entitled "Optimization on Low Rank Nonconvex Structures" to be published from Kluwer Academic Publishers in 1996. This book is based upon about 100 papers published by Konno, Thach, Tuy, Kuno and Yajima in the past 10 years.

该研究项目的主要重用是以下内容。（1）我们提出了一种词典订购方法，以防止外部附属方法可能收敛到点x^<**> epsilon^p，其中P是Pareto的集合。与最小化凸功能相关的最佳解决方案P.我们现在能够通过使用这种新方法在PO上获得P上的解决方案。（2）我们开发了一种用于凹入成本生产传输网络的外近似方法，并证明了它对于低级问题的效率，即包含相对较少的凹成本弧的问题。（3）我们开发了一种效率算法，用于通过使用Rosen的切割平面和Tuy的切割平面方法来解决低级凹形二次编程问题。这种方法非常有效，我们也许可以通过将其与Tabusearch方法等启发式方法结合使用来获得更有效的方法。（4）Konno在Joho-Shori发表了一篇有关低级全球优化问题的调查文章，该文章发表在Joho-Shori中。 。 。

项目成果

H.KONNO,SUZUKI,K.: "A Mean Variance Sbeuness Portfolio Optimization Madel" J.of the Operations Research Society of Japan. (掲載予定). (1995)

H.KONNO, SUZUKI, K.：“A Mean Variance Sbeuness Portfolio Optimization Madel”，日本运筹学会杂志（1995 年）。

今野 浩: "大域的最適化の現状:低ランク非凸型の問題を中心に" 情報処理. 36. 1062-1069 (1995)

Hiroshi Konno：“全局优化的现状：关注低秩非凸问题”信息处理 36. 1062-1069 (1995)。

KONNO,H.,KUNO,T,ほか: "Hand book of Global Optimization" Kluwer Academic Publishers, 960 (1995)

KONNO, H.、KUNO, T. 等人：“全局优化手册”Kluwer 学术出版社，960 (1995)

Kuno, T., Yajima, Y., Konno, H.and Yamamoto, Y.: ""Convex Programs with an Additional Constraint on the product of Several Convex Functions"" European J.of Operational Research. 77. 314-324 (1994)

Kuno, T.、Yajima, Y.、Konno, H. 和 Yamamoto, Y.：““对多个凸函数的乘积具有附加约束的凸规划””欧洲运筹学杂志。

Yajima, Y.and Konno, H.: ""A Finitely Convergent Outer Approximation Method for Lower Rank Bilinear Programming Problems"" J.of the Operations Resrearch Society of Japan. 38. 230-239 (1995)

Yajima, Y. 和 Konno, H.：“低阶双线性规划问题的有限收敛外近似方法””日本运筹学会杂志。