Solving an optimization packing problem of circles and non-convex polygons with rotations into a multiply connected region

作     者：Stoyan, Y. G. Zlotnik, M. V. Chugay, A. M. 

作者机构：Natl Acad Sci Ukraine Dept Math Modelling & Optimal Design Inst Mech Engn Problems UA-61046 Kharkov Ukraine 

出 版 物：《JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY》 (英国运筹学会志)

年 卷 期：2012年第63卷第3期

页      面：379-391页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

主　　题：cutting stock problem optimization non-linear programming 

摘      要：This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the Phi-function technique, a mathematical model of the problem is constructed and its characteristics are investigated. Based on the characteristics, a solution approach to the problem is offered. The approach includes the following methods: an optimization method by groups of variables to construct starting points, a modification of the Zoutendijk feasible direction method to search for local minima and a special non-exhaustive search of local minima to find an approximation to a global minimum. A number of numerical results are given. The numerical results are compared with the best known ones. Journal of the Operational Research Society (2012) 63, 379-391. doi:10.1057/jors.2011.41 Published online 1 June 2011