2D multi-objective placement algorithm for free-form components

This article presents a generic method to solve 2D multi-objective placement problem for free-form components. The proposed method is a relaxed placement technique combined with an hybrid algorithm based on a genetic algorithm and a separation algorithm. The genetic algorithm is used as a global optimizer and is in charge of efficiently exploring the search space. The separation algorithm is used to legalize solutions proposed by the global optimizer, so that placement constraints are satisfied. A test case illustrates the application of the proposed method. Extensions for solving the 3D problem are given at the end of the article.Comment: ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, San Diego : United States (2009

Discrete No-Fit Polygon,A Simple Structure for the 2-D Irregular Packing Problem

提出了一个用于求解二维不规则排样问题的离散临界多边形模型.burkE等人的blf算法是求解排样问题的一种有效算法,但其算法对一些特殊实例会产生非法的解.为了解决这个问题,提出了一种基于离散临界多边形模型,并对其正确性作了严格证明.新模型是只含有点和区间的简单模型,在大大降低原问题几何复杂性的同时,也使许多启发式策略可以更容易地求解该问题.计算结果表明,基于离散临界多边型模型的排样算法是很有效的.This paper presents a model based on discrete no-fit polygon for the two-dimensional irregular packing problem.Burke et al.have presented an effective BLF algorithm to solve the irregular packing problem, however, their algorithm might generate invalid results for some special cases.To solve this problem, a model based on discrete no-fit polygon is proposed, and its correctness has been strictly proved.Only points and intervals are only considered by this model, which greatly decreases the geometry complexity of the original problem and makes the problem easily solved by many heuristic strategies.Computational results show that the algorithm based on discrete no-fit polygon model is very efficient.国家自然科学基金No.60773126;福建省自然科学基金No.A07100234;厦门大学985二期信息科技基金No.0000-X07204;厦门大学院士启动基金No.X01109---

Biblioteca Geométrica para a resolução de problemas de corte de formas irregulares

Tese de mestrado integrado. Engenharia Electrotécnica e de Computadores (Major Automação). Faculdade de Engenharia. Universidade do Porto. 200

A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums

The nofit polygon is a powerful and effective tool for handling the geometric requirements of solution approaches to irregular cutting and packing problems. Although the concept was first described in 1966, it was not until the early 90s that the general trend of research moved away from direct trigonometry to favour the nofit polygon. Since then, the ability to calculate the nofit polygon has practically become a pre-requisite for researching irregular packing problems. However, realisation of this concept in the form of a robust algorithm is a highly challenging task with few instructive approaches published. In this paper, a procedure using the mathematical concept of Minkowski sums for the calculation of the nofit polygon is presented. The described procedure is more robust than other approaches using Minkowski Sum knowledge and includes details of the removal of internal edges to find holes, slits and lock and key positions. The procedure is tested on benchmark data sets and gives examples of complicated cases