Solving Irregular Strip Packing Problems With Free Rotations Using Separation Lines

Solving nesting problems or irregular strip packing problems is to position polygons in a fixed width and unlimited length strip, obeying polygon integrity containment constraints and non-overlapping constraints, in order to minimize the used length of the strip. To ensure non-overlapping, we used separation lines. A straight line is a separation line if given two polygons, all vertices of one of the polygons are on one side of the line or on the line, and all vertices of the other polygon are on the other side of the line or on the line. Since we are considering free rotations of the polygons and separation lines, the mathematical model of the studied problem is nonlinear. Therefore, we use the nonlinear programming solver IPOPT (an algorithm of interior points type), which is part of COIN-OR. Computational tests were run using established benchmark instances and the results were compared with the ones obtained with other methodologies in the literature that use free rotation

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