Decomposition Algorithm for Irregular Placement Problems

A placement problem of irregular 2D&3D objects in a domain (container) of minimum area (volume), that related to the field of Packing and Cutting problems is considered. Placement objects may be continuously translated and rotated. A general nonlinear programming model of the problem is presented employing the phi-function technique. We propose a decomposition algorithm that generalizes previously published compaction algorithms of searching for local optimal solutions for some packing and cutting problems. Our decomposition algorithm reduces the optimization placement problem to a sequence of nonlinear programming subproblems of considerably smaller dimension. © 2020, Springer Nature Switzerland AG.