Intelligent Technology in Geometric Design

An integrated intelligent approach for solving geometric design problems is studied. A general optimization placement problem of objects with arbitrary shapes in a bounded container is constructed as a mathematical programming problem in terms of the phi-function technique. Various technological requirements (geometric and mechanical) are considered, including continuous translations and rotations of the objects, allowable distances between objects, prohibited zones in the container, balancing conditions, and mechanical strength constraints. Grouping the optimization placement problems based on the typology of the geometric design problems is provided. Solution strategies and various approaches to solve different variants of the model are discussed. A methodology of solving optimization placement problems is developed and illustrated with different examples.