Orthogonal packing of rectangular items within arbitrary convex regions by nonlinear optimization

The orthogonal packing of rectangular items in an arbitrary convex region is considered in this work. The packing problem is modeled as the problem of deciding for the feasibility or infeasibility of a set of nonlinear equality and inequality constraints. A procedure based on nonlinear programming is introduced and numerical experiments which show that the new procedure is reliable are exhibited. Scope and purpose: We address the problem of packing orthogonal rectangles within an arbitrary convex region. We aim to show that smooth nonlinear programming models are a reliable alternative for packing problems and that well-known general-purpose methods based on continuous optimization can be used to solve the models. Numerical experiments illustrate the capabilities and limitations of the approach.