Layout problems for arc objects in convex domains

• Дата: 2016
• Автори: Pankratov, A., Romanova, T., Kotelevskiy, A.
• Формат: Стаття
• Мова: English
• Опубліковано: Journal of Mechanical Engineering 2016
• Теми: irregular shapes; convex domains; phi-functions; object rotations; allowable distances; solution tree; solution algorithms; local optimisation; УДК 519.85; задача упаковки; произвольные объекты; непрерывные вращения; допустимые расстояния; phi -функции; генератор пространства решений; нелинейная оптимизация; довільні об’єкти; неперервні обертання; допустимі відстані; phi-функції; генератор простору розв’язків; вирішувач; нелінійна оптимізація
• Онлайн доступ: https://journals.uran.ua/jme/article/view/78787
• Назва журналу: Journal of Mechanical Engineering

We introduce a new methodology for solving layout problems. Our objects and containers are bounded by circular arcs and line segments. We allow continuous object translations and rotations as well as minimal allowable distances between objects. For describing non-overlapping, containment and distance constraints the phi-function technique is used. We provide a general mathematical model as nonlinear programming problem with nonsmooth functions. We propose here the automatic feasible region generator, using phi-trees. The generator allows us to form ready-to-use systems of inequalities with smooth functions in order to apply efficient nonlinear optimisation procedures. We develop an efficient solution algorithm and original solver for layout problems which uses the core representation of inequlities in a sybmol form and provides exact calculation of Jacobian and Hessian matrixes. The search for local minima of NLP-problems is performed by IPOPT algorithm. An essential part of our local optimisation scheme is LORA algorithm that simplifies description of feasible region of the problem and reduces the runtime of local optimisation. It is due to this reduction our strategy can work efficiently with collections of composed objects and search for “good” local-optimal solutions for layout problems in reasonable time.