A balanced layout problem of cylinders in a cylindrical container of the minimal radius

• Main Authors: Панкратов, А. В., Романова, Т. Е., Коваленко, А. А.
• Format: Article
• Language: Russian
• Published: Journal of Mechanical Engineering 2015
• Subjects: balanced layout; cylinders; behavior constraints; mathematical modeling; nonlinear programming; УДК 519.85; равновесная компоновка; цилиндры; ограничения поведения; математическое моделирование; нелинейное программирование; рівноважна компоновка; циліндри; обмеження поведінки; математичне моделювання; нелінійне програмування
• Online Access: https://journals.uran.ua/jme/article/view/40261

We study a balanced layout problem of a collection of homogeneous circular cylinders onto the given bearing plates of a cylindrical container of minimal radius  taking into account behavior constraints. We consider a reduced model of a spacecraft as the mechanical system. The latter is formed by means of a cylindrical container with placed objects (technical equipment) onto the given bearing plates. Behavior constraints include dynamic equilibrium, moments of inertia, stability constraints. A mathematical model of the problem is constructed in the form of nonlinear programming problem, using phi-functions. We develop the efficient algorithm, involving the multistart method, an algorithm for constructing a set of feasible starting points and IPOPT to solve nonlinear programming problems. In order to simplify a nontrivial procedure of searching for a feasible starting point we apply a special algorithm, which is based on homothetic transformations of circles. The proposed solution method allows us: to search for local optimal solutions for the balanced layout problem of cylinders in a cylindrical container of the minimal radius, improve a convergence of the local optimization and reduce the computational time. We present a number of known benchmark instances to demonstrate the high efficiency of our approach.