Packing non-equal hyperspheres into a hypersphere of minimal radius

The problem of packing different hyperspheres into a hypersphere of minimal  radius is considered. All hypersphere radii are supposed to be variable. Solving the problem is reduced to solving a sequence of mathematical programming problems. A special way of construction of starting pointsis suggeste...

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Збережено в:
Бібліографічні деталі
Дата:2014
Автор: Yaskov, G. N.
Формат: Стаття
Мова:English
Опубліковано: Journal of Mechanical Engineering 2014
Теми:
Онлайн доступ:https://journals.uran.ua/jme/article/view/27174
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Назва журналу:Journal of Mechanical Engineering

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Journal of Mechanical Engineering
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Резюме:The problem of packing different hyperspheres into a hypersphere of minimal  radius is considered. All hypersphere radii are supposed to be variable. Solving the problem is reduced to solving a sequence of mathematical programming problems. A special way of construction of starting pointsis suggested. A smooth transition from one local minimum point to another providing a decrease of the objective value is realized using the jump algorithm is fulfilled. Then, solution results are improved due to reduction of the solution space dimension by step-by-step fixing radii of hyperspheres and rearrangements of hypersphere pairs. Non-linear mathematical programming problems are solved with the IPOPT (Interior Point Optimizer) solver and the concept of active inequalities. A number of numerical results are given.