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...
Збережено в:
Дата: | 2014 |
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Автор: | |
Формат: | Стаття |
Мова: | English |
Опубліковано: |
Journal of Mechanical Engineering
2014
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Теми: | |
Онлайн доступ: | https://journals.uran.ua/jme/article/view/27174 |
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Назва журналу: | Journal of Mechanical Engineering |
Репозитарії
Journal of Mechanical EngineeringРезюме: | 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. |
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