A collision detection approach for maximizing the material utilization

Volker Maag ()

Computational Optimization and Applications, 2015, vol. 61, issue 3, 781 pages

Abstract: We introduce a new method for a task of maximal material utilization, which is to fit a flexible, scalable three-dimensional body into another aiming for maximal volume whereas position and shape may vary. The difficulty arises from the containment constraint which is not easy to handle numerically. We use a collision detection method to check the constraint and reformulate the problem such that the constraint is hidden within the objective function. We apply methods from parametric optimization to proof that the objective function remains at least continuous. We apply the new approach to the problem of fitting a gemstone into a roughstone. For this previous approaches based on semi-infinite optimization exist, to which we compare our algorithm. The new algorithm is more suitable for necessary global optimization techniques and numerical results show that it works reliably and in general outperforms the previous approaches in both runtime and solution quality. Copyright Springer Science+Business Media New York 2015

Keywords: Nonlinear programming; Maximal material utilization; Design centering; Collision detection; Semi-infinite programming (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10589-015-9729-5

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