The paper studies the optimal layout problem of 3D-objects (solid spheres, straight circular cylinders, spherocylinders, straight regular prisms, cuboids and tori) in a container (a cylindrical, a parabolic, or a truncated conical shape) with circular racks. The problem takes into account a given minimal and maximal allowable distances between objects, as well as, behaviour constraints of the mechanical system (equilibrium, moments of inertia and stability constraints). We call the problem the Balance Layout Problem (BLP) and develop a continuous nonlinear programming model (NLP-model) of the problem, using the phi-function technique. We also consider several BLP subproblems; provide appropriate mathematical models and solution algorithms, using nonlinear programming and nonsmooth optimization methods, illustrated with computational experiments.
Balance Layout Problems: Mathematical Modeling and Nonlinear Optimization
Springer Optimization
2017-01-01
32 pages
Article/Chapter (Book)
Electronic Resource
English
Layout problems , Behaviour constraints , Distance constraints , <italic>Phi</italic>-functions , Quasi-<italic>phi</italic>-functions , NLP-models , Optimization algorithms Mathematics , Optimization , Computational Mathematics and Numerical Analysis , Mathematical Applications in the Physical Sciences , Applications of Mathematics , Mathematics and Statistics
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