Space Engineering pp 369-400 | Cite as

# Balance Layout Problems: Mathematical Modeling and Nonlinear Optimization

## Abstract

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.

## Keywords

Layout problems Behaviour constraints Distance constraints*Phi*-functions Quasi-

*phi*-functions NLP-models Optimization algorithms

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