Optimized Packings in Space Engineering Applications: Part I

Stoyan, Yu. G.; Pankratov, Alexander; Romanova, Tatiana; Fasano, Giorgio; Pintér, János D.; Stoian, Y. E.; Chugay, A. M.

doi:10.1007/978-3-030-10501-3_15

Cited by 22 publications

(2 citation statements)

References 73 publications

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“…Відомі застосування задачі в медицині під час лікування онкологічних пухлин гамма-променями [4,5] та діабетичної ретинопатії за допомогою лазерної коагуляції сітківки ока [6]. Застосування у космічній техніці досліджено у [7,8]. Найвідоміші моделі та методи для задач компонування сферичних об'єктів у просторах різної вимірності наведено в [9].…”

Section: оптимізація компонування сферичних об'єктів у багатогранній областіunclassified

Optimized Layout of Spherical Objects in a Polyhedral Domain

Romanova

Yaskov

Chugay

et al. 2020

Cybernetics and Computer Technologies

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Introduction. The article studies the problem of arranging spherical objects in a bounded polyhedral domain in order to maximize the packing factor. The spherical objects have variable placement parameters and variable radii within the given upper and lower bounds. The constraints on the allowable distance between each pair of spherical objects are taken into account. The phi-function technique is used for analytical description of the placement constraints, involving object non-overlapping and containment conditions. The problem is considered as a nonlinear programming problem. The feasible region is described by a system of inequalities with differentiable functions. To find the local maximum of the problem the decomposition algorithm is used. We employ the strategy of active set of inequalities for reducing the computational complexity of the algorithm. IPOPT solver for solving nonlinear programming subproblems is used. The multistart strategy allows selecting the best local maximum point. Numerical results and the appropriate graphic illustration are given. The purpose of the article is presenting a mathematical model and developing a solution algorithm for arranging spherical objects in a polyhedral region with the maximum packing factor. It allows obtaining a locally optimal solution in a reasonable time. Results. A new formulation of the problem of arranging spherical objects in a polyhedral domain is considered, where both the placement parameters and the radii of the spherical objects are variable. A mathematical model in the form of nonlinear programming problem is derived. A solution approach based on the decomposition algorithm and multistart strategy is developed. The numerical results combined with the graphical illustration are given. Conclusions. The proposed approach allows modeling optimized layouts of spherical objects into a polyhedral domain. Keywords: layout, spherical objects, polyhedral domain, phi-function.

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Section: оптимізація компонування сферичних об'єктів у багатогранній областіunclassified

Optimized Layout of Spherical Objects in a Polyhedral Domain

Romanova

Yaskov

Chugay

et al. 2020

Cybernetics and Computer Technologies

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“…All packing problems are NP-hard optimization problems for which there are no algorithms of polynomial complexity to solve them, which makes it urgent to develop algorithms that provide suboptimal solutions in an acceptable time. Modern methods for solving problems of packing objects of complex geometric shape are based on the use of the hodograph vector function of dense placement, which requires the subsequent application of nonlinear programming methods characterized by high computational complexity [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Application of Algorithms for Placement of Orthogonal Polyhedrons for Solving the Problems of Packing Objects of Complex Geometric Shape

Chekanin¹,

Chekanin²

2021

EPJ Web Conf.

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The article is devoted to the development and research of algorithms for placing objects of complex geometric shapes. To solve the placement problem is proposed an approach which consists in transforming the shape of all objects and further application of the developed algorithm for placing orthogonal polyhedrons of arbitrary dimension to the resulting transformed objects. In the process of transforming the shape of the objects being placed, they are initially voxelized, after which the developed decomposition algorithm is applied to the resulting voxelized objects, which provides the formation of orthogonal polyhedrons consisting of the largest possible orthogonal objects. The proposed model of potential containers is used to describe the free space of containers as a set of orthogonal areas. The developed algorithm for the placement of orthogonal polyhedrons provides a fast solution to NP-hard problems of placing objects of complex geometric shapes without resorting to the use of time-consuming nonlinear programming methods. Examples of the practical application of the developed algorithms for modeling the dense layout of parts of complex geometric shapes on the platform of a 3D printer are given.

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