Generalized Models of Logistics Problems and Approaches to Their Solution Based on the Synthesis of the Theory of Optimal Partitioning and Neuro-Fuzzy Technologies

Bulat, Anatolii; Kiseleva, Elena; Hart, Liudmyla; Prytomanova, Olga

doi:10.1007/978-3-031-37450-0_21

Cited by 1 publication

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“…It also can be applied to a broader class of containers, e.g., circular hyperboloids (single-and double-sheeted), spheroids or ellipsoids. Packing problems on surfaces [35] can also be considered, as well as various applications of spherical systems [36] and logistics [37]. Some results in these directions are forthcoming.…”

Section: Discussionmentioning

confidence: 99%

Packing Spheres into a Minimum-Height Parabolic Container

Stoyan,

Yaskov,

Romanova

et al. 2024

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Sphere packing consists of placing several spheres in a container without mutual overlapping. While packing into regular-shape containers is well explored, less attention is focused on containers with nonlinear boundaries, such as ellipsoids or paraboloids. Packing n-dimensional spheres into a minimum-height container bounded by a parabolic surface is formulated. The minimum allowable distances between spheres as well as between spheres and the container boundary are considered. A normalized Φ-function is used for analytical description of the containment constraints. A nonlinear programming model for the packing problem is provided. A solution algorithm based on the feasible directions approach and a decomposition technique is proposed. The computational results for problem instances with various space dimensions, different numbers of spheres and their radii, the minimal allowable distances and the parameters of the parabolic container are presented to demonstrate the efficiency of the proposed approach.

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Section: Discussionmentioning

confidence: 99%