On unequal balls packing problem in three-dimensional space
A. L. Kazakov, A. A. Lempert, Trung Thanh Ta

References
1.	Akopyan A.V., Kabatyanskii G.A., Musin O.R., “Kontaktnye chisla, kody i sfericheskie mnogochleny”, Matematicheskoe prosveschenie. Ser. 3, 16, 2012, 57–74
2.	Bashurov V.V., “Primenenie metodov geometricheskoi optiki k resheniyu zadach bezopasnosti ob'ekta”, Vychislitelnye tekhnologii, 11:4 (2006), 23–28
3.	Berezovskii O.A., “O zadache upakovki sharov v kub”, Kibernetika i sistemnyi analiz, 50:4 (2014), 170–179
4.	Kazakov A.L., Lebedev P.D., “Algoritmy postroeniya optimalnykh upakovok dlya kompaktnykh mnozhestv na ploskosti”, Vychislitelnye metody i programmirovanie, 16:2 (2015), 307–317
5.	Kazakov A.L., Lempert A.A., “Ob odnom podkhode k resheniyu zadach optimizatsii, voznikayuschikh v transportnoi logistike”, Avtomatika i telemekhanika, 2011, no. 7, 50–57
6.	Kazakov A.L., Lempert A.A., Le K.M., “O zadachakh postroeniya mnogokratnykh pokrytii i upakovok v dvumernom neevklidovom prostranstve”, Upravlenie bolshimi sistemami, 81 (2019), 6–25
7.	Kazakov A.L., Lempert A.A., Nguen G.L., “Ob odnom algoritme postroeniya upakovki kongruentnykh krugov v neodnosvyaznoe mnozhestvo s neevklidovoi metrikoi”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 17:2 (2016), 177–188
8.	Lebedev P.D., Lavrov N.G., “Algoritmy postroeniya optimalnykh upakovok sharov v ellipsoidy”, Izvestiya Instituta matematiki i informatiki Udmurtskogo gosudarstvennogo universiteta, 52 (2018), 59–74
9.	Sloen N.Dzh.A., “Upakovka sharov”, V mire nauki, 1984, no. 3, 72–82
10.	Tot L.F., Raspolozheniya na ploskosti, na sfere i v prostranstve, Fizmatlit, M., 1958, 364 pp.
11.	Khlud O.M., Subbota I.A., Romanova T.E., “Matematicheskaya model i metod resheniya zadachi upakovki gomoteticheskikh odinakovo orientirovannykh ellipsoidov”, Radioelektronika i informatika, 2015, no. 3, 26–32
12.	Yaskov G.N., “Upakovka bolshogo chisla kongruentnykh sharov v tsilindre”, Dokl. NAN Ukrainy, 2009, no. 12, 45–48
13.	Akeb H., “A Two-Stage Look-Ahead Heuristic for Packing Spheres into a Three-Dimensional Bin of Minimum Length”, Recent Advances in Computational Optimization, Results of the Workshop on Computational Optimization WCO 2014, 2016, 127–144
14.	Alkhandari A., “3D packing of balls in different containers by VNS”, School of Information Systems, Computing and Mathematics (Brunel University, 2013) https://bura.brunel.ac.uk/handle/2438/8052
15.	Birgin E.G., Csendes T., “New and improved results for packing identical unitary radius circles within triangles, rectangles and strips”, Computers and Operations Research, 37:7 (2010), 1318–1327
16.	Chernov N., Stoyan Yu., Romanova T., “Mathematical model and efficient algorithms for object packing problem”, Computational Geometry, 43:5 (2010), 535–553
17.	Gensane T., “Dense packing of equal spheres in a cube”, The Electronic Journal of Combinatorics, 11 (2004), 1–17
18.	Graham R.L., Lubachevsky B.D., Nurmela K.J., Ostergard P.R.J., “Dense packings of congruent circles in a circle”, Discrete Mathematics, 181 (1998), 139–154
19.	Grosso A., Jamali A.R., Locatelli M., Schoen F., “Solving the problem of packing equal and unequal circles in a circular container”, Journal of Global Optimization, 47:1 (2010), 63–81
20.	Hales T.C., “Cannonballs and honeycombs”, Notices of the American Mathematical Society, 47 (2000), 440–449
21.	Harrary F., Randolph W., Mezey P.G., “A study of maximum unit-circle caterpillars-tools for the study of the shape of adsorption patterns”, Discrete Applied Mathematics, 67:1-3 (1996), 127–135
22.	Huang W., Yu L., Serial symmetrical relocation algorithm for the equal sphere packing problem, 2012, arXiv: abs/1202.4149
23.	Kazakov A.L., Lempert A.A., Ta T.T., “The sphere packing problem into bounded containers in threedimension non-Euclidean space”, IFAC-PapersOnLine, 51:32 (2018), 782–787
24.	Kazakov A.L., Lempert A.A., Ta T.T., “On the algorithm for equal balls packing into a multiconnected set”, Advances in Intelligent Systems Research, 169 (2019), 216–222
25.	Khlud O.M., Yaskov G.N., “Packing homothetic spheroids into a larger spheroid with the jump algorithm”, Control, navigation and communication systems, 6:46 (2017), 131–135
26.	Lempert A.A., Kazakov A.L., “On Mathematical Models for Optimization Problem of Logistics Infrastructure”, Int. J. Artificial Intelligence, 13:1 (2015), 200–210
27.	Lopez C.O., Beasley J.E., “A Heuristic for the Circle Packing Problem with a Variety of Containers”, European Journal of Operation Research, 214:3 (2001), 512–525
28.	Markot M.C., Csendes T.A., “A new verified optimization technique for the «packing circles in a unit square» problems”, SIAM Journal on Optimization, 16 (2005), 193–219
29.	Nurmela K.J., Ostergard P.R.J., “Packing up to 50 equal circles in a square”, Discrete and Computational Geometry, 18 (1997), 111–120
30.	Pfoertner H., Densest packings of n equal spheres in a sphere of radius 1, http://www.randomwalk.de/sphere/insphr/spisbest.txt, 2008 (data obrascheniya: 03.12.2019)
31.	Specht E., Packomania, http://www.packomania.com (data obrascheniya: 13.03.2020)
32.	Stoyan Y.G., Yaskov G., “Packing identical spheres into a rectangular parallelepiped”, Intelligent Decision Support, eds. Bortfeldt A., Homberg-er J., Kopfer H., Pankratz G., Strangmeier R., Gabler, 2008, 47–67
33.	Stoyan Y.G., Yaskov G., “Packing identical spheres into a cylinder”, International Transactions in Operational Research, 17 (2009), 51–70
34.	Sutou A., Dai Y., “Global Optimization Approach to Unequal Global Optimization Approach to Unequal Sphere Packing Problems in 3D”, Journal of Optimization Theory and Applications, 114:3 (2002), 671–694
35.	Tatarevic M., “On Limits of Dense Packing of Equal Spheres in a Cube”, The Electronic Journal of Combinatorics, 22:1 (2015), 35
36.	Wang J., “Packing of unequal spheres and automated radiosurgical treatment planning”, Journal of Combinatorial Optimization, 3 (1999), 453–463