Abstract

The packing optimization of three-dimensional components into a design space is a challenging and time-intensive task. Of particular concern is the thermal performance of the system, as tightly packed components typically exhibit poor heat dissipation performance which can result in overheating and system failure. As temperature modeling can be quite complex, there is a growing demand in the industry for software tools that aid designers in the packing process whilst considering heat transfer. This work outlines a novel multi-objective algorithm that considers temperature and thermal effects directly within the packing optimization process itself using thermal optimization objectives. In addition, the algorithm can consider functional objectives such as a desired center of mass position and minimizing rotational inertia. The algorithm packs components from initial to optimal positions within a design domain using a set of dynamic acceleration fields. There are multiple accelerations, each designed to improve the objective values for the systems (e.g., minimize temperature variance). Component temperatures are calculated using thermal finite element analyses modeling conduction and natural convection. Forced convection is approximated via computational fluid dynamics simulations. Numerical results for two academic and one real-world case studies are presented to demonstrate the efficacy of the presented algorithm.

References

1.
Perboli
,
G.
,
Gobbato
,
L.
, and
Perfetti
,
F.
,
2014
, “
Packing Problems in Transportation and Supply Chain: New Problems and Trends
,”
Proc. Soc. Behav. Sci.
,
111
(
1
), pp.
672
681
.
2.
Fadel
,
G. M.
, and
Wiecek
,
M. M.
,
2015
, “
Packing Optimization of Free-Form Objects in Engineering Design
,”
Comput. Optim. Appl.
,
105
(
1
), pp.
37
66
.
3.
Joung
,
Y. K.
, and
Noh
,
S. D.
,
2014
, “
Intelligent 3D Packing Using a Grouping Algorithm for Automotive Container Engineering
,”
J. Comput. Des. Eng.
,
1
(
2
), pp.
140
151
.
4.
Lee
,
C.
, and
Subbiah
,
S.
,
1991
, “
Prediction of Protein Side-Chain Conformation by Packing Optimization
,”
J. Mol. Biol.
,
217
(
2
), pp.
373
388
.
5.
Sanches
,
C. A. A.
, and
Soma
,
N. Y.
,
1988
, “
A Polynomial-Time DNA Computing Solution for the Bin-Packing Problem
,”
Comput. Methods Appl. Mech. Eng.
,
71
(
2
), pp.
197
224
.
6.
Martinez
,
J.
, and
Martinez
,
L.
,
2003
, “
Packing Optimization for Automated Generation of Complex System's Initial Configurations for Molecular Dynamics and Docking
,”
J. Comput. Chem.
,
24
(
7
), pp.
819
825
.
7.
Würtz
,
D.
,
Monagan
,
M.
, and
Peikert
,
R.
,
1994
, “
The History of Packing Circles in a Square
,”
Maple Technical Newsletter
,
1
, pp.
35
42
.
8.
Torres
,
J.
,
Hitschfeld
,
N.
,
Ruiz
,
R. O.
, and
Ortiz-Bernardin
,
A.
,
2020
, “
Convex Polygon Packing Based Meshing Algorithm for Modeling of Rock and Porous Media
,”
Int. Conf. Comput. Sci.
,
2020
(
1
), pp.
257
269
.
9.
Zhao
,
H.
,
She
,
Q.
,
Zhu
,
C.
,
Yang
,
Y.
, and
Xu
,
K.
,
2020
, “
Online 3D Bin Packing With Constrained Deep Reinforcement Learning
,”
Proceedings of the AAAI Conference on Artificial Intelligence
,
Virtual
,
Feb. 2–9
, pp.
741
749
.
10.
Romanova
,
T.
,
Pankratov
,
A.
,
Litvinchev
,
I.
,
Pankratova
,
Y.
, and
Urniaieva
,
I.
,
2019
, “
Optimized Packing Clusters of Objects in a Rectangular Container
,”
Math. Probl. Eng.
,
2019
(
1
), pp.
1
12
.
11.
Cagan
,
J.
,
Shimada
,
K.
, and
Yin
,
S.
,
2002
, “
A Survey of Computational Approaches to Three-Dimensional Configuration Problems
,”
Comput. Aided Des.
,
34
(
8
), pp.
597
611
.
12.
Papadimitriou
,
C. H.
,
1994
,
Computational Complexity
,
Addison-Weseley
,
Reading, MA
.
13.
Garey
,
M. R.
, and
Johnson
,
D. S.
,
1979
, “
Computers and Intractability: A Guide to the Theory of NP-Completeness
”.
14.
Lawler
,
E. L.
,
1985
,
The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization
,
Wiley
,
New York
.
15.
Loiola
,
E. M.
,
de Abreu
,
N. M. M.
,
Boaventura-Netto
,
P. O.
,
Hahn
,
P.
, and
Querido
,
T.
,
2007
, “
A Survey for the Quadratic Assignment Problem
,”
Eur. J. Oper. Res.
,
176
(
2
), pp.
657
690
.
16.
Garey
,
M. R.
, and
Johnson
,
D. S.
,
1996
, “
Approximation Algorithms for Bin-Packing: A Survey
,”
Approximation Algorithms NP-Hard Probl.
,
266
(
1
), pp.
147
172
.
17.
Li
,
W.
,
Ding
,
Y.
,
Yang
,
Y.
,
Sherratt
,
R. S.
,
Park
,
J. H.
, and
Wang
,
J.
,
2020
, “
Parameterized Algorithms of Fundamental NP-Hard Problems: A Survey
,”
Hum.-Centric Comput. Inf. Sci.
,
10
(
1
), p.
1
.
18.
Yang
,
P.
, and
Qin
,
X.
,
2009
, “
A Hybrid Optimization Approach for Chip Placement of Multi-Chip Module Packaging
,”
Microelectron. J.
,
40
(
8
), pp.
1235
1243
.
19.
Tiwari
,
S.
,
Fadel
,
G.
, and
Fenyes
,
P.
,
2010
, “
A Fast and Efficient Compact Packing Algorithm for SAE and ISO Luggage Packing Problems
,”
ASME J. Comput. Inf. Sci. Eng.
,
10
(
2
), p.
021010
.
20.
Carrick
,
C.
, and
Kim
,
I. Y.
,
2019
, “
Packaging Optimization Using the Dynamic Vector Fields Method
,”
Int. J. Numer. Methods Eng.
,
120
(
7
), pp.
1
20
.
21.
Douglas
,
C.
,
2022
, “
Packaging Optimization of Practical Systems Using a Dynamic Acceleration Methodology
,”
M.A.Sc. thesis
,
Department of Mechanical and Materials Engineering, Queen’s University
,
Kingston, ON, Canada
.
22.
Bar-Cohen
,
A.
,
1999
, “
Thermal Packaging for the 21st Century: Challenges and Options
,”
Proceedings of the Fifth Therminic-International Workshop Thermal Investigations of ICs and Systems
,
Rome, Italy
,
Oct. 3–6
, pp.
3
6
.
23.
Hsieh
,
C.-C.
,
Wu
,
C.-H.
, and
Yu
,
D.
,
2016
, “
Analysis and Comparison of Thermal Performance of Advanced Packaging Technologies for State-of-the-Art Mobile Applications
,”
Proceedings of the Fifth 2016 IEEE 66th Electronic Components and Technology Conference (ECTC)
,
Las Vegas, NV
,
May 31–June 3
, pp.
1430
1438
.
24.
Kwon
,
Y.-H.
,
Bang
,
H.-S.
, and
Bang
,
H.-S.
,
2016
, “
Viscoplasticity Behavior of a Solder Joint on a Drilled Cu Pillar Bump Under Thermal Cycling Using FEA
,”
J. Electron. Mater.
,
46
(
2
), pp.
833
840
.
25.
Zivcak
,
J.
,
Sarik
,
M.
, and
Hudak
,
R.
,
2016
, “
FEA Simulation of Thermal Processes During the Direct Metal Laser Sintering of Ti64 Titanium Powder
,”
Meas. J. Int. Meas. Confed.
,
94
(
1
), pp.
893
901
.
26.
Lu
,
T.
,
2019
, “
A Thermal FEA Modeling of Multiple Machining Processes for Practical Machining Process Optimization
,”
Proc. Manuf.
,
33
(
1
), pp.
208
215
.
27.
Zhou
,
L.
,
Vieira
,
R.
,
Harrison
,
S.
,
Karnes
,
D.
, and
Lipschultz
,
B.
,
2014
, “
Thermal FEA for Alcator C-Mod Advanced Outer Divertor
,”
IEEE Trans. Plasma Sci.
,
42
(
3
), pp.
563
567
.
28.
Abid
,
M.
,
Nash
,
D. H.
,
Javed
,
S.
, and
Wajid
,
H. A.
,
2018
, “
Performance of a Gasketed Joint Under Bolt up and Combined Pressure, Axial and Thermal Loading—FEA Study
,”
Int. J. Press. Vessels Pip.
,
168
(
1
), pp.
166
173
.
29.
Dede
,
E. M.
,
Gao
,
Y.
,
Zhou
,
Y.
,
Sankaranarayanan
,
V.
,
Zhou
,
F.
,
Maksimovic
,
D.
, and
Erickson
,
R. W.
,
2021
, “
Thermal Design, Optimization, and Packaging of Planar Magnetic Components
,”
IEEE Trans. Compon. Packag. Manuf. Technol.
,
11
(
9
), pp.
1480
1488
.
31.
Secil
,
S.
, and
Ozkan
,
M.
,
2022
, “
Minimum Distance Calculation Using Skeletal Tracking for Safe Human-Robot Interaction
,”
Rob. Comput. Integr. Manuf.
,
73
(
1
), p.
102253
.
32.
Lien
,
J. M.
, and
Amato
,
N. M.
,
2007
, “
Approximate Convex Decomposition of Polyhedral and Its Applications
,”
Proceedings of the ACM Symposium on Solid and Physical Modeling
,
Beijing, China
,
June 4–6
, pp.
121
131
.
33.
Mamou
,
K.
, and
Ghorbel
,
F.
,
2009
, “
A Simple and Efficient Approach for 3D Mesh Approximate Convex Decomposition
,”
Proceedings of the 16th IEEE International Conference on Image Processing
,
Cairo, Egypt
,
Nov. 7–10
, pp.
3501
3504
.
34.
Conway
,
J. H.
, and
Sloane
,
N. J. A.
,
1993
,
Sphere Packings, Lattices and Groups
, Vol.
290
,
Springer-Verlag
,
New York
.
35.
Song
,
C.
,
Wang
,
P.
, and
Makse
,
H. A.
,
2008
, “
A Phase Diagram for Jammed Matter
,”
Nature
,
453
(
7195
), pp.
629
632
.
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