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Packing Problems in Space Solved by CPLEX: An Experimental Analysis

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Space Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 114))

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Abstract

Cargo loading of module and vehicles, as well as satellite/spacecraft layout design, notoriously represent very challenging space engineering tasks, deemed to become, day after day, ever more demanding in the perspective of the upcoming exploration adventures. Extremely thought provoking packing optimization problems have to be coped with, in the presence of intricate geometries, operational conditions and, usually, very tight balancing requirements.

A modeling-based (as opposed to a pure algorithmic) approach has been the object of a dedicated long lasting research, carried out by Thales Alenia Space. In this chapter, an extension of the classical container loading problem is considered, allowing for tetris-like items, (convex) non-rectangular domains, (non-prefixed) separation planes and static balancing.

The relevant space engineering framework is illustrated firstly, contextualizing its relationship with the more general subject of packing optimization and the topical literature. The problem in question is stated, outlining the underlying mathematical model in use (formulated in terms of Mixed Integer Linear Programming, MILP) and the overall heuristic approach adopted to obtain efficient solutions in practice. An extensive experimental analysis, based on the utilization of CPLEX, as the MILP optimizer, represents the core of this work. Both the MILP model and the related heuristic have been tested on a number of quite demanding case studies, investigating effective MILP strategies up to obtaining satisfactory solutions from a global-optimization point of view. The results shown well pave the way for a promising further dedicated research.

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References

  1. Addis, B., Locatelli, M., Schoen, F.: Efficiently packing unequal disks in a circle: a computational approach which exploits the continuous and combinatorial structure of the problem. Oper. Res. Lett. 36(1), 37–42 (2008)

    MathSciNet  MATH  Google Scholar 

  2. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation (Corrected Ed.). Springer, Berlin (2003). ISBN 978-3540654315

    Google Scholar 

  3. Bennell, J.A., Han, W., Zhao, X., Song, X.: Construction heuristics for two-dimensional irregular shape bin packing with guillotine constraints. Eur. J. Oper. Res. 230(3), 495–504 (2013)

    MathSciNet  MATH  Google Scholar 

  4. Bennell, J.A., Oliveira, J.F.: A tutorial in irregular shape packing problems. J. Oper. Res. Soc. 60(S1), S93–S105 (2009)

    MATH  Google Scholar 

  5. Cagan, J., Shimada, K., Yin, S.: A survey of computational approaches to three-dimensional layout problems. Comput. Aided Des. 34, 597–611 (2002)

    Google Scholar 

  6. Caprara, A., Monaci, M.: On the 2-dimensional knapsack problem. Oper. Res. Lett. 1(32), 5–14 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Cassioli, A., Locatelli, M.: A heuristic approach for packing identical rectangles in convex regions. Comput. Oper. Res. 38(9), 1342–1350 (2011)

    MathSciNet  MATH  Google Scholar 

  8. Castillo, I., Kampas, F.J., Pintér, J.D.: Solving circle packing problems by global optimization: numerical results and industrial applications. Eur. J. Oper. Res. 191(3), 786–802 (2008)

    MathSciNet  MATH  Google Scholar 

  9. Chen, C.S., Lee, S.M., Shen, Q.S.: An analytical model for the container loading problem. Eur. J. Oper. Res. 80, 68–76 (1995)

    MATH  Google Scholar 

  10. Chernov, N., Stoyan, Y.G., Romanova, T.: Mathematical model and efficient algorithms for object packing problem. Comput. Geom. Theory Appl. 43(5), 535–553 (2010)

    MathSciNet  MATH  Google Scholar 

  11. Birgin, E., Martinez, J., Nishihara, F.H., Ronconi, D.P.: Orthogonal packing of rectangular items within arbitrary convex regions by nonlinear optimization. Comput. Oper. Res. 33(12), 3535–3548 (2006)

    MathSciNet  MATH  Google Scholar 

  12. Bortfeldt, A., Wäscher, G.: Container loading problems—a state-of-the-art review. FEMM Working Papers 120007. Otto-von-Guericke University Magdeburg, Faculty of Economics and Management (2012)

    Google Scholar 

  13. Dyckhoff, H., Scheithauer, G., Terno, J.: Cutting and packing. In: Dell’Amico, M., Maffioli, F., Martello, S. (eds.) Annotated Bibliographies in Combinatorial Optimization, pp. 393–412. Wiley, Chichester (1997)

    Google Scholar 

  14. Egeblad, J., Nielsen, B.K., Odgaard, A.: Fast neighborhood search for two-and three-dimensional nesting problems. Eur. J. Oper. Res. 183(3), 1249–1266 (2007)

    MathSciNet  MATH  Google Scholar 

  15. Egeblad, J.: Placement of two- and three-dimensional irregular shapes for inertia moment and balance. In: Morabito, R., Arenales, M.N., Yanasse, H.H. (eds.) Int. Trans. Oper. Res. Special Issue on Cutting, Packing and Related Problems 16(6), 789–807 (2009)

    Google Scholar 

  16. European Space Agency (ESA): Automated transfer vehicle (ATV). www.esa.int/Our\_Activities/Human\_Spaceflight/ATV. Accessed 3 Jan 2016

  17. Fadel, G.M., Wiecek, M.M.: Packing optimization of free-form objects in engineering design. In: Fasano, G., Pintér, J.D. (eds.) Optimized Packings and Their Applications. Springer Optimization and Its Applications, pp. 37–66. Springer Science+Business Media, New York (2015)

    Google Scholar 

  18. Fasano, G.: Solving Non-standard Packing Problems by Global Optimization and Heuristics. SpringerBriefs in Optimization. Springer Science+Business Media, New York (2014)

    MATH  Google Scholar 

  19. Fasano, G.: A modeling-based approach for non-standard packing problems. In: Fasano, G., Pintér, J.D. (eds.) Optimized Packings and Their Applications. Springer Optimization and Its Applications, pp. 67–85. Springer Science+Business Media, New York (2015)

    Google Scholar 

  20. Fasano, G., Lavopa, C., Negri, D., Vola, M.C.: CAST: a successful project in support of the International Space Station logistics. In: Fasano, G., Pintér, J.D. (eds.) Optimized Packings and Their Applications. Springer Optimization and Its Applications, pp. 87–117. Springer Science+Business Media, New York (2015)

    Google Scholar 

  21. Fasano, G., Vola, M.C.: Space module on-board stowage optimization exploiting containers’ empty volumes. In: Fasano, G., Pintér, J.D. (eds.) Modeling and Optimization in Space Engineering, pp. 249–269. Springer Science+Business Media, New York (2013)

    Google Scholar 

  22. Fekete, S., Schepers, J., van der Veen, J.C.: An exact algorithm for higher-dimensional orthogonal packing. Oper. Res. 55(3), 569–587 (2007)

    MathSciNet  MATH  Google Scholar 

  23. Fischer, A., Scheithauer, G.: Cutting and packing problems with placement constraints. In: Fasano, G., Pintér, J.D. (eds.) Optimized Packings and Their Applications. Springer Optimization and Its Applications, pp. 119–156. Springer Science+Business Media, New York (2015)

    MATH  Google Scholar 

  24. Fischetti, M., Luzzi, I.: Mixed-integer programming models for nesting problems. J. Heuristics 15(3), 201–226 (2009)

    MATH  Google Scholar 

  25. Gliozzi, S., Castellazzo, A., Fasano, G.: Container loading problem MIP-based heuristics solved by CPLEX: an experimental analysis. In: Fasano, G., Pintér, J.D. (eds.) Optimized Packings and Their Applications. Springer Optimization and Its Applications, pp. 157–173. Springer Science+Business Media, New York (2015)

    Google Scholar 

  26. Goldreich, O.: Computational Complexity: A Conceptual Perspective. Cambridge University Press, Cambridge (2008)

    MATH  Google Scholar 

  27. Ibaraki, T., Imahori, S., Yagiura, M.: Hybrid metaheuristics for packing problems. In: Blum, C., Aguilera, M.J., Roli, A., Sampels, M. (eds.) Hybrid Metaheuristics: An Emerging Approach to Optimization. Studies in Computational Intelligence (SCI), vol. 114, pp. 185–219. Springer, Berlin (2008)

    Google Scholar 

  28. IBM: CPLEX 12.6.0 User Manual. http://www-01.ibm.com/support/knowledgecenter/SSSA5P_12.6.2/ilog.odms.studio.help/Optimization_Studio/topics/COS_home.html?lang=en (2015)

  29. Iori, M., Martello, S., Monaci, M.: Metaheuristic algorithms for the strip packing problem. In: Pardalos, P.M., Korotkikh, V. (eds.) Optimization and Industry: New Frontiers, pp. 159–179. Kluwer Academic, Hardbound (2003)

    Google Scholar 

  30. Jünger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A. (eds.): 50 Years of Integer Programming 1958–2008: From the Early Years to the State-of-the-Art. Springer, Berlin (2010)

    Google Scholar 

  31. Junqueira, L., Morabito, R., Yamashita, D.S., Yanasse, H.H.: Optimization models for the three-dimensional container loading problem with practical constraints. In: Fasano, G., Pintér, J.D. (eds.) Modeling and Optimization in Space Engineering, pp. 271–294. Springer Science+Business Media, New York (2013)

    MATH  Google Scholar 

  32. Kallrath, J.: Cutting circles and polygons from area minimizing rectangles. J. Global Optim. 43, 299–328 (2009)

    MathSciNet  MATH  Google Scholar 

  33. Litvinchev, I., Infante, L., Ozuna, L.: Approximate packing: integer programming models, valid inequalities and nesting. In: Fasano, G., Pintér, J.D. (eds.) Optimized Packings and Their Applications. Springer Optimization and Its Applications, pp. 187–205. Springer Science+Business Media, New York (2015)

    MATH  Google Scholar 

  34. Martello, S., Pisinger, D., Vigo, D.: The Three-Dimensional Bin Packing Problem. Oper. Res. 48(2), 256–267 (2000)

    MathSciNet  MATH  Google Scholar 

  35. Martello, S., Pisinger, D., Vigo, D., Den Boef, E., Korst, J.: Algorithms for general and robot-packable variants of the three-dimensional bin packing problem. ACM Trans. Math. Softw. 33(1), 7 (2007)

    MATH  Google Scholar 

  36. NASA (National Aeronautics and Space Administration): International Space Station (ISS). www.nasa.gov/mission\_pages/station. Accessed 3 Jan 2016

  37. Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, NewYork (1988)

    MATH  Google Scholar 

  38. Oliveira, J.F., Gomes, A.M., Ferreira, J.S.: TOPOS—a new constructive algorithm for nesting problems. OR Spectr 22(2), 263–284 (2000)

    MathSciNet  MATH  Google Scholar 

  39. Padberg, M.W.: Packing small boxes into a big box. Office of Naval Research, N00014-327, New York University (1999)

    Google Scholar 

  40. Pisinger, D.: Heuristics for the container loading problem. Eur. J. Oper. Res. 141(2), 382–392 (2002)

    MathSciNet  MATH  Google Scholar 

  41. Pisinger, D., Sigurd, M.: The two-dimensional bin packing problem with variable bin sizes and costs. Discret. Optim. 2(2), 154–167 (2005)

    MathSciNet  MATH  Google Scholar 

  42. Preparata, F.P., Shamos, M.I.: Computational Geometry. Monographs in Computer Science. Springer, Berlin (1990)

    Google Scholar 

  43. Ramakrishnan, K., Bennel, J.A., Omar, M.K.: Solving two dimensional layout optimization problems with irregular shapes by using meta-heuristic. In: 2008 IEEE International Conference on Industrial Engineering and Engineering Management, pp. 178–182 (2008)

    Google Scholar 

  44. Silva, J.L.C., Soma, N.Y., Maculan, N.: A greedy search for the three- dimensional bin packing problem: the packing static stability case. Int. Trans. Oper. Res. 10(2), 141–153 (2003)

    MathSciNet  MATH  Google Scholar 

  45. Stetsyuk, P., Romanova, T., Scheithauer, G.: On the global minimum in a balanced circular packing problem. Opt. Lett. (2015). doi:10.1007/s11590-015-0937-9

    MathSciNet  MATH  Google Scholar 

  46. Stoyan, Y., Pankratov, A., Romanova, T.: Quasi-phi-functions and optimal packing of ellipses. J. Glob. Optim. (2015). doi:10.1007/s10898-015-0331-2

    MathSciNet  MATH  Google Scholar 

  47. Stoyan, Y., Romanova, T.: Mathematical models of placement optimization: two- and three-dimensional problems and applications. In: Fasano, G., Pintér, J.D. (eds.) Modeling and Optimization in Space Engineering, pp. 249–269. Science+Business Media, New York (2013)

    Google Scholar 

  48. Stoyan, Y., Romanova, T., Pankratov, A., Chugay, A.: Optimized object packings using quasi-phi-functions. In: Fasano, G., Pintér, J.D. (eds.) Optimized Packings and Their Applications. Springer Optimization and Its Applications, pp. 265–293. Springer Science+Business Media, New York (2015)

    MATH  Google Scholar 

  49. Stoyan, Y., Romanova, T., Pankratov, A., Kovalenko, A., Stetsyuk, P.: Balance layout problems: mathematical modeling and nonlinear optimization. In: Fasano, G., Pintér, J.D. (eds.) Space Engineering: Modeling and Optimization with Case Studies. Springer Science+Business Media, New York (2016)

    MATH  Google Scholar 

  50. Sun, Z., Teng, H.: Optimal layout design of a satellite module. Eng. Opt. 35(5), 513–530 (2003)

    Google Scholar 

  51. Taha, H.A.: Operations Research, 7th edn. Macmillan, New York (2003)

    Google Scholar 

  52. Terashima-Marín, H., Ross, P., Farías-Zárate, C.J., López-Camacho, E., Valenzuela-Rendón, M.: Generalized hyper-heuristics for solving 2D regular and irregular packing problems. Ann. Oper. Res. 179, 369–392 (2010)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

We are very grateful to Jane Evans, for her accurate revision of the whole text and the number of suggestions provided.

Author information

Authors and Affiliations

  1. IBM Italia S.p.A., Rome, Italy

    Stefano Gliozzi

  2. Altran Italia S.p.A.Consultant c/o Thales Alenia Space Italia S.p.A., Turin, Italy

    Alessandro Castellazzo

  3. Exploration and Science, Thales Alenia Space, Turin, Italy

    Giorgio Fasano

Authors
  1. Stefano Gliozzi
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  2. Alessandro Castellazzo
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  3. Giorgio Fasano
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Corresponding author

Correspondence to Stefano Gliozzi .

Editor information

Editors and Affiliations

  1. Exploration and Science Thales Alenia Space, Turin, Italy

    Giorgio Fasano

  2. PCS Inc., Halifax, NS, Canada

    János D. Pintér

Appendix

Appendix

A list of selected test cases and their correspondence within the ‘Three Dimensional Cutting and Packing Data Sets - THPACK 1–7 BR’ is reported below.

 

THPACK tests

 

THPACK tests

 

THPACK tests

Article test name

Set number

Test case

Article test name

Set number

Test case

Article test name

Set number

Test case

GC_1

1

11

NC_1

1

1

GS_1

1

74

GC_2

1

43

NC_2

1

4

GS_2

1

98

GC_3

1

46

NC_3

1

7

GS_3

3

52

GC_4

1

99

NC_4

1

32

GS_4

3

87

GC_5

2

20

NC_5

1

41

GS_5

6

9

GC_6

2

30

NC_6

2

7

GS_6

6

33

GC_7

2

65

NC_7

2

10

GS_7

6

42

GC_8

2

76

NC_8

2

17

GS_8

6

85

GC_9

2

99

NC_9

2

50

GS_9

7

28

GC_10

3

2

NC_10

2

54

GS_10

7

54

GC_11

3

20

NC_11

2

56

   

GC_12

3

29

NC_12

2

58

   

GC_13

3

53

NC_13

2

76

   

GC_14

3

83

NC_14

2

88

   

GC_15

4

4

NC_15

3

13

   

GC_16

4

27

NC_16

3

30

NS_1

1

2

GC_17

4

30

NC_17

3

68

NS_2

1

6

GC_18

4

65

NC_18

3

99

NS_3

3

16

GC_19

4

85

NC_19

4

45

NS_4

3

72

GC_20

4

87

NC_20

4

73

NS_5

4

19

GC_21

5

2

NC_21

4

82

NS_6

4

29

GC_22

5

19

NC_22

4

88

NS_7

4

96

GC_23

5

37

NC_23

5

15

NS_8

5

5

GC_24

5

38

NC_24

5

58

NS_9

5

99

GC_25

5

45

NC_25

5

65

NS_10

6

59

GC_26

5

87

NC_26

5

66

   

GC_27

5

96

NC_27

5

86

   

GC_28

6

29

NC_28

6

1

   

GC_29

6

49

NC_29

6

10

   

GC_30

6

56

NC_30

6

12

   

GC_31

6

66

NC_31

6

34

   

GC_32

6

84

NC_32

6

35

   

GC_33

6

89

NC_33

6

38

   

GC_34

7

45

NC_34

6

65

   

GC_35

7

57

NC_35

6

68

   

GC_36

7

84

NC_36

7

2

   

GC_37

7

99

NC_37

7

11

   
   

NC_38

7

13

   
   

NC_39

7

21

   
   

NC_40

7

50

   
   

NC_41

7

61

   
   

NC_42

7

75

   
   

NC_43

7

78

   

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Gliozzi, S., Castellazzo, A., Fasano, G. (2016). Packing Problems in Space Solved by CPLEX: An Experimental Analysis. In: Fasano, G., Pintér, J.D. (eds) Space Engineering. Springer Optimization and Its Applications, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-319-41508-6_5

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