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Hybrid genetic algorithms for the three-dimensional multiple container packing problem

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Abstract

The three-dimensional multiple container packing problem (3DMCPP) is used to determine non-overlapping packing of a set of finite three-dimensional rectangular items into the minimum number of identical containers. The decision framework consists of two main activities: item assignment and packing. This paper presents new hybrid genetic algorithms (HGAs) that address current limitations related to the 3DMCPP and enable use of relatively few containers. Rotation constraints are also addressed. An HGA is developed for small problems, and another HGA is created for large problems. Both of the HGAs combine the largest left space first item assignment strategy, a basic genetic algorithm, and the deepest bottom left with fill strategy. Experiments were conducted to demonstrate the performances of the HGAs with two different types of data sets. The results show that the proposed HGAs yield solutions, in a reasonable amount of time, in which relatively few containers are needed.

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Acknowledgments

The authors are grateful for the useful comments from an associate editor and two anonymous referees. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0025714).

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Authors and Affiliations

  1. Engineering Research Institute, Seoul National University, Seoul, 151-744, Korea

    Xuehao Feng

  2. Department of Industrial Engineering, Seoul National University, Seoul, 151-744, Korea

    Ilkyeong Moon

  3. Dongkuk Steel Group, Seoul, 100-210, Korea

    Jeongho Shin

Authors
  1. Xuehao Feng
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  2. Ilkyeong Moon
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  3. Jeongho Shin
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Corresponding author

Correspondence to Ilkyeong Moon.

Appendix

Appendix

See Table 7.

Table 7 Solution of a small problem of Class 1
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Feng, X., Moon, I. & Shin, J. Hybrid genetic algorithms for the three-dimensional multiple container packing problem. Flex Serv Manuf J 27, 451–477 (2015). https://doi.org/10.1007/s10696-013-9181-8

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