Fast Neighborhood Search Heuristics for the Colorful Bin Packing Problem: Conclusion and Referencesby@heuristicsearch

Fast Neighborhood Search Heuristics for the Colorful Bin Packing Problem: Conclusion and References

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Our bin packing approaches have proven highly effective, achieving solutions close to optimal even in scenarios with numerous items. The success stems from the Two-by-Two heuristic's quality, efficient neighborhoods, and the strong relaxation properties of Gilmore and Gomory Formulation. These strategies collectively contribute to near-optimal solutions and are particularly useful in color-constrained bin packing scenarios.
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(1) Renan F. F. da Silva, Institute of Computing, University of Campinas;

(2) Yulle G. F. Borges, Institute of Computing, University of Campinas;

(3) Rafael C. S. Schouery, Institute of Computing, University of Campinas.

9 Conclusion

Our approaches were quite effective, enabling us to find solutions very close to the optimal solution, even in instances with many items. These results are partly due to the excellent quality of the solutions given by Two-by-Two, which efficiently handles color constraints. Another positive factors are our neighborhoods, which are efficient in quality and time complexity. Lastly, Gilmore and Gomory Formulation has a strong relaxation for the BPP, and this property may extend to CBPP. For a strong relaxation, the values for the optimal fractional and integer solutions are very close, so the patterns used by relaxation probably belong to integer solutions of high quality. Therefore, this is an excellent method to find a good set of patterns for the initial build of GRASP.

Acknowledgements This project was supported by the S˜ao Paulo Research Foundation (FAPESP) grants #2015/11937-9 and #2020/06511-0; and the Brazilian National Council For Scientific and Technological Development (CNPq) grants #144257/2019-0, #311039/2020-0 and #425340/2016 3.


Conflict of interest All authors declare that they have no conflicts of interest.


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