Fast Neighborhood Search Heuristics for the Colored Bin Packing Problem (2310.04471v2)
Abstract: The Colored Bin Packing Problem (CBPP) is a generalization of the Bin Packing Problem (BPP). The CBPP consists of packing a set of items, each with a weight and a color, in bins of limited capacity, minimizing the number of used bins and satisfying the constraint that two items of the same color cannot be packed side by side in the same bin. In this article, we proposed an adaptation of BPP heuristics and new heuristics for the CBPP. Moreover, we propose a set of fast neighborhood search algorithms for CBPP. These neighborhoods are applied in a meta-heuristic approach based on the Variable Neighborhood Search (VNS) and a matheuristic approach that combines linear programming with the meta-heuristics VNS and Greedy Randomized Adaptive Search (GRASP). The results indicate that our matheuristic is superior to VNS and that both approaches can find near-optimal solutions for a large number of instances, even for those with many items.
- Belov G, Scheithauer G (2006) A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting. European Journal of Operational Research 171(1):85–106. https://doi.org/10.1016/j.ejor.2004.08.036
- Brandão F, Pedroso JP (2016) Bin packing and related problems: General arc-flow formulation with graph compression. Computers & Operations Research 69:56–67. https://doi.org/10.1016/j.cor.2015.11.009
- Buljubašić M, Vasquez M (2016) Consistent neighborhood search for one-dimensional bin packing and two-dimensional vector packing. Computers & Operations Research 76:12–21. https://doi.org/10.1016/j.cor.2016.06.009
- Carvalho JMVd (1999) Exact solution of bin‐packing problems using column generation and branch‐and‐bound. Annals of Operations Research 86(0):629–659. https://doi.org/10.1023/A:1018952112615
- Castelli M, Vanneschi L (2014) A hybrid harmony search algorithm with variable neighbourhood search for the bin-packing problem. 2014 Sixth World Congress on Nature and Biologically Inspired Computing (NaBIC 2014) pp 1–6. https://doi.org/10.1109/NaBIC.2014.6921849
- Delorme M, Iori M (2020) Enhanced pseudo-polynomial formulations for bin packing and cutting stock problems. INFORMS Journal on Computing 32(1):101–119. https://doi.org/10.1287/ijoc.2018.0880
- Demšar J (2006) Statistical comparisons of classifiers over multiple data sets. The Journal of Machine learning research 7:1–30
- Feo TA, Resende MG (1989) A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters 8(2):67–71. https://doi.org/https://doi.org/10.1016/0167-6377(89)90002-3
- Fleszar K, Hindi KS (2002) New heuristics for one-dimensional bin-packing. Computers & Operations Research 29(7):821–839. https://doi.org/10.1016/S0305-0548(00)00082-4
- Friedman M (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association 32(200):675–701. https://doi.org/10.1080/01621459.1937.10503522
- Gilmore PC, Gomory RE (1961) A linear programming approach to the cutting-stock problem. Operations Research 9(6):849–859. https://doi.org/10.1287/opre.29.6.1092
- Gupta JND, Ho JC (1999) A new heuristic algorithm for the one-dimensional bin-packing problem. Production Planning & Control 10(6):598–603. https://doi.org/10.1080/095372899232894
- Iman RL, Davenport JM (1980) Approximations of the critical region of the fbietkan statistic. Communications in Statistics - Theory and Methods 9(6):571–595. https://doi.org/10.1080/03610928008827904
- Mladenović N, Hansen P (1997) Variable neighborhood search. Computers & Operations Research 24(11):1097–1100. https://doi.org/10.1016/S0305-0548(97)00031-2
- Nemenyi PB (1963) Distribution-free multiple comparisons. PhD thesis, Princeton University
- Vance PH (1998) Branch-and-price algorithms for the one-dimensional cutting stock problem. Computational Optimization and Applications 9(3):211–228. https://doi.org/10.1023/A:1018346107246
- Renan F. F. da Silva (2 papers)
- Yulle G. F. Borges (3 papers)
- Rafael C. S. Schouery (17 papers)