att_abstract={{We present a novel multi-population biased random-key genetic algorithm
(BRKGA) for the 2D and 3D bin packing problem.  The approach uses a 
maximal-space representation to manage the free spaces in the bins.
The proposed algorithm uses a decoder based on a novel placement
procedure within a multi-population genetic algorithm based on random
keys. The BRKGA is used to evolve the order in which the boxes are packed
into the bins and the parameters used by the placement procedure. Two
heuristic procedures are used to determine the bin and the free maximal
space where each box is placed. A novel fitness function that improves
significantly the quality of the solutions produced is also developed.
The new approach is extensively tested on 858 problem instances from
the literature. The computational experiments demonstrate not only that
the approach performs extremely well, but that it obtains the best
overall results when compared with other approaches published in the
literature. It reduced the total number of bins used from 9803 to 9772
for the 3D instances and from 7241 to 7234 for the 2D instances.
	att_categories={C_CCF.7, C_CCF.8},
	att_copyright_notice={{The definitive version was published in  2012. {{, Volume 145}}{{, Issue 2}}{{, 2012-12-31}}{{, http://dx.doi.org/10.1016/j.ijpe.2013.04.019}}
	att_tags={Bin packing,  heuristic,  genetic algorithm,  biased random-key genetic algorithm,  three-dimensional,  random keys},
	author={Mauricio Resende and José F. Gonçalves},
	institution={{International Journal of Production Economics}},
	title={{A biased random-key genetic algorithm for a 2D and 3D bin packing