att_abstract={{This paper presents a multi-population biased random-key genetic algorithm
(BRKGA) for the Single Container Loading Problem (CLP) where several
rectangular boxes of different sizes are loaded into a single rectangular
container. The approach uses a maximal-space representation to manage
the free spaces in the container. The proposed algorithm hybridizes a
novel placement procedure with a multi-population genetic algorithm based
on random keys. The BRKGA is used to evolve the order in which the box
types are loaded into the container and the corresponding type of layer
used in the placement procedure. A heuristic is used to determine the
maximal space where each box is placed. A novel procedure is developed
for joining free spaces in the case where full support from below is
required. The approach is extensively tested on the complete set of test
problem instances of Bischoff and Ratcliff (1995) and Davies and Bischoff
(1999) and is compared with other approaches. The test set consists of
weakly to strongly heterogeneous instances. The experimental results
validate the high quality of the solutions as well as the effectiveness
of the proposed heuristic.
	att_categories={C_CCF.1, C_CCF.2, C_CCF.7, C_CCF.8},
	att_copyright_notice={{The definitive version was published in Computers and Operations Research (Elsevier). {{, Volume 29}}{{, 2011-12-01}}{{, :10.1016/j.cor.2011.03.009 }} }},
	att_tags={container loading,  genetic algorithm,  multi-population,  random keys, 3D packing},
	author={Mauricio Resende and José F. Gonçalves},
	institution={{Computers and Operations Research
	title={{A parallel multi-population biased random-key genetic algorithm for a container loading problem}},