A caving degree based flake arrangement approach for the container loading problem

A caving degree based flake arrangement (CDFA) approach for the NP-hard container loading problem is presented in this paper. Based on the caving degree approach, CDFA binds items in the same size into a larger flake whose binding number is 1 in one of its three dimensions, and then it tries to pack the flake into a corner nearest to the eight vertices of the container. Then, caving degree is redefined to evaluate different placements of flakes, such that an action is selected whose packing flake is as compact and close as possible with other flakes already in (the six surfaces of the container can be regarded as six special flakes). CDFA is extensively tested over two sets of famous benchmarks: 15 LN instances and 1500 BR instances. Experimental results show the high performance of this new approach. Especially for the LN set, CDFA improved current highest volume utilization by 1.3% and 0.5% for two difficult instances LN2 and LN6 respectively; at the same time it got optimal layouts for the other 13 instances, equalling current best records. This breaks current best record created and held by Bortfeldt and Gehring since 1998. Besides, CDFA achieved the second highest average volume utilization among several top efficient algorithms for the BR set.