Heuristics with a new block strategy for the single and multiple containers loading problems

A heuristic algorithm using new block strategy for the heterogeneous single and multiple containers loading problem (CLP) is proposed in this paper. In order to solve the single CLP, this algorithm fills unused spaces with the homogeneous load-blocks of identically oriented boxes and splits residual space into three child-spaces starting with an empty container. An initial container pattern is first built applying this approach recursively until all boxes are stowed or no unused spaces are left. And then, alternative container patterns are generated after replacing the load-blocks of the pattern-determining spaces in the initial container pattern with the alternative-blocks previously stored. Finally, an improvement procedure compares these alternatives with the initial container pattern to identify an improved container pattern. An algorithm for the multiple CLP uses the single CLP algorithm to generate an initial solution and uses improvement procedures to improve the initial solution. Numerical experiments with 715 test cases for the single CLP and 47 test cases for the multiple the CLP revealed the excellent performance of this algorithm.