Solving the 3D Container Ship Loading Planning Problem by Representation by Rules and Beam Search

This paper formulates the 3D Container ship Loading Planning Problem (3D CLPP) and also proposes a new and compact representation to efficiently solve it. Containers on board a Container ship are placed in vertical stacks, located in different sections. The only way to access the containers is through the top of the stack. In order to unload a container at a given port j, it is necessary to remove the container whose destination is the port j+1, because it is located above the container we want to download. This operation is called “shifting”. A ship container carrying cargo to several ports may require a large number of shifting operations. These operations spend a lot of time and cost and can be avoided by using efficient stowage planning. The key objective of the stowage planning is to minimize the number of container movements and also the ship instability. The binary formulation of this problem is properly described and also an alternative formulation called representation by rules is proposed. A Beam Search is combined with representation by rules to solve the 3D CLPP in manner that ensures that every solution analyzed in the optimization process is compact and feasible.