Multi-objective routing of multi-terminal rectilinear pipe in 3D space by MOEA/D and RSMT

Pipe routing generally exist as various sub-problems such as two-terminal pipe routing, branch pipe routing, single-objective routing and multi-objective routing. In this paper, the 3D branch routing graph is established by using the rectilinear steiner minimal tree (RSMT) theory. In order to solve the model, multi-objective evolutionary algorithm based on decomposition (MOEA/D) is applied to search the final routing optimal solutions. The pipe length, the number of branch points, the energy value and pipe bends are selected as routing objective. Using the energy value to reduce the number of nodes on the Escape Graph, and the program running time is reduced to 1/3. Particularly, when some model parameters are set as specified values, the model becomes some special sub-problems, and the proposed routing algorithm is still available. Finally, some numerical calculations are performed on a 3D routing model, which demonstrate the effectiveness of the proposed method.