Heuristic sequencing methods for time optimal tracking of nested, open and closed paths

Tracking sequences of predefined open and closed paths is of crucial interest for applications like laser cutting and similar production processes. The disconnected paths are connected by non-productive, four times continuously differentiable trajectories, which also account for the overall process time. Heuristic methods are applied in order to find a proper sequencing of the open and closed path and thereby minimize the overall process time while respecting constraints given by the system limits. To this end, the exact traversing times of the non-productive linking trajectories are computed, which also have to be time optimal subject to the system limits. While problems with only closed paths present can be formulated as travelling salesman problem, handling open and nested paths introduce additional constraints. Two heuristic algorithms for travelling salesman problems are extended for open path processing and compared with respect to solution quality and calculation time using randomly generated problems. Finally, problems with nested cutting path structures are addressed by extending the heuristic algorithm with the best performance to account for the precedence constraints, associated with these nested structures.