Optimization Models of Tool Path Problem for CNC Sheet Metal Cutting Machines

The problem of tool path optimization for CNC sheet metal cutting equipment is considered. Sheet metal cutting equipment includes laser/plasma/gas/water-jet machines and some others. Users of CAD/CAM systems develop numerical control programs for the cutting equipment after nesting of parts onto the sheet. The control programs contain information about tool path. The tool path is a routing of cutter head used for cutting of sheet material. Classification and the correspondent mathematical models of tool path problem are considered. The tasks of cost/time minimization for various types of cutting techniques are formalized. Mathematical formalization of technological constraints for these tasks is also described. Unlike the known analogs this formalization allows to consider constraints of thermal cutting. In some cases the optimization tasks can be interpreted as discrete optimization problem (generalized travel salesman problem with additional constraints, GTSP). In paper also the developed exact algorithm and some heuristic algorithms of tool path optimization based on described models is reported. Results of computing experiments for some instances are given © 2016The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0006