Use of technological constraints as enumeration criteria for the solution of a travelling salesman problem applicable to production machinery

Abstract

The routing of tools, dies, torches, electric arcs, ray beams and jets to produce features on a workpiece is a travelling salesman problem (TSP) of variable size and unpredictable node distribution. The orientation of the nodes may be in two-dimensional planes or three-dimensional spaces. An optimal path for the TSP can be found using tour construction, subtour elimination and tour-to- tour improvement procedures. Exact solution of the TSP for large numbers of nodes incurs a high computing cost. Enumeration of the problem domain can lead to a globally optimal solution at reduced computing cost. Technological constraints can be used to reduce the problem size for formulation as a TSP under multiple constraints. The solution of a TSP with constraints results in large savings in non-productive movement with no changes in productive movement. The savings in non-productive movement in repetitive batch-type manufacturing lead to reduced machine tool residence time and lower power consumption.