Model of megalopolises in the tool path optimisation for CNC plate cutting machines

Abstract

We consider the issues of tool path optimisation under constraints and formulate a mathematical problem of visiting megalopolises. The megalopolises model is the result of the discretisation of the tool path problem for CNC plate cutting machines. The order of visits is subject to precedence constraints. In addition, the cost functions depend on the set of pending tasks. The quality criterion is a variety of the additive criterion. The problem is established within the dynamic programming framework, however, a heuristic is proposed and implemented to solve practical problems of large dimensionality.

Keywords:

• CNC cutting machines
• nesting
• tool path
• travelling salesman problem
• precedence constraints
• CAD/CAM
• dynamic programming
• heuristics

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Act 211 Government of the Russian Federation, [contract number 02.A03.21.0006], and by the Russian Foundation for Basic Research, [project number 17-08-01385].