About one optimal solution example to the integrated 2d nesting and routing problem for cnc sheet cutting machines

Abstract

Subject of research: a new scientific optimization problem, tentatively called "The Integrated Nesting and Routing Problem (INRP)". INRP combines two well-known optimization problems: the problem of 2D cutting of sheet material into shaped parts (Nesting Problem) and the problem of optimal tool routing for CNC sheet cutting machines (Cutting Path Problem). Purpose of research: to investigate the possibility of developing exact or efficient approximate algorithms for solving practical INRP problems. Methods and objects of research: the object of the study is the mathematical formalization of the substantive formulation of the INRP, the methods are discrete optimization methods and computer-aided design methods used in systems for generating control programs. Main results of research: the paper provides a mathematical formalization of the problem under consideration and provides a model example of designing 2D cutting for shaped parts, which, along with another practical example, shows the using feasibility an integrated cost criterion at solving the practical problems. In particular, it is show the independence the global extremum of the INRP problem from the global extremum of the nesting problem. In this regard, the question of the possibility of developing effective approximate algorithms for solving practical INRP problems was investigated.