Optimal layout and path planning for flame cutting of sheet metals

This paper presents a two-stage methodology for the optimisation of layout and path planning that can be used in flame cutting of sheet metals. The main objective of this paper is to minimise the total travel distance of the flame gun that will not only reduce the cutting time but also the heat effect. The first stage is to use a heuristic to cluster a set of small rectangular items (called workpieces) into one or more large rectangular objects (called blocks) and then best fit these blocks into a given stock. By allowing clustered small items to be cut along common borderlines, the travel distance within blocks is minimised. The second stage is to use genetic algorithms (GAs) to determine an optimal path in consideration of multiple start points for each block. The proposed path planning method provides an advantage by minimising the travel distance between blocks. The combination of the two solutions leads to minimisation of the total travel distance. To demonstrate the effectiveness of the proposed method, a number of cases are studied with results showing a 20% average reduction in the total travel distance in comparison to conventional methods.

[1]  Li Pei-gen.  The cutting process system for metal sheet in CIMS , 2002 .

[2]  Mhand Hifi,et al.  Best-first search and dynamic programming methods for cutting problems: the cases of one or more stock plates , 1997 .

[3]  Gerhard Wäscher.  An LP-based approach to cutting stock problems with multiple objectives , 1990 .

[4]  T. Narendran,et al.  A genetic algorithm approach to the machine-component grouping problem with multiple objectives , 1992 .

[5]  Luca Maria Gambardella,et al.  Ant-Q: A Reinforcement Learning Approach to the Traveling Salesman Problem , 1995, ICML.

[6]  Marco Dorigo,et al.  Distributed Optimization by Ant Colonies , 1992 .

[7]  H. Tolle,et al.  Optimization Methods , 1975 .

[8]  Harald Dyckhoff,et al.  A typology of cutting and packing problems , 1990 .

[9]  D. R. Hayhurst,et al.  Determination of optimal path under approach and exit constraints , 1999, Eur. J. Oper. Res..

[10]  Gerhard Wäscher,et al.  Simulated annealing for order spread minimization in sequencing cutting patterns , 1998, Eur. J. Oper. Res..

[11]  R. Gomory,et al.  A Linear Programming Approach to the Cutting-Stock Problem , 1961 .

[12]  Ralph E. Gomory,et al.  A Linear Programming Approach to the Cutting Stock Problem---Part II , 1963 .

[13]  Cihan H. Daǧli,et al.  Knowledge-based systems for cutting stock problems , 1990 .

[14]  Cihan H. Dagli,et al.  An approach to two-dimensional cutting stock problems , 1987 .

[15]  R. W. Haessler,et al.  Cutting stock problems and solution procedures , 1991 .

[16]  Mohamed F. Hassan,et al.  An Intelligent Approach to Stock Cutting Optimization , 2000 .

[17]  Martina Vandebroek,et al.  A dynamic programming based heuristic for industrial buying of cardboard , 1989 .