Multi-objective optimization of a two-dimensional cutting problem using genetic algorithms

Abstract The work presented here describes a method of optimizing the layout of rectangular parts placed on a rectangular sheet to cut out various parts. Two types of cutting problems have been investigated (i) in which guillotine cutting (cutting from edge to edge) is required (mostly metallic sheets where each cut is made individually for one single sheet), and (ii) the one in which guillotine cutting is not essential (e.g. cuts which can be made using a punch) i.e. for materials like paper or rubber where the sheets to be cut can be laid side by side or on top of one another and one single cut can be made. The optimization of the layout of rectangular parts is achieved with respect to two design objectives involving minimization of (i) the length of the mother sheet required, and (ii) also the total number of cuts required to obtain all the parts from the mother sheet. A tree encoded multi-objective genetic algorithm has been used to study both guillotine and non-guillotine cutting cases, using a binary representation of the variables, and it is shown for the known cases that the globally optimum solutions are obtained.

[1]  M. S. Shunmugam,et al.  Multi-objective optimization of wire-electro discharge machining process by Non-Dominated Sorting Genetic Algorithm , 2005 .

[2]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[3]  Randy L. Haupt,et al.  Practical Genetic Algorithms , 1998 .

[4]  Dong Wang,et al.  Computational Intelligence-Based Process Optimization for Tandem Cold Rolling , 2005 .

[5]  Janez Kopac,et al.  Testing of machinability of mould steel 40CrMnMo7 using genetic algorithm , 2005 .

[6]  S. M. Hwang,et al.  Application of a genetic algorithm to the optimal design of the die shape in extrusion , 1997 .

[7]  Mahdi Mahfouf,et al.  Optimal Design of Alloy Steels Using Multiobjective Genetic Algorithms , 2005 .

[8]  George S. Dulikravich,et al.  Chemical Composition Design of Superalloys for Maximum Stress, Temperature, and Time-to-Rupture Using Self-Adapting Response Surface Optimization , 2005 .

[9]  Hasan Kurtaran,et al.  Application of response surface methodology in the optimization of cutting conditions for surface roughness , 2005 .

[10]  Tapan P. Bagchi,et al.  Multiobjective Scheduling by Genetic Algorithms , 1999 .

[11]  Catarina F. Castro,et al.  Eliminating Forging Defects Using Genetic Algorithms , 2005 .

[12]  Primoz Potocnik,et al.  Nonlinear model predictive control of a cutting process , 2002, Neurocomputing.

[13]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[14]  George S. Dulikravich,et al.  Control of Unsteady Solidification Via Optimized Magnetic Fields , 2005 .

[15]  Luísa Costa Sousa,et al.  Optimisation of shape and process parameters in metal forging using genetic algorithms , 2004 .

[16]  Miran Brezocnik,et al.  Modeling of Hot Yield Stress Curves for Carbon Silicon Steel by Genetic Programming , 2005 .

[17]  Miran Brezocnik,et al.  Comparison Between Genetic Algorithm and Genetic Programming Approach for Modeling the Stress Distribution , 2005 .

[18]  Nirupam Chakraborti,et al.  Regulating Crown and Flatness During Hot Rolling: A Multiobjective Optimization Study Using Genetic Algorithms , 2005 .

[19]  J. Jackiewicz.  Application of the Evolution Strategy for Assessment of Deformation and Fracture Response of Ferritic Steel During Its Manufacturing , 2005 .

[20]  Nirupam Chakraborti,et al.  Genetic algorithms in these changing steel times , 2005 .

[21]  Nirupam Chakraborti,et al.  Genetic algorithms in materials design and processing , 2004 .

[22]  Nirupam Chakraborti,et al.  A Genetic-Algorithms-Based Multiobjective Approach for a Three-Dimensional Guillotine Cutting Problem , 2005 .

[23]  Somnath Ghosh,et al.  Computer aided approach for design and optimization of cold forging sequences for automotive parts , 1994 .

[24]  J. A. Spim,et al.  Application of a Solidification Mathematical Model and a Genetic Algorithm in the Optimization of Strand Thermal Profile Along the Continuous Casting of Steel , 2005 .

[25]  Biswajit Mahanty,et al.  Optimization of Hot Rolled Coil Widths Using a Genetic Algorithm , 2003 .

[26]  T. Slivnik,et al.  The optimal cut of sheet metal belts into pieces of given dimensions , 1997 .

[27]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 2000, Springer Berlin Heidelberg.

[28]  Kozo Osakada,et al.  Determination of hammering sequence in incremental sheet metal forming using a genetic algorithm , 1996 .