ORIGINAL ARTICLE An integrated evolutionary approach for modelling and optimization of laser beam cutting process D. Kondayya & A. Gopala Krishna Received: 25 May 2011 /Accepted: 10 April 2012 # Springer-Verlag London Limited 2012 Abstract This paper presents a new integrated methodology based on evolutionary algorithms (EAs) to model and optimize the laser beam cutting process. The proposed study is divided into two parts. Firstly, genetic programming (GP) approach is used for empirical modelling of kerf width (Kw) and material removal rate (MRR) which are the important performance measures of the laser beam cutting process. GP, being an extension of the more familiar genetic algorithms, recently has evolved as a powerful optimization tool for nonlinear modelling resulting in credible and accurate models. Design of experiments is used to conduct the experiments. Four prom- inent variables such as pulse frequency, pulse width, cutting speed and pulse energy are taken into consideration. The de- veloped models are used to study the effect of laser cutting parameters on the chosen process performances. As the output parameters Kw and MRR are mutually conflicting in nature, in the second part of the study, they are simultaneously optimized by using a multi-objective evolutionary algorithm called non- dominated sorting genetic algorithm II. The Pareto optimal solutions of parameter settings have been reported that provide the decision maker an elaborate picture for making the optimal decisions. The work presents a full-fledged evolutionary ap- proach for optimization of the process. Keywords Laser beam cutting . Modelling . Genetic programming . Multi-objective optimization . NSGA-II 1 Introduction Laser beam cutting belongs to the group of thermal cutting processes wherein the output of high-power laser is directed and focused to a small spot on the material to be cut. The material then either melts or vaporizes. As the beam moves relative to the material, a cut channel (the kerf) is formed, having an edge with a high-quality surface finish. The molten material is blown out of the developing kerf by using a relatively high-pressure coaxial assist gas. The principle of laser beam cutting is shown in Fig. 1. Of all the industrial laser cutting applications, the vast majority of these are used for the cutting of metal sheets worldwide and this applica- tion has progressed dramatically in the past 5 years [1]. The reasons for the widespread usage of lasers for cutting of metallic sheets is: process is fast and noncontact, superior edge quality, low surface roughness, small heat-affected zones (HAZ), ability to create fine and intricate details [2]. The most important performance measures in laser cutting are kerf width (Kw) and material removal rate (MRR) [3]. Kerf width indicates the degree of accuracy, whereas material re- moval rate decides the production rate and economics of machining. These performance measures are affected by input cutting variables such as laser power, pulse frequency, pulse duration, type of assist gas and gas pressure. Laser cutting is a highly complicated process wherein a large number of param- eters need to be precisely controlled in unison, hence experi- mental optimization of the process is costly and time- consuming. Moreover owing to the nonlinearity and the highly complicated interactions between process parameters of the laser process, the current analytical models cannot provide D. Kondayya (*) Department of Mechanical Engineering, Sreenidhi Institute of Science and Technology, Hyderabad PIN-501 301 Andhra Pradesh, India e-mail: d_kondayya@yahoo.co.in A. Gopala Krishna Department of Mechanical Engineering, University College of Engineering, Jawaharlal Nehru Technological University, Kakinada PIN-533 003 Andhra Pradesh, India e-mail: dr.a.gopalakrishna@gmail.com Int J Adv Manuf Technol DOI 10.1007/s00170-012-4165-5