【正文】 ece materials, 11 L 17 free machining steel, 62 353 free machining brass and 2024 aluminium using a single fluted HSS milling cutter. It has been found that pressure and friction act on the chip – tool interface decrease with the increase of feed rate and with the decrease of the flow angle, while the cutting speed has a negligible effect on some of the material dependent parameters. Process parameters are summarized into empirical equations as functions of feed rate and tool rotation angle for each work material. However, researchers have not taken into account the effects of cutting conditions and tool geometry simultaneously。 besides these studies have not considered the optimization of the cutting process. As end milling is a process which involves a large number f parameters, bined influence of the significant parameters an only be obtained by modelling. Mansour and Abdallaet al. [5] have developed a surface roughness model for the end milling of EN32M (a semifree cutting carbon case hardening steel with improved merchantability). The mathematical model has been developed in terms of cutting speed, feed rate and axial depth of cut. The affect of these parameters on the surface roughness has been carried out using response surface methodology (RSM). A first order equation covering the speed range of 30–35 m/min and a second order equation covering the speed range of 24–38 m/min were developed under dry machining conditions. Alauddin et al. [6] developed a surface roughness model using RSM for the end milling of 190 BHN steel. First and second order models were constructed along with contour graphs for the selection of the proper bination of cutting speed and feed to increase the metal removal rate without sacrificing surface quality. Hasmi et al. [7] also used the RSM model for assessing the influence of the workpiece material on the surface roughness of the machined surfaces. The model was developed for milling operation by conducting experiments on steel specimens. The expression shows, the relationship between the surface roughness and the various parameters。 namely, the cutting speed, feed and depth of cut. The above models have not considered the affect of tool geometry on surface roughness. Since the turn of the century quite a large number of attempts have been made to find optimum values of machining parameters. Uses of many methods have been reported in the literature to solve optimization problems for machining parameters. Jain and Jain [8] have used neural works for modeling and optimizing the machining conditions. The results have been validated by paring the optimized machining conditions obtained using geic algorithms. Suresh et al. [9] have developed a surface roughness prediction model for turning mild steel using a response surface methodology to produce the factor affects of the individual process parameters. They have also optimized the turning process using the surface roughness prediction model as the 4 objective function. Considering the above, an attempt has been made in this work to develop a surface roughness model with tool geometry and cutting conditions on the basis of experimental results and then optimize it for the selection of these parameters within the given constraints in the end milling operation. 3 Methodology In this work, mathematical models have been developed using experimental results with the help of response surface methodology. The purpose of developing mathematical models relating the machining responses and their factors is to facilitate the optimization of the machining process. This mathematical model has been used as an objective function and the optimization was carried out with the help of geic algorithms. Mathematical formulation Response surface methodology (RSM) is a bination of mathematical and statistical techniques useful for modelling and analyzing the problems in which several independent variables influence a dependent variable or response. The mathematical models monly used are represented by: where Y is the machining response, ? is the response function and S, f , α, r are milling variables and ∈ is the error which is normally distributed about the observed response Y with zero mean. The relationship between surface roughness and other independent variables can be represented as follows， where C is a constant and a, b, c and d are exponents. To facilitate the determination of constants and exponents, this mathematical model will have to be linearized by performing a logarithmic transformation as follows: The constants and exponents C, a, b, c and d can be determined by the method of least squares. The first order linear model, developed from the above functional relationship using least squares method, can be represented as follows: where Y1 is the estimated response based on the firstorder equation, Y is the measured surface roughness on a logarithmic scale, x0 = 1 (dummy variable), x1, x2, x3 and x4 are logarithmic transformations of cutting speed, feed rate, radial rake angle and nose radius respectively, ∈ is the experimental error and b values are the estimates of corresponding parameters. The general second order polynomial response is as given below: where Y2 is the estimated response based on the second order equation. The parameters, . b0, b1, b2, b3, b4, b12, b23, b14, etc. are to be estimated by the method of least squares. Validity of 5 the selected model used for optimizing the process parameters has been tested with the help of statistical tests, such as Ftest, chi square test, etc. [10]. Optimization using geic algorithms Most of the researchers have used traditional optimization techniques for solving machining problems. The traditional methods of optimization and search do not fare well over a broad spectrum of problem domains. Traditional techn