【正文】 在加文的程式 中實(shí)現(xiàn)了 最低值，表面粗糙度及各自的 值 都達(dá)到了 最佳條件。這些參數(shù)對(duì)表面粗糙度 的 建立，方差分析 極具意義 。第一次和第二次 為建立 數(shù)學(xué)模型，從加工參數(shù) 方面 ，制訂了表面粗糙度預(yù)測(cè)響應(yīng)面方法（丹參） ，在此基礎(chǔ)上的實(shí)驗(yàn)結(jié)果。 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 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: Y = ?(S, f, α , r)+∈ 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: Ra = CSa f bα crd , (1) 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: ln Ra = ln C+a ln S+b ln f +c ln α +d ln r . (2) 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: Y1 = Y?∈ =b0x0 +b1x1+b2x2+b3x3 +b4x4 (3) 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: Y2 = Y?∈ =b0x0 +b1x1+b2x2 +b3x3+b4x4 +b12x1x2 +b23x2x3 +b14x1x4 +b24x2x4 +b13x1x3 +b34x3x4 +b11x21 +b22x22 +b33x23 +b44x24 (4) 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 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 techniques are not efficient when the practical search space is too large. These algorithms are not robust. They are inclined to obtain a local optimal solution. Numerous constraints and number of passes make the machining optimization problem more plicated. So, it was decided to employ geic algorithms as an optimization technique. GA e under the class of nontraditional search and optimization techniques. GA are different from traditional optimization techniques in the following ways: work with a coding of the parameter set, not the parameter themselves. search from a population of points and not a single point. use information of fitness function, not derivatives or other auxiliary knowledge. use probabilistic transition rules not deterministic rules. is very likely that the expected GA solution will be the global solution. Geic algorithms (GA) form a class of adaptive heuristics based on principles derived from the dynamics of natural population geics. The searching process simulates the natural evaluation of biological creatures and turns out to be an intelligent exploitation of a random search. The mechanics of a GA is simple, involving copying of binary strings. Simplicity of operation and putational efficiency are the two main attractions of the geic algorithmic approach. The putations are carried out in three stages to get a result in one generation or iteration. The three stages are reproduction, crossover and mutation. In order to use GA to solve any problem, the variable is typically encoded into a string (binary coding) or chromosome structure which represents a possible solution to the