【正文】 the second order model was adequate to represent this process. Hence the second order model was considered as an objective function for optimization using geic algorithms. This second order model was also validated using the chi square test. The calculated chi square value of the model was and them tabulated value at χ 2 is , as shown in Table 6, which indicates that % of the variability in surface roughness was explained by this model. Using the second order model, the surface roughness of the ponents produced by end milling can be estimated with reasonable accuracy. This model would be optimized using geic algorithms (GA). The optimization of end milling Optimization of machining parameters not only increases the utility for machining economics, but also the product quality toa great extent. In this context an effort has been made to estimate the optimum tool geometry and machining conditions to produce the best possible surface quality within the constraints. The constrained optimization problem is stated as follows: Minimize Ra using the model given here: where xil and xiu are the upper and lower bounds of process variables xi and x1, x2, x3, x4 are logarithmic transformation of cutting speed, feed, radial rake angle and nose radius. The GA code was developed using MATLAB. This approach makes a binary coding system to represent the variables cutting speed (S), feed rate ( f ), radial rake angle (α ) and nose radius (r), . each of these variables is represented by a ten bit binary equivalent, limiting the total string length to 40. It is known as a chromosome. The variables are represented as genes (substrings) in the chromosome. The randomly generated 20 such chromosomes (population size is 20), fulfilling 9 the constraints on the variables, are taken in each generation. The first generation is called the initial population. Once the coding of the variables has been done, then the actual decoded values for the variables are estimated using the following formula: where xi is the actual decoded value of the cutting speed, feed rate, radial rake angle and nose radius, x(L) i is the lower limit and x(U) i is the upper limit and li is the substring length, which is equal to ten in this case. Using the present generation of 20 chromosomes, fitness values are calculated by the following transformation: where f(x) is the fitness function and Ra is the objective function. Out of these 20 fitness values, four are chosen using the roulettewheel selection scheme. The chromosomes corresponding to these four fitness values are taken as parents. Then the crossover and mutation reproduction methods are applied to generate 20 new chromosomes for the next generation. This processof generating the new population from the old population is called one generation. Many such generations are run till the maximum number of generations is met or the average of four selected fitness values in each generation bees steady. This ensures that the optimization of all the variables (cutting speed, feed rate, radial rake angle and nose radius) is carried out simultaneously. The final statistics are displayed at the end of all iterations. In order to optimize the present problem using GA, the following parameters have been selected to obtain the best possible solution with the least putational effort: Table 7 shows some of the minimum values of the surface roughness predicted by the GA program with respect to input machining ranges, and Table 8 shows the optimum machining conditions for the corresponding minimum values of the surface roughness shown in Table 7. The MRR given in Table 8 was calculated by where f is the table feed (mm/min), aa is the axial depth of cut (20 mm) and ar is the radial depth of cut (1 mm). It can be concluded from the optimization results of the GA program that it is possible to select a bination of cutting speed, feed rate, radial rake angle and nose radius for achieving the best possible surface finish giving a reasonably good material removal rate. This GA program provides optimum machining conditions for the corresponding given minimum values of the surface roughness. The application of the geic algorithmic approach to obtain optimal machining conditions will be quite useful at the puter aided process planning (CAPP) stage in the production of high quality goods with tight tolerances by a variety of machining operations, and in the adaptive control of automated machine tools. With the known boundaries of surface roughness and machining conditions, machining could be performed with a relatively high rate of success with the selected machining conditions. 10 6 Conclusions The investigations of this study indicate that the parameters cutting speed, feed, radial rake angle and nose radius are the primary actors influencing the surface roughness of medium carbon steel uring end milling. The approach presented in this paper provides n impetus to develop analytical models, based on experimental results for obtaining a surface roughness model using the response surface methodology. By incorporating the cutter geometry in the model, the validity of the model has been enhanced. The optimization of this model using geic algorithms has resulted in a fairly useful method of obtaining machining parameters in order to obtain the best possible surface quality. 11 中文翻譯 選擇最佳工具，幾何形狀和切削條件 利用表面粗糙度預(yù)測模型端銑 摘要： 刀具幾何形狀 對 工件表面 質(zhì)量產(chǎn)生 的影響 是人所共知的 ， 因此，任何 成型面 端銑設(shè)計(jì) 應(yīng)包括刀具的幾何形狀。該模型 取得的 優(yōu)化 效果 已得到證實(shí)， 并通過了 卡方檢驗(yàn)。 車削過程對表面光潔度造成的影響歷來倍受研究關(guān)注，對于加工過程采用多刀，用機(jī)器制造處理，都是研究員需要注意的。 對于制造業(yè)，建立高效率的加工參數(shù)幾乎是將近一個(gè)世紀(jì)的問題，并且仍然是許多研究的主題。生產(chǎn)過程的特點(diǎn)是多重 性的動(dòng)態(tài)互動(dòng)過程中的變數(shù)。調(diào)查顯示銑刀與左手螺 旋角一般不太具有成本效益比。這些參數(shù)對表面粗糙度的影響已進(jìn)行了響應(yīng)面分析法（丹參）。 自從世紀(jì)之交的相當(dāng)多的嘗試已找到了最佳值的加工參數(shù)。旨在促進(jìn)數(shù)學(xué)模型與加工的反應(yīng)及其因素，是要促進(jìn)優(yōu)化加工過程。 優(yōu)化中的應(yīng)用遺傳算法 大部分的研究人員一直使用傳統(tǒng)的優(yōu)化技術(shù)，為解決