多因素试验优化算法及医学应用

【作者】 仇丽霞；

【导师】 何大卫； 刘桂芬；

【作者基本信息】 山西医科大学 ， 流行病与卫生统计， 2003， 硕士

【摘要】 多因素、多水平试验设计和优化的目的是研究如何在实验区域内最有效地选择试验点，以最少的试验次数研究各因素的作用和因素间的交互作用，并确定影响试验结果的最优条件。本文利用木豆叶中总黄酮提取量的最大优化问题与胃蛋白酶中残留蛋白含量控制的最小优化问题中的正交试验结果，突破传统的方差分析模型，将回归分析方法应用于其结果分析，拟合二次响应面回归模型，两模型均有统计学意义，拟合效果较好，在总黄酮提取量最大的优化问题中，R~2达到99.91％，一次项、二次项有统计学意义，其决定系数分别为55.34％、44.56％；在残留蛋白含量最小的优化问题中，R~2达到98.61％，一次项、二次项有统计学意义，其决定系数分别为65.94％、32.67％；在两实例中，因素间均无交互作用，不存在模型的拟合不足，残差围绕零随机分布，cook’s距离均在±2之间，所以两实例的试验数据拟合二次响应面回归模型的效果好。在二次响应面回归模型的基础上，分别利用最速上升法、遗传算法搜索最优试验条件，并与正交试验设计的直接寻优法进行比较。最速上升法沿着曲面最大增量的方向逐步移动，直到观察到的响应不再增加为止的寻优方法，最速上升法能保证局部收敛性，因而易陷入局部最优。遗传算法(genetic algorithm，GA)是一种模拟自然进化过程的随机搜索方法，能保证全局最优。对于木豆叶中总黄酮提取的最大优化问题，最速上升法所确定的最优试验条件为：加水量为木豆叶重量的10.2倍、煎煮温度93℃、煎煮3次、每次1.5小时，此时总黄酮提取量将达到0.896029mg／g。利用遗传算法，在种群规模为30，染色体串用二进制表示的总长度为80位，采用单点交叉的方式，交叉概率P_c=0.80，变异概率P_m=0.05，最大进化世代数为100，所确定山西医科大学硕士学位论文2003的最优试验条件为:加水量为木豆叶重量的10.5倍、温度99.70c、煎煮3次、每次1.5小时，总黄酮的提取量为1.0713mg/g。与最速上升法相比，总黄酮的提取量增加了0.1753m留g，提高了20%。若将煎煮时间的搜索范围扩大为0.75一2.0小时，算法参数不变，遗传算法确定的最优试验条件为:加水量10.5倍，煎煮温度99.4OC，煎煮3次，每次煎煮2小时，总黄酮提取量达到1.8499m岁g，比在试验范围内的条件下增加了0.7786m创g，提取量提高了72.68%。从分析结果看，在优化试验条件时遗传算法比最速上升法更具优势。对于胃蛋白酶中残留蛋白含量控制的最小优化问题，最速上升法所确定的最佳工艺条件为:水解温度为45.40C、水解3.95小时，加3.0%的盐酸、烘房温度61.50c，此时残留蛋白含量约降到0.007569mol。利用遗传算法，在种群的规模为40，包含四个影响因素的每个染色体串用二进制表示的总长度为80位，采用单点交又的方式，交叉概率尸c=0.85，变异概率尸m=0.05，最大进化世代数为100，所确定的最佳工艺条件为:水解温度为46.7oe、水解3.75小时、加3.oo’o的HeL、烘房温度64.1“e，此时胃蛋白酶中残留蛋白的含量约降到0.OO01mol。较最速上升法减少了0.OO75mol，降低了98.68%。而正交试验设计寻优的直接法只能在试验设计的各因素水平上确定最优试验条件，不能预测残留蛋白的含量。更多还原

【Abstract】 The purpose for multiple levels of multiple factors experiment and optimization is to test the significance of individual factor and to search the best experimental condition for the response variable. The study introduces the method of regression analysis to the analysis of data of orthogonal experiment about withdrawing total flavone from wood bean leaves and measuring residual protein in the production of pepsin by fitting quadratic response surface regression model. The results showed that two the quadratic response surface regression models were significant in the significance of linear term and quadratic term but no significance of cross product term. The fitting effect of the models was good.The best experimental condition was searched by the steepest ascending method and genetic algorithm (GA). The steepest ascending method finds the best local point by climbing the steepest permissible gradient around search space until the gradient of object function equal to zero. A genetic algorithm emulates biological evolutionary theories to solve optimization problems. According to evolutionary theories, only the most suited strings in the population are likely to survive and generate their offspring, thus transmitting their biological heredity to new generations.The best local point of withdrawing total flavone from wood bean leaves was that with 10.2 times of water, 3 times of decoction of 1.5 hours each, in the water temperatured 93 , the withdrawing measure of total flavone reached 0.896029mg/g, according to the steepest ascending method. According to GA, under the following condition when population size=30,chromosome length=80, crossover probability=0.80, mutation probability=0.05, max generation=100, an excellent design strategy was that with 10.5 times of water, 3 times of decoction of 1.5 hours each, in the water temperatured 99.7 , the withdrawing measure of total flavone reached 1.0713mg/g. The result showed GA was more excellent than the steepest ascending method. The total flavone was increased 0.1753mg/g, that was it was increased 20%. If extending the searching scope of decoction time from 0.75 to 2.0 hours, the best experimental condition was that with 10.5 times of water, 3 times of decoction of 1.5 hours each, in the water temperatured 99.4 , the withdrawing measure of total flavone attained to 1.8499 mg/g, which was increased 0.7786 mg/g, increaseing 72.68% than the former by GA. The best local point of measuring residual protein in the production of pepsin was that with 45.4 of the hydrolysis temperature, 3.95 hours of the hydrolysis time 3.0%HCL and 61.5 of the bake-house’s temperature, the measure of residual protein in the production of pepsin reduced to 0.007569mol, according to the steepest ascending method. According to GA, under the following condition when population size=40, chromosome length=80, crossover probability=0.85, mutation probability=0.05, max generation=100, an excellent design strategy was that with 46.7 of the hydrolysis temperature, 3.75 hours of the hydrolysis time 3.0%HCL and 64.1 C of the bake-house’s temperature, the measure of residual protein in the production of pepsin reduced to 0.0001mol. The result showed GA was more excellent than the steepest ascending method. The measure of residual protein was decreased 0.0075mol, that was it was decreased 98.68%, than the former by GA.更多还原