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1、最优化与存储模型实验1.曲线拟合有关部门希望研究车速与刹车距离之间的关系y=β0+β1x其中x为车速，y为刹车距离，现测得50组数据（xi,yi）(i=1,2,…,50)(见表3.1),用三种方法（（1）平方和最小；（2）绝对偏差和最小；（3）最大偏差最小）估计系数β0和β1，并分析三种方法的计算效果（注：用LINGO软件求解，用其他软件画出散点图和回归直线），说明哪一种方法得到有结果更合理。解答：（1）平方和最小，即为最小二乘法，相应的无约束问题为：maxβ0，β1Z=i=1n（β0+β1x-y）2LINGO语句：se
2、ts:quantity/1..50/:x,y;endsetsdata:x=4,4,7,7,8,9,10,10,10,11,11,12,12,12,12,13,13,13,13,14,14,14,14,15,15,15,16,16,17,17,17,18,18,18,18,19,19,19,20,20,20,20,20,22,23,24,24,24,24,25;y=2,10,4,22,16,10,18,26,34,17,28,14,20,24,28,26,34,34,46,26,36,60,80,20,26,54,32,4
3、0,32,40,50,42,56,76,84,36,46,68,32,48,52,56,64,66,54,70,92,93,120,85;enddatamin=@sum(quantity:(a*x+b-y)^2);@free(a);@free(b);运行结果：Localoptimalsolutionfound.Objectivevalue:11353.52Infeasibilities:0.000000Extendedsolversteps:5Totalsolveriterations:18VariableValueRe
4、ducedCostA3.9324090.000000B-17.579090.000000结果分析：Y=3.9324x-17.5791（1）绝对偏差和最小，即为最小一乘法，相应的无约束问题为：maxβ0，β1Z=i=1nβ0+β1x-yLINGO语句：sets:quantity/1..50/:x,y;endsetsdata:x=4,4,7,7,8,9,10,10,10,11,11,12,12,12,12,13,13,13,13,14,14,14,14,15,15,15,16,16,17,17,17,18,18,18,18,
5、19,19,19,20,20,20,20,20,22,23,24,24,24,24,25;y=2,10,4,22,16,10,18,26,34,17,28,14,20,24,28,26,34,34,46,26,36,60,80,20,26,54,32,40,32,40,50,42,56,76,84,36,46,68,32,48,52,56,64,66,54,70,92,93,120,85;enddatamin=@sum(quantity:@abs(a*x+b-y));@free(a);@free(b);运行结果：Glob
6、aloptimalsolutionfound.Objectivevalue:563.8000Objectivebound:563.8000Infeasibilities:0.000000Extendedsolversteps:0Totalsolveriterations:82VariableValueA3.400000B-11.60000结果分析：Y=3.4x-11.6（1）最大偏差最小，即为最小无穷模法，相应的无约束问题为：maxβ0，β1Z=max1≤i≤nβ0+β1x-yLINGO语句：sets:quantity/
7、1..50/:x,y;endsetsdata:x=4,4,7,7,8,9,10,10,10,11,11,12,12,12,12,13,13,13,13,14,14,14,14,15,15,15,16,16,17,17,17,18,18,18,18,19,19,19,20,20,20,20,20,22,23,24,24,24,24,25;y=2,10,4,22,16,10,18,26,34,17,28,14,20,24,28,26,34,34,46,26,36,60,80,20,26,54,32,40,32,40,50,4
8、2,56,76,84,36,46,68,32,48,52,56,64,66,54,70,92,93,120,85;enddatamin=@max(quantity:@abs(a*x+b-y));@free(a);@free(b);运行结果：Globaloptimalsolutionfound.Objectiveval
