自己做的多峰函数求极值算例
最近开始接触isight，通过几天的学习，对isight有了一些了解。现在把自己做的一个多峰函数求极值的算例同大家分享。
定义：
f=4-(x1^2+2*x2^2-0.3*cos(3*3.1415926*x1)*cos(4*3.1415926*x2))
x1，x2 E(-1.024,1.024)
精确值 max f =4.3 ，x1=x2=0
由于存在多峰性，采用了Multi-Island Genetic Algorithm 和NLPQL的组合优化策略。
下面是优化结果，可以看出，再用两种优化方法组合优化，得到了很好的结果。
Multi-Island Genetic Algorithm
Starting design point:
x1 = -1.0 [-1.024 < x < 1.024] x2 = -1.0 [-1.024 < x < 1.024]
Completed on Wed Jun 30 22:44:58 CST 2010
Total design evaluations: 1001 Number of feasible designs: 1001
Optimum design point:
Run # = 680 Objective = -4.244864158525382 Penalty = 0.0 ObjectiveAndPenalty = -4.244864158525382 x1 = -4.218814373997404E-4 x2 = 0.04695384145876247 f = 4.244864158525382
NLPQL
Starting design point:
x1 = -4.218814373997404E-4 [-1.024 < x < 1.024] x2 = 0.04695384145876247 [-1.024 < x < 1.024]
Completed on Wed Jun 30 22:44:58 CST 2010
Total design evaluations: 20 Number of feasible designs: 20
NLPQL termination reason: OPTIMALITY CONDITIONS SATISFIED
Optimum design point:
Run # = 19 Objective = -4.29999992320409 Penalty = 0.0 ObjectiveAndPenalty = -4.29999992320409 x1 = -4.998311753110878E-5 x2 = 3.995661834215807E-5 f = 4.29999992320409
不错不错，优化是一种理念，关键在于人的钻研。具体就是在时间耗费和精度控制上的博弈了。
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