自己做的多峰函数求极值算例

turbinesv

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

jacicka1984

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。