#!/usr/bin/env python
'''
Solves Langermann Multimodal Problem with Automatic Optimization Refinement.
'''

# =============================================================================
# Standard Python modules
# =============================================================================
import os, sys, time

# =============================================================================
# External Python modules
# =============================================================================
from numpy import cos,pi,exp
from numpy.linalg import norm

# =============================================================================
# Extension modules
# =============================================================================
from pyOpt import Optimization
from pyOpt import NSGA2
from pyOpt import SLSQP


# =============================================================================
# 
# =============================================================================
def objfunc(x):
    
    a = [3,5,2,1,7]
    b = [5,2,1,4,9]
    c = [1,2,5,2,3]
    
    f = 0.0
    for i in xrange(5):
        f += -(c[i]*exp(-(1/pi)*((x[0]-a[i])**2 + (x[1]-b[i])**2))*cos(pi*((x[0]-a[i])**2 + (x[1]-b[i])**2)))
    #end
    
    g = [0.0]*1
    g[0] = 20.04895 - (x[0]+2.0)**2 - (x[1]+1.0)**2
    
    fail = 0
    
    return f,g,fail
    

# =============================================================================
# 
# =============================================================================
opt_prob = Optimization('Langermann Function 11',objfunc)
opt_prob.addVar('x1','c',lower=-2.0,upper=10.0,value=8.0)
opt_prob.addVar('x2','c',lower=-2.0,upper=10.0,value=8.0)
opt_prob.addObj('f')
opt_prob.addCon('g','i')
print opt_prob

# Global Optimization
nsga2 = NSGA2()
nsga2(opt_prob)
print opt_prob.solution(0)

# Local Optimization Refinement
slsqp = SLSQP()
slsqp(opt_prob.solution(0))
print opt_prob.solution(0).solution(0)