#!/usr/bin/env python

"""
Zimmermann's function

References::
    [1] Storn, R. and Price, K. Differential Evolution - A Simple and Efficient
    Heuristic for Global Optimization over Continuous Spaces. Journal of Global
    Optimization 11: 341-359, 1997.

    [2] Storn, R. and Price, K.
    (Same title as above, but as a technical report.)
    http://www.icsi.berkeley.edu/~storn/deshort1.ps
"""

def zimmermann(x):
    """
    Zimmermann function: a non-continuous function, Equation (24-26) of [2]

    minimum is f(x)=0.0 at x=(7.0,2.0)
    """

    x0, x1 = x #must provide 2 values (x0,y0)
    f8 = 9 - x0 - x1
    c0,c1,c2,c3 = 0,0,0,0
    if x0 < 0: c0 = -100 * x0
    if x1 < 0: c1 = -100 * x1
    xx =  (x0-3.)*(x0-3) + (x1-2.)*(x1-2)
    if xx > 16: c2 = 100 * (xx-16)
    if x0 * x1 > 14: c3 = 100 * (x0*x1-14.)
    return max(f8,c0,c1,c2,c3)