example of pure random search in python

random-search-example.py

from random import random

# function to optimize: takes in a list of decision variables, returns an objective value
# this is the Rosenbrock function: http://en.wikipedia.org/wiki/Rosenbrock_function
# the global minimum is located at x = (1,1) where f(x) = 0
def my_function(x):
  return (1-x[0])**2 + 100*(x[1] - x[0]**2)**2

# function to perform (a very crude, stupid) optimization
# bounds = lower and upper bounds for each decision variable (2D list)
# NFE = number of function evaluations to perform
# f = the function to be optimized
def optimize(bounds, NFE, f):
  D = len(bounds) # number of decision variables
  best_f = 9999.0 # initialize the "best found" - both the function value and the x values
  best_x = [None]*D

  for i in range(NFE):
    # use an "operator" to generate a new candidate solution
    # this is "uniform mutation" in MOEA lingo
    new_x = [bounds[d][0] + random()*(bounds[d][1] - bounds[d][0]) for d in range(D)]
    new_f = f(new_x)
    if new_f < best_f: # see if it's an improvement -- in multiobjective, this is the Pareto sort
      best_f = new_f
      best_x = new_x

  return {'best_x': best_x, 'best_f': best_f}


# now let's try it...
# (the Rosenbrock problem technically doesn't have "bounds", but we'll make some up..)
bounds = [[-1,5], [-1,5]]
result = optimize(bounds, 10000, my_function)
print result # it should be near best_f = 0.0 and best_x = [1,1], hopefully