Steepest descent tool for discrete optimization

Question

I have a discrete optimization problem containing a complicated objective function that is a float resulting from parameters passed to it, which are only available in discretized steps (here ints).

Is there a standard steepest descent tool for bounded discrete optimizations?

Python is ideal since I have everything brute-forcing all this in that language already.

I've investigated scipy.optimize.brute, but I'd like to avoid brute forcing the whole problem repeatedly since I am varying the objective function and this type of problem is repeatedly occurring in my research.

My objective function here is the RMS error of a set of values (tabulated using the discretized parameters) versus a reference set of values.

EDIT:

Examining a simulated annealing package (https://github.com/perrygeo/python-simulated-annealing) per recommendation in Discrete optimzation in python This still isn't ideal as the surface shouldn't be that complex (here 4-5-dimensional with weak dependence on parameters).

EDIT2:

Still seems like there should be a better way to do this, but the simulated annealing approach with a finite time scale seems to be passable- including my code below

from random import *
from copy import deepcopy
def move(params): #has specific steps of parameters included
    p=deepcopy(params)
    a=randint(0,3)
    b=randint(0,1)
    #print a,b
    if b==1:
        if a!=3:
            p[a]=params[a]+5
        else:
            p[a]=params[a]+50
    else:
        if a!=3:
            p[a]=params[a]-5
        else:
            p[a]=params[a]-50
    return p

def isvalid(params,temp): #checks for boundary conditions and temperature constraint
    for i in xrange(3):
        if params[i]<60:
            return False
        if params[i]>135:
            return False
    if params[-1]>1500:
        return False
    if params[-1]<600:
        return False
    if objfun(params,quiet=True)<temp:
        return True
    else:
        return False

params=[75,85,70,1400]
temp=0.075
best=deepcopy(params)
bestval=objfun(best)
runlength=1000
for i in xrange(runlength):
    newp=move(params)
    if isvalid(newp,temp):
        params=newp
        en=objfun(params)
        if en<bestval:
            best=deepcopy(params)
            bestval=en
print best,bestval