Varying over multiple parameters with scipy's differential evolution

Question

I'm finding the maximum of a function f over the parameter nu in Python using Scipy's built-in differential evolution, while keeping the other terms (args) fixed. My code

max = scipy.optimize.differential_evolution(lambda nu:-f(args,nu),bounds)
 
fopt = max.fun

Gives me the correct value I desire. However, now I want to do the same thing but vary over two parameters; call them nu and mu. I tried

max = scipy.optimize.differential_evolution(lambda nu,mu:-f(args,nu,mu),bounds)

fopt = max.fun

But I get an error. What is the correct way to implement optimization over several parameters using the above?

Answer 1

You can optimize multiple parameters by passing them as a list to scipy.optimize.differential_evolution. For example, assume the following function that takes a list x as an argument:

def fun(x):
    return x[0] + x[1]

Let's assume the first parameter is nu (corresponds to x[0]) and the second one is mu (corresponds to x[1]). Define bounds accordingly for nu and mu and then you can optimize both at once as:

from scipy.optimize import differential_evolution

bounds = [(0,2), (0,3)] # for e.g., (0,2) for nu and (0,3) for mu
max = differential_evolution(fun, bounds)
fopt = max.fun

Using lambda:

from scipy.optimize import differential_evolution

fun = lambda x: x[0]+x[1]
bounds = [(0,2), (0,3)] # for e.g., (0,2) for nu and (0,3) for mu
max = differential_evolution(fun, bounds)
fopt = max.fun

In your specific case, your lambda function lambda nu,mu:-f(args,nu,mu) is returning negative value of function f. Here you can pass nu and mu in a list x as lambda x:-f(args,x) and unpack x in f for nu and mu respectively.