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Last Commit
Apr. 16, 2019
Feb. 19, 2016

blackbox: A Python module for parallel optimization of expensive black-box functions

What is this?

Let's say you need to find optimal parameters of some computationally intensive system (for example, hyperparameters of a neural network). If you can construct a simple Python function, that takes a set of trial parameters, performs evaluation, and returns some scalar measure of how good chosen parameters are, then the problem becomes a mathematical optimization. However, a corresponding function is expensive (one evaluation can take hours) and is a black-box (has input-output nature).

blackbox is a minimalistic and easy-to-use Python module that efficiently searches for a global optimum (minimum) of an expensive black-box function. User needs to provide a function, a search region (ranges of values for each input parameter) and a number of function evaluations available. A code scales well on clusters and multicore CPUs by performing all expensive function evaluations in parallel.

A mathematical method behind the code is described in this arXiv note (there were few updates to the method recently):

Feel free to cite this note if you are using method/code in your research.


(a) - function given on 0 < x,y < 1.

(b) - running a procedure using 15 evaluations.

(c) - running a procedure using 30 evaluations.

How do I represent my objective function?

It simply needs to be wrapped into a Python function. If an external application is used, it can be accessed using system call:

def fun(par):

    # running external application for given set of parameters
    # calculating output
    return output

par is a vector of input parameters (a Python list), output is a scalar measure to be minimized.

How do I run the procedure?

No installation is needed. Just place into your working directory. Main file should look like that:

import blackbox as bb

def fun(par):
    return par[0]**2 + par[1]**2 # dummy 2D example

def main():,  # given function
              box=[[-10., 10.], [-10., 10.]],  # range of values for each parameter (2D case)
              n=20,  # number of function calls on initial stage (global search)
              m=20,  # number of function calls on subsequent stage (local search)
              batch=4,  # number of calls that will be evaluated in parallel
              resfile='output.csv')  # text file where results will be saved

if __name__ == '__main__':


  • All function calls are divided into batches that are evaluated in parallel. Total number of these parallel cycles is (n+m)/batch.
  • n must be greater than the number of parameters (also, n >= 10 is recommended), m must be greater than 1, batch should not exceed the number of CPU cores available.
  • An optional parameter executor=... should be specified when calling in case when code is used on a cluster with some custom parallel engine (ipyparallel, dask.distributed, pathos etc). executor should be an object that has a map method.

How about results?

Iterations are sorted by function value (best solution is in the top) and saved in a text file with the following structure:

Parameter #1 Parameter #2 ... Parameter #n Function value
+1.6355e+01 -4.7364e+03 ... +6.4012e+00 +1.1937e-04
... ... ... ... ...


Paul Knysh (

I receive tons of useful feedback that helps me to improve the code. Feel free to email me if you have any questions or comments.