StochOPy

StochOPy (STOCHastic OPtimization for PYthon) provides user-friendly routines to sample or optimize objective functions with the most popular algorithms.

Version:	1.7.3
Author:	Keurfon Luu
Web site:	https://github.com/keurfonluu/stochopy
Copyright:	This document has been placed in the public domain.
License:	StochOPy is released under the MIT License.

NOTE: StochOPy has been implemented in the frame of my Ph. D. thesis. If you find any error or bug, or if you have any suggestion, please don't hesitate to contact me.

Features

StochOPy provides routines for sampling of a model parameter space:

• Pure Monte-Carlo
• Metropolis-Hastings algorithm
• Hamiltonian (Hybrid) Monte-Carlo [1] [2]

or optimization of an objective function:

• Differential Evolution [3]
• Particle Swarm Optimization [4] [5]
• Competitive Particle Swarm Optimization [6]
• Covariance Matrix Adaptation - Evolution Strategy [7]
• VD-CMA [8]

Installation

The recommended way to install StochOPy is through pip (internet required):

pip install stochopy

Otherwise, download and extract the package, then run:

python setup.py install

Usage

New in 1.4.0: added support for MPI for evolutionary algorithms (you may need to install the package MPI4PY beforehand). Run the example script inside the folder examples:

mpiexec -n 4 python example_mpi.py

Note that StochOPy still work even though MPI4PY is not installed.

New in 1.3.0: run StochOPy Viewer to see how popular stochastic algorithms work, and play with the tuning parameters on several benchmark functions.

from stochopy.gui import main

main()

First, import StochOPy and define an objective function (here Rosenbrock):

import numpy as np
from stochopy import MonteCarlo, Evolutionary

f = lambda x: 100*np.sum((x[1:]-x[:-1]**2)**2)+np.sum((1-x[:-1])**2)

You can define the search space boundaries if necessary:

n_dim = 2
lower = np.full(n_dim, -5.12)
upper = np.full(n_dim, 5.12)

Initialize the Monte-Carlo sampler:

max_iter = 1000
mc = MonteCarlo(f, lower = lower, upper = upper, max_iter = max_iter)

Now, you can start sampling with the simple method 'sample':

mc.sample(sampler = "hamiltonian", stepsize = 0.005, n_leap = 20, xstart = [ 2., 2. ])

Note that sampler can be set to "pure" or "hastings" too. The models sampled and their corresponding energies are stored in:

print(mc.models)
print(mc.energy)

Optimization is just as easy:

n_dim = 10
lower = np.full(n_dim, -5.12)
upper = np.full(n_dim, 5.12)
popsize = 4 + np.floor(3.*np.log(n_dim))
ea = Evolutionary(f, lower = lower, upper = upper, popsize = popsize, max_iter = max_iter)
xopt, gfit = ea.optimize(solver = "cmaes")
print(xopt)
print(gfit)

Related works

• StochOPy WebApp: StochOPy WebApp allows the users to see how popular stochastic algorithms perform on different benchmark functions.
• StochANNPy: StochANNPy (STOCHAstic Artificial Neural Network for PYthon) provides user-friendly routines compatible with Scikit-Learn for stochastic learning.
• StochOptim: StochOptim provides user friendly functions written in modern Fortran to solve optimization problems using stochastic algorithms in a parallel environment (MPI).

References

[1]	S. Duane, A. D. Kennedy, B. J. Pendleton and D. Roweth, Hybrid Monte Carlo, Physics Letters B., 1987, 195(2): 216-222

[2]	N. Radford, MCMC Using Hamiltonian Dynamics, Handbook of Markov Chain Monte Carlo, Chapman and Hall/CRC, 2011

[3]	R. Storn and K. Price, Differential Evolution - A Simple and Efficient Heuristic for global Optimization over Continuous Spaces, Journal of Global Optimization, 1997, 11(4): 341-359

[4]	J. Kennedy and R. Eberhart, Particle swarm optimization, Proceedings of ICNN'95 - International Conference on Neural Networks, 1995, 4: 1942-1948

[5]	F. Van Den Bergh, An analysis of particle swarm optimizers, University of Pretoria, 2001

[6]	K. Luu, M. Noble, A. Gesret, N. Balayouni and P.-F. Roux, A parallel competitive Particle Swarm Optimization for non-linear first arrival traveltime tomography and uncertainty quantification, Computers & Geosciences, 2018, 113: 81-93

[7]	N. Hansen, The CMA evolution strategy: A tutorial, Inria, Université Paris-Saclay, LRI, 2011, 102: 1-34

[8]	Y. Akimoto, A. Auger and N. Hansen, Comparison-Based Natural Gradient Optimization in High Dimension, Proceedings of the 2014 conference on Genetic and evolutionary computation, 2014, 373-380