pymoo - Multi-Objective Optimization Framework

You can find the detailed documentation here: https://www.egr.msu.edu/coinlab/blankjul/pymoo/

Requirements

Before using the installer check if the following requirements are fulfilled:

Python 3

python --version

pip>=9.0.0

pip --version

Cython:

pip install cython

Installation

The test problems are uploaded to the PyPi Repository.

pip install pymoo

For the current development version:

git clone https://github.com/msu-coinlab/pymoo
cd pymoo
python setup.py install

Just locally to be used directly in another project:

git clone https://github.com/msu-coinlab/pymoo
cd pymoo
pyhton setup.py build_ext --inplace

Implementations

Algorithms

Genetic Algorithm: A simple genetic algorithm to solve single-objective problems.

NSGA-II : Non-dominated sorting genetic algorithm for bi-objective problems. The mating selection is done using the binary tournament by comparing the rank and the crowding distance. The crowding distance is a niching measure in a two-dimensional space which sums up the difference to the neighbours in each dimension. The non-dominated sorting considers the rank determined by being in the ith front and the crowding distance to achieve a good diversity when converging.

NSGA-III : A referenced-based algorithm used to solve many-objective problems. The survival selection uses the perpendicular distance to the reference directions. As normalization the boundary intersection method is used [5].

MOEAD/D : The classical MOEADD implementation using the Tchebichew decomposition function.

Differential Evolution : The classical single-objective differential evolution algorithm where different crossover variations and methods can be defined. It is known for its good results for effective global optimization.

Methods

Simulated Binary Crossover : This crossover simulates a single-point crossover in a binary representation by using an exponential distribution for real values. The polynomial mutation is defined accordingly which performs basically a binary bitflip for real numbers.

Usage

from pymoo.optimize import minimize
from pymoo.util import plotting
from pymop.factory import get_problem

# create the optimization problem
problem = get_problem("zdt1")

# solve the given problem using an optimization algorithm (here: nsga2)
res = minimize(problem,
               method='nsga2',
               method_args={'pop_size': 100},
               termination=('n_gen', 200),
               pf=problem.pareto_front(100),
               save_history=False,
               disp=True)
plotting.plot(res.F)

Contact

Feel free to contact me if you have any question:

Julian Blank (blankjul [at] egr.msu.edu)

Michigan State University

Computational Optimization and Innovation Laboratory (COIN)

East Lansing, MI 48824, USA