pymoo - Multi-Objective Optimization

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

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

import time

import numpy as np

from pymoo.util.plotting import plot, animate
from pymop.problems.zdt import ZDT1


def run():

    # create the optimization problem
    problem = ZDT1()

    start_time = time.time()

    # solve the given problem using an optimization algorithm (here: nsga2)
    from pymoo.optimize import minimize
    res = minimize(problem,
                   method='nsga2',
                   method_args={'pop_size': 100},
                   termination=('n_gen', 200),
                   seed=1,
                   save_history=True,
                   disp=True)
    F = res['F']

    print("--- %s seconds ---" % (time.time() - start_time))

    scatter_plot = True
    save_animation = False

    if scatter_plot:
        plot(F, problem)

    if save_animation:
        H = np.concatenate([e['pop'].F[None, :, :] for e in res['history']], axis=0)
        animate('%s.mp4' % problem.name(), H, problem)


if __name__ == '__main__':
    run()

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