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

if __name__ == '__main__':

    from pymop.problems.zdt import ZDT1
    problem = ZDT1(n_var=30)

    start_time = time.time()

    from pymoo.optimize import minimize
    res = minimize(problem,
                   method='nsga3',
                   method_args={'pop_size': 92},
                   termination=('n_eval', 92 * 200),
                   seed=2,
                   save_history=True,
                   disp=True)

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

    scatter_plot = True
    save_animation = True

    if scatter_plot:
        plot(res['F'])

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

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