Documentation of the module main.py used for the experimentation of: Towards a
Pareto Front Shape Invariant Multi-Objective Evolutionary Algorithm Using
Pair-Potential Functions.
NAME
main.py - test a multi-objective evolutionary algorithm (MOEA)
SYNOPSIS
main.py MOEA H1 H2 MOP OBJS GENS RUNS
main.py OPTION
DESCRIPTION
This module is used to test a MOEA on a selected multi-objective problem
(MOP) with a given number of objective functions for a specific number
of independent runs. The required arguments are described as follows:
MOEA
It must be a valid MOEA name. The valid MOEA names are: NSGA-III,
NSGA-III-RSE, NSGA-III-GAE, NSGA-III-COU, NSGA-III-PT,
NSGA-III-MPT, NSGA-III-GPT, and NSGA-III-KRA.
H1
It must be an integer greater than zero. It represents the number
of divisions per objective function for the boundary layer used
for the generation of a weight vector-based reference set. The
values 12, 6, 3, and 3 are selected for MOPs with 3, 5, 8, and 10
objective functions, respectively.
H2
It must be an integer greater than or equal to zero. It
represents the number of divisions per objective function for the
inner layer used for the generation of a weight vector-based
reference set. The inner layer is not generated when a value of
zero is given. The values 0, 0, 2, and 2 are selected for MOPs
with 3, 5, 8, and 10 objective functions, respectively.
MOP
It must be a valid MOP name. The valid MOP names are: DTLZ1,
DTLZ2, DTLZ3, DTLZ4, DTLZ5, DTLZ6, DTLZ7, DTLZ1_MINUS,
DTLZ2_MINUS, DTLZ3_MINUS, DTLZ4_MINUS, DTLZ5_MINUS, DTLZ6_MINUS,
and DTLZ7_MINUS.
OBJS
It must be an integer greater than one. It represents the number
of objective functions of the MOP. In our experiments, all MOPs
are scaled to 3, 5, 8, and 10 objective functions.
GENS
It must be an integer greater than or equal to zero. It
represents the maximum number of generations for the execution of
the MOEA. For DTLZ1, DTLZ5, DTLZ6, and DTLZ7 the values 400, 600,
750, and 1000 are selected for the versions with 3, 5, 8, and 10
objective functions, respectively. For DTLZ2 the values 250, 350,
500, and 750 are selected for the versions with 3, 5, 8, and 10
objective functions, respectively. For DTLZ3 the values 1000,
1000, 1000, and 1500 are selected for the versions with 3, 5, 8,
and 10 objective functions, respectively. For DTLZ4 the values
600, 1000, 1250, and 2000 are selected for the versions with 3,
5, 8, and 10 objective functions, respectively. The same values
are used for the MINUS versions of each MOP.
RUNS
It must be an integer greater than zero. It represents the number
of independent runs that the MOEA will be tested on the selected
MOP. In our experiments, all MOEAs are executed for 30
independent runs in each MOP.
The following option can be used:
--help
Display this help and exit.
REQUIREMENTS
A computer with the installation of Python 3.8 is needed. The modules
numpy, matplotlib, and scipy are required.
EXAMPLE
For running the module main.py, go to NSGA-III-K/ and write:
IPython console users:
%run main.py NSGA-III-RSE 12 0 DTLZ1_MINUS 3 400 1
Windows users:
python main.py NSGA-III-RSE 12 0 DTLZ1_MINUS 3 400 1
Linux users:
python3 main.py NSGA-III-RSE 12 0 DTLZ1_MINUS 3 400 1
The previous line executes the module main.py to test the NSGA-III-RSE
on the DTLZ1_MINUS with three objective functions for one independent
run. A boundary layer with twelve divisions per objective function is
used for the weight vector-based reference set and the inner layer is
not required. The maximum number of generations is set to four hundred
generations.
RESULTS
On success, the output files containing the approximation sets are
generated in NSGA-III-K/Results/.
CONTENTS
The folder "NSGA-III-K" contains the source code of the module main.py.
The folder "Supplementary material" contains the supplementary material
of the paper: Towards a Pareto Front Shape Invariant Multi-Objective
Evolutionary Algorithm Using Pair-Potential Functions.
REFERENCE
L. A. Márquez-Vega, J. G. Falcón-Cardona, E. Covantes Osuna, Towards a
Pareto Front Shape Invariant Multi-Objective Evolutionary Algorithm Using
Pair-Potential Functions, in Batyrshin, I., Gelbukh, A., Sidorov, G. (eds)
Advances in Computational Intelligence, MICAI 2021, vol 13067 of Lecture
Notes in Computer Science, Springer International Publishing, 2021,
pp. 369-382. doi: 10.1007/978-3-030-89817-5_28
Or you can use the following BibTex entry:
@inproceedings{Marquez2021,
author={M{\'a}rquez-Vega, Luis A. and Falc{\'o}n-Cardona, Jes{\'u}s Guillermo and {Covantes Osuna}, Edgar},
editor={Batyrshin, Ildar and Gelbukh, Alexander and Sidorov, Grigori},
title="{Towards a Pareto Front Shape Invariant Multi-Objective Evolutionary Algorithm Using Pair-Potential Functions}",
booktitle={Advances in Computational Intelligence, MICAI 2021},
year={2021},
publisher={Springer International Publishing},
pages={369--382},
isbn={978-3-030-89817-5},
doi={10.1007/978-3-030-89817-5_28},
volume={13067},
series={Lecture Notes in Computer Science}
}