L-SHADE implementation

[AlesGartner]

Summary

Added Implementation Success-history based adaptive differential evolution algorithm with Linear population size reduction in shade.py. Also added test (test_shade.py) and example (run_shade) files and updated algorithms/modified/innit.py .

The algorithm is explained this article.

I created a Individual class SolutionSHADE for the algorithm. SolutionSHADE additionally stores f and cr values of each Individual.

The SuccessHistoryAdaptiveDifferentialEvolution class implements the SHADE 1.1 algorithm which is the base for the L-SHADE algorithm implemented in the LpsrSuccessHistoryAdaptiveDifferentialEvolution class.

The algorithm uses the current-to-pbest mutation strategy with binomial crossover which is implemented in the cross_curr2pbest1 function. Trial vectors created by this function are repaired with the parent_medium function.

[firefly-cpp]

Thank you, @AlesGartner for all the hard work! I want to ask @zStupan for an initial review of this implementation.

[firefly-cpp]

@GregaVrbancic, can you please check the following issue regarding the flake settings?

from flake8.options.config import ConfigFileFinder ImportError: cannot import name 'ConfigFileFinder' from 'flake8.options.config' (/home/runner/work/NiaPy/NiaPy/.venv/lib/python3.8/site-packages/flake8/options/config.py)

@AlesGartner, are the results achieved by your implementation similar to those provided by the original implementation? Can you please also compare your results with the original publication?

[AlesGartner]

@GregaVrbancic, can you please check the following issue regarding the flake settings?

from flake8.options.config import ConfigFileFinder ImportError: cannot import name 'ConfigFileFinder' from 'flake8.options.config' (/home/runner/work/NiaPy/NiaPy/.venv/lib/python3.8/site-packages/flake8/options/config.py)

@AlesGartner, are the results achieved by your implementation similar to those provided by the original implementation? Can you please also compare your results with the original publication?

I did some tests on cec2014 functions using the NiaPy-examples repo.

I ran my L-SHADE implementation with default parameters (which i assume run_cec.py uses)of population_size= 180, extern_arc_rate= 2.6, pbest_factor=0.11 and hist_mem_size=6 which i believe where used in the publication

i did 51 runs on test functions 2, 5, 14, 19 and 27 of dimensionality D=10 and got the following results: (numbers shown are based of the error value between the best fitness values found in each run and the true optimal value)

F. num.	Best	Worst	Median	Mean	Std.
2	0.00e+00	0.00e+00	0.00e+00	0.00e+00	0.00e+00
5	2.34e-01	2.0e+01	2.0e+01	1.35e+01	8.83e+00
14	1.48e-02	1.48e-01	5.05e-02	5.39e-02	2.02e-02
19	5.30e-02	1.04e+00	2.13e-01	2.30e-01	1.39e-01
27	1.06e+00	4.00e+02	1.73e+00	1.01e+02	1.49e+02

Results in the publication:

F. num.	Best	Worst	Median	Mean	Std.
2	0.0e+00	0.0e+00	0.0e+00	0.0e+00	0.0e+00
5	1.5e-01	2.0e+01	2.0e+01	1.4e+01	8.8e+00
14	4.5e-02	1.6e-01	7.6e-02	8.1e-02	2.6e-02
19	1.3e-02	3.8e-01	6.2e-02	7.7e-02	6.4e-02
27	8.5e-01	4.0e+02	1.5e+00	5.8e+01	1.3e+02

[firefly-cpp]

Thanks @AlesGartner!

It looks consistent. Can you please also copy one or two results tables for the dimensions higher than 10, e.g., 20, 30, or 50?

When #391 is ready, we can merge this PR.

[AlesGartner]

I ran tests on D=30 and D=50, but these took really long to finish, so i only did 10 runs per problem function.

D=30

these tests where ran with population_size = 540 (18 * D)

F. num.	Best	Worst	Median	Mean	Std.
5	2.01e+01	2.02e+01	2.01e+01	2.01e+01	2.29e-02
9	6.92e+00	1.12e+01	9.10e+00	9.03e+00	1.23e+00
14	1.56e-01	4.32e-01	1.95e-01	2.16e-01	7.65e-02
19	3.19e+00	4.88e+00	4.36e+00	4.21e+00	5.56e-01

Results in the publication(based on 51 runs):

F. num.	Best	Worst	Median	Mean	Std.
5	2.0e+01	2.0e+01	2.0e+01	2.0e+01	3.7e-02
9	3.3e+00	9.2e+00	7.1e+00	6.8e+00	1.5e+00
14	1.8e-01	3.0e-01	2.4e-01	2.4e-01	3.0e-02
19	1.6e+00	4.9e+00	3.9e+00	3.7e+00	6.8e-01

D=50

these tests where ran with population_size = 900 (18 * D)

F. num.	Best	Worst	Median	Mean	Std.
5	2.02e+01	2.03e+01	2.03e+01	2.03e+01	2.19e-02
9	1.06e+01	1.78e+01	1.37e+01	1.37e+01	2.42e+00
14	2.02e-01	6.54e-01	2.50e-01	3.02e-01	1.34e-01
19	6.73e+00	1.23e+01	7.69e+00	8.90e+00	2.17e+00

Results in the publication(based on 51 runs):

F. num.	Best	Worst	Median	Mean	Std.
5	2.0e+01	2.0e+01	2.0e+01	2.0e+01	4.6e-02
9	5.4e+00	1.5e+01	1.1e+01	1.1e+01	2.1e+00
14	2.4e-01	3.5e-01	2.9e-01	3.0e-01	2.5e-02
19	5.4e+00	1.2e+01	7.9e+00	8.3e+00	1.8e+00