DetPy (Differential Evolution Tools): A Python toolbox for solving optimization problems using differential evolution

📖 Citation

If you use DetPy in your research, please cite:

Zieliński, B., Ściegienny, S., Orlicki, H., & Książek, W. (2025).
DetPy (Differential Evolution Tools): A Python toolbox for solving optimization problems using differential evolution.
SoftwareX, 29, 102014.
https://doi.org/10.1016/j.softx.2024.102014

BibTeX

@article{Zielinski2025DetPy,
  title   = {DetPy (Differential Evolution Tools): A Python toolbox for solving optimization problems using differential evolution},
  author  = {Zieliński, Błażej and Ściegienny, Szymon and Orlicki, Hubert and Książek, Wojciech},
  journal = {SoftwareX},
  volume  = {29},
  pages   = {102014},
  year    = {2025},
  doi     = {10.1016/j.softx.2024.102014}
}

Introduction

The DetPy library contains implementations of the differential evolution algorithm and 18 modifications of this algorithm. It can be used to solve advanced optimization problems. The following variants have been implemented:

No.	Algorithm	Year
1	DE (Differential evolution) [1]	1997
2	COMDE (Constrained optimization-based differential evolution) [2]	2012
3	DERL (Differential evolution random locations) [3]	2006
4	NMDE (Novel modified differential evolution algorithm) [4]	2011
5	FIADE (Fitness-Adaptive DE) [5]	2011
6	EMDE (Efficient modified differential evolution) [6]	2015
7	IDE (Improved differential evolution) [7]	2019
8	SADE (Self-adaptive differential evolution) [8]	2008
9	JADE (Adaptive differential evolution with optional external archive) [9]	2009
10	OppBasedDE (Opposition-based differential evolution) [10]	2010
11	AADE (Auto adaptive differential evolution algorithm) [11]	2019
12	DEGL (Differential evolution with neighborhood-based mutation) [12]	2009
13	DELB (Differential evolution with localization using the best vector) [3]	2006
14	EIDE (An efficient improved differential evolution algorithm) [13]	2012
15	MGDE (A many-objective guided differential evolution) [14]	2022
16	ImprovedDE (DE with dynamic mutation parameters) [15]	2023
17	SHADE (Success-History Based Parameter Adaptation for Differential Evolution) [16]	2013
18	LSHADE_RSP (Algorithm with a Rank-based Selective Pressure Strategy) [17]	2018
19	LSHADE (Improving the Search Performance of SHADE Using Linear Population Size Reduction) [18]	2014
20	SPS_LSHADE_EIG (Self-Optimizing L-SHADE with Eigenvector Crossover ) [19]	2015
21	AL-SHADE (Adaptive L-SHADE with current-to-Amean strategy and adaptive mutation selection scheme) [20]	2022
22	DETCR (Hybrid DE Algorithm With Adaptive Crossover Operator) [21]	2011
23	EPSDE (Epsilon Constrained Differential Evolution) [22]	2006
24	EPSDEAG (Constrained Optimization by the ε Constrained Differential Evolution with an Archive and Gradient-Based Mutation) [23]	2010
25	LSHADE_EPSIN (L-SHADE with Ensemble Sinusoidal Parameter Adaptation) [24]	2016
26	EPSDEG (Epsilon Constrained Differential Evolution with Gradient-Based Mutation) [25]	2009
27	EPSADE (Epsilon Constrained adaptive Differential Evolution) [26]	2010
28	EPSRDE (Epsilon Constrained Rank-Based Differential Evolution) [27]	2012
29	SHADE 1.1 (Success-History Based Parameter Adaptation for Differential Evolution) [16]	2014
30	EPSDEwDC (Epsilon Constrained Differential Evolution with Dynamic ε-Level Control) [28]	2012

Installation

pip install detpy

Example - optimization of the Ackley function based SADE

from detpy.DETAlgs.data.alg_data import SADEData
from detpy.DETAlgs.sade import SADE
from detpy.functions import FunctionLoader
from detpy.models.enums.boundary_constrain import BoundaryFixing
from detpy.models.enums.optimization import OptimizationType
from detpy.models.fitness_function import BenchmarkFitnessFunction

function_loader = FunctionLoader()
ackley_function = function_loader.get_function(function_name="ackley", n_dimensions=2)
fitness_fun = BenchmarkFitnessFunction(ackley_function)

params = SADEData(
    max_nfe=10000,
    population_size=100,
    dimension=2,
    lb=[-32.768, -32.768],
    ub=[32.768, 32.768],
    optimization_type=OptimizationType.MINIMIZATION,
    boundary_constraints_fun=BoundaryFixing.RANDOM,
    function=fitness_fun,
    log_population=True,
    parallel_processing=['thread', 4]
)

default2 = SADE(params, db_conn="Differential_evolution.db", db_auto_write=False)
results = default2.run()

Using FunctionLoader

You can also use one of predefined functions to solve your problem. To do this, call the FunctionLoader method and pass as an argument the name of a function from the folder and variables, which u want to use in your calculations.

function_loader = FunctionLoader()
function_name = "ackley"
variables = [0.0, 0.0]
n_dimensions = 2

result = function_loader.evaluate_function(function_name, variables, n_dimensions)

Available functions:

        self.function_classes = {
            "ackley": Ackley,
            "rastrigin": Rastrigin,
            "rosenbrock": Rosenbrock,
            "sphere": Sphere,
            "griewank": Griewank,
            "schwefel": Schwefel,
            "michalewicz": Michalewicz,
            "easom": Easom,
            "himmelblau": Himmelblau,
            "keane": Keane,
            "rana": Rana,
            "pits_and_holes": PitsAndHoles,
            "hypersphere": Hypersphere,
            "hyperellipsoid": Hyperellipsoid,
            "eggholder": EggHolder,
            "styblinski_tang": StyblinskiTang,
            "goldstein_and_price": GoldsteinAndPrice
        }

Test functions prepared based on https://gitlab.com/luca.baronti/python_benchmark_functions

References

1. Storn, Rainer and Price, Kenneth. Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization, vol. 11, no. 4, 1997.
2. Mohamed, Ali Wagdy and Sabry, Hegazy Zaher. Constrained optimization based on modified differential evolution algorithm. Information Sciences, vol. 194, 2012.
3. Kaelo, Paul and Ali, Mohamed M. A numerical study of some modified differential evolution algorithms. European Journal of Operational Research, vol. 169, no. 3, 2006.
4. Zou, Dexuan, Liu, Haikuan, Gao, Liqun, Li, Steven. A novel modified differential evolution algorithm for constrained optimization problems. Computers & Mathematics with Applications, vol. 61, no. 6, 2011.
5. Ghosh, Arnob, Das, Swagatam, Chowdhury, Aritra, Giri, Ritwik. An improved differential evolution algorithm with fitness-based adaptation of the control parameters. Information Sciences, vol. 181, no. 18, 2011.
6. Mohamed, Ali Wagdy. An efficient modified differential evolution algorithm for solving constrained non-linear integer and mixed-integer global optimization problems. International Journal of Machine Learning and Cybernetics, vol. 8, no. 3, 2015.
7. Ma, Jian and Li, Haiming. Research on Rosenbrock Function Optimization Problem Based on Improved Differential Evolution Algorithm. Journal of Computer and Communications, vol. 7, no. 11, 2019.
8. Wu Zhi-Feng, Huang Hou-Kuan, Yang Bei, Zhang Ying. A modified differential evolution algorithm with self-adaptive control parameters. 2008 3rd International Conference on Intelligent System and Knowledge Engineering, IEEE, 2008.
9. Zhang, Jingqiao and Sanderson, A.C. JADE: Adaptive Differential Evolution With Optional External Archive. IEEE Transactions on Evolutionary Computation, vol. 13, no. 5, 2009.
10. Rahnamayan, Shahryar, Tizhoosh, Hamid R., Salama, Magdy M. A. Opposition-Based Differential Evolution. Studies in Computational Intelligence, Springer, Berlin, Heidelberg.
11. Sharma, Vivek, Agarwal, Shalini, Verma, Pawan Kumar. Auto Adaptive Differential Evolution Algorithm. 2019 3rd International Conference on Computing Methodologies and Communication (ICCMC), IEEE, 2019.
12. Das, Swagatam, Abraham, Ajith, Chakraborty, Uday K., Konar, Amit. Differential Evolution Using a Neighborhood-Based Mutation Operator. IEEE Transactions on Evolutionary Computation, vol. 13, no. 3, 2009.
13. Zou, Dexuan and Gao, Liqun. An efficient improved differential evolution algorithm. Proceedings of the 31st Chinese Control Conference, 2012.
14. Zouache, Djaafar, Abdelaziz, Fouad Ben. MGDE: a many-objective guided differential evolution with strengthened dominance relation and bi-goal evolution. Annals of Operations Research, Springer, 2022.
15. Lin, Yifeng, Yang, Yuer, Zhang, Yinyan. Improved differential evolution with dynamic mutation parameters. Soft Computing, Springer, 2023.
16. Ryoji Tanabe, Alex Fukunaga. Success-history based parameter adaptation for Differential Evolution. IEEE Congress on Evolutionary Computation, 2013.
17. Vladimir Stanovov, Shakhnaz Akhmedova, Eugene Semenkin. Algorithm with a Rank-based Selective Pressure mutation (LSAHDE-RSP). IEEE Congress on Evolutionary Computation, 2018.
18. Ryoji Tanabe, Alex Fukunaga. Improving the Search Performance of SHADE Using Linear Population Size Reduction. IEEE Congress on Evolutionary Computation, 2014.
19. Shu-Mei Guo, Jason Sheng-Hong Tsai, Chin-Chang Yang, Pang-Han Hsu. A self-optimization approach for L-SHADE incorporated with eigenvector-based crossover and successful-parent-selecting framework on CEC 2015 benchmark set. IEEE Congress on Evolutionary Computation (CEC), 2015.
20. Yintong Li, Tong Han, Huan Zhou, Shangqin Tang, Hui Zhao. A novel adaptive L-SHADE algorithm and its application in UAV swarm resource configuration problem. Information Sciences, vol. 606, pp. 350–367, 2022.
21. Gilberto Reynoso-Meza, Javier Sanchis, Xavier Blasco, Juan M. Herrero, Hybrid DE algorithm with adaptive crossover operator for solving real-world numerical optimization problems. IEEE Congress of Evolutionary Computation (CEC), New Orleans, LA, USA, 2011, doi: 10.1109/CEC.2011.5949800, 2011.
22. Tetsuyuki Takahama, Setsuko Sakai, Noriyuki Iwane, Solving Nonlinear Constrained Optimization Problems by the Epsilon Constrained Differential Evolution IEEE International Conference on Systems, Man and Cybernetics, 2006.
23. Tetsuyuki Takahama, Setsuko Sakai, Constrained optimization by the ε constrained differential evolution with an archive and gradient-based mutation. IEEE Congress on Evolutionary Computation, 2010.
24. Noor H. Awad, Mostafa Z. Ali, Ponnuthurai N. Suganthan, Robert G. Reynolds. L-SHADE with Ensemble Sinusoidal Parameter Adaptation. IEEE Congress on Evolutionary Computation, 2016.
25. T. Takahama and S. Sakai, Solving difficult constrained optimization problems by the ε constrained differential evolution with gradient based mutation, in Constraint-Handling in Evolutionary Optimization, E. Mezura-Montes, Ed. Springer-Verlag, pp. 51–72, 2009
26. Tetsuyuki Takahama and Setsuko Sakai, Efficient Constrained Optimization by the ε Constrained Adaptive Differential Evolution. IEEE Congress on Evolutionary Computation, 2010
27. Tetsuyuki Takahama and Setsuko Sakai, Efficient Constrained Optimization by the ε Constrained Rank-Based Differential Evolution. IEEE Congress on Evolutionary Computation, 2012
28. Tetsuyuki Takahama and Setsuko Sakai, Epsilon Constrained Differential Evolution with Dynamic ε-Level Control. Chakraborty, U.K. (eds) Advances in Differential Evolution. Studies in Computational Intelligence, vol 143. Springer, Berlin, Heidelberg, 2008

Documentation

Full documentation is available: https://blazej-zielinski.github.io/detpy/