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Platform for robust design optimization

Project description


Ārtap is a framework for robust design optimization in Python. It contains an integrated, multi-physical FEM solver: Agros suite, furthermore it provides simple interfaces for commercial FEM solvers (COMSOL) and meta-heuristic, bayesian or neural network based optimization algorithms surrogate modelling techniques and neural networks.


Artap and its dependencies are available as wheel packages for Windows and Linux* distributions: We recommend to install Artap under a virtual environment.

pip install --upgrade pip # make sure that pip is reasonably new
pip install artap

*The Windows versions are only partially, the linux packages are fully supported at the current version.


You can install the full package, which contains the agrossuite package by the following command:

pip install --upgrade pip # make sure that pip is reasonably new
pip install artap[full]

Basic usage

The goal of this example to show, how we can use Artap to solve a simple, bi-objective optimization problem.

The problem is defined in the following way [GDE3]:

Minimize f1 = x1
Minimize f2 = (1+x2) / x1

subject to
        x1 e [0.1, 1]
        x2 e [0, 5]

The Pareto - front of the following problem is known, it is a simple hyperbola. This problem is very simple for an Evolutionary algorithm, it finds its solution within 20-30 generations. NSGA - II algorithm is used to solve this example.

The Problem definition and solution with NSGA-II in Ārtap:

class BiObjectiveTestProblem(Problem):

    def set(self): = 'Biobjective Test Problem'
        self.parameters = [{'name':'x_1', 'bounds': [0.1, 1.]},
                           {'name':'x_2', 'bounds': [0.0, 5.0]}]

        self.costs = [{'name': 'f_1', 'criteria': 'minimize'},
                      {'name': 'f_2', 'criteria': 'minimize'}]

    def evaluate(self, individual):
        f1 = individual.vector[0]
        f2 = (1+individual.vector[1])/individual.vector[0]
    return [f1, f2]

# Perform the optimization iterating over 100 times on 100 individuals.
problem = BiObjectiveTestProblem()
algorithm = NSGAII(problem)
algorithm.options['max_population_number'] = 100
algorithm.options['max_population_size'] = 100


  • [GDE3] Saku Kukkonen, Jouni Lampinen, The third Evolution Step of Generalized Differential Evolution


If you use Ārtap in your research, the developers would be grateful if you would cite the relevant publications:

[1] Karban, Pavel, David Pánek, Tamás Orosz, Iveta Petrášová, and Ivo Doležel. “FEM based robust design optimization with Agros and Ārtap.” Computers & Mathematics with Applications (2020)

[2] Pánek, David, Tamás Orosz, and Pavel Karban. ” Ārtap: robust design optimization framework for engineering applications.” arXiv preprint arXiv:1912.11550 (2019).


[3] Karban, P., Pánek, D., & Doležel, I. (2018). Model of induction brazing of nonmagnetic metals using model order reduction approach. COMPEL-The international journal for computation and mathematics in electrical and electronic engineering, 37(4), 1515-1524,

[4] Pánek, D., Orosz, T., Kropík, P., Karban, P., & Doležel, I. (2019, June). Reduced-Order Model Based Temperature Control of Induction Brazing Process. In 2019 Electric Power Quality and Supply Reliability Conference (PQ) & 2019 Symposium on Electrical Engineering and Mechatronics (SEEM) (pp. 1-4). IEEE,

[5] Pánek, D., Karban, P., & Doležel, I. (2019). Calibration of Numerical Model of Magnetic Induction Brazing. IEEE Transactions on Magnetics, 55(6), 1-4,

[6] Pánek, D., Orosz, T., Karban, P., & Doležel, I. (2020), “Comparison of simplified techniques for solving selected coupled electroheat problems”, COMPEL – The international journal for computation and mathematics in electrical and electronic engineering, Vol. 39 No. 1, pp. 220-230.

[7] Orosz, T.; Pánek, D.; Karban, P. FEM Based Preliminary Design Optimization in Case of Large Power Transformers. Appl. Sci. 2020, 10, 1361,


If you have any questions, do not hesitate to contact us:


Ārtap is published under MIT license

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