Application of a Genetic Algorithm for the Optimal Calibration of Hysteretic Models

Sabatino Di Benedetto1, *, Massimo Latour1, Gianvittorio Rizzano1
1 Department of Civil Engineering, University of Salerno, Salerno, Italy

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© 2023 Di Benedetto et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Civil Engineering, University of Salerno, Salerno, Italy; E-mail:



Recent computing improvements have allowed a considerable use of numerical models to predict phenomena concerning various topics. In particular, considering the field of civil engineering, the possibility of having greater computational capabilities has guaranteed to explore both the global and local behaviour of buildings with greater attention and precision so that currently, many software programs allow modelling different structural components with high accuracy.


One of the aspects of interest concerns the calibration of phenomenological laws to model the mechanical behaviour of specific structural members, devices or connections. With this in mind, many efforts have recently been dedicated to solving this problem by implementing computational codes called “Genetic Algorithms”, which provide optimal configurations of parameters following procedures that emulate Darwin’s theory of evolution. However, generally, these algorithms are encoded in C++ formats, which are difficult to be modified basing on the needs of the users.

With this in mind, the present work's novelty consists of implementing a Genetic Algorithm that, starting from the knowledge of assigned hysteretic curves, allows their modelling through an appropriate calibration of the parameters of the “hysteretic” uniaxialmaterial element of the OpenSees software. In particular, the originality of the code proposed in this paper is its development in the Matlab environment, which is more easily editable and more flexible to customers' specific needs than traditional C++ compilers, such as MultiCal, a calibration software already available in research.


Genetic Algorithms are instructions through which it is possible to reach the optimal calibration of mathematical models according to a procedure that conceptually refers to the evolutionary process of living species.


The proposed GA has been validated against MultiCal tool by calibrating 44 force-displacement hysteretic curves obtained from finite element simulations relating to the cyclic behaviour of connections between circular hollow section profiles and passing-through plates subjected to displacement histories in the axial direction.


The results have shown that the proposed algorithm calibrates the known responses with acceptable accuracy, in line with or even better than the outcomes provided by MultiCal.

Keywords: Genetic, Algorithm, Mutation, Cross-over, Optimisation, Hysteresis.