Mathematical models are a powerful tool used to describe the processes of nature. Different techniques may be used and many of them have in common the need of an optimization algorithm in order to obtain the value of the parameters which describe the behaviour of a specific situation. The usual way of modelling nature processes is deterministic. However, nature is not deterministic, but stochastic. There are many situations where data is not available, or the situation has random behaviour, and in such cases, uncertainty must be taken into account. In that sense, uncertainty quantification is an emerging area in mathematics. Its main goal is determining information about the uncertainty in the outputs of a mathematical system, from the available information about the randomness in the inputs. In the setting of mathematical modelling, uncertainty quantification seeks to better explain the model answer taking into account the variability often met in natural and physical phenomena One usual approach of the uncertainty quantification is the study of models whose input data are assumed to be random variables. In most of them, it is assumed that the probability distributions of the parameters are known and follow standard patterns (uniform, Gaussian, exponential, etc.). However, this assumption may be unreal. Determining appropriate probability distributions of the model parameters is becoming a key part of the problem when dealing with real applications. In other words, when we try to describe real phenomena, usually it is not enough to build coherent models, but also consider and treat adequately the uncertainty involved in both sample data and model parameters as well as to control their effect on the solution. In this latter sense, a key issue is the computation of the probability distributions of the model parameters that make that the solution stochastic process of the model, at certain time instants, capture the uncertainty embedded in sample data.
In such a context, the resolution of the problems that arise from modelling the uncertainty of real escenarios, are non affordable to be solved by means of exact algorithms [1]. In that sense, approximate algorithms have postulated as a real alternative for such optimizations. In this context, evolutionary computation approaches have not been investigated extensively with the exception of some papers that use metaheuristics and evolutionary algorithms with successful results [2-5]. Nevertheless, such scientific works have been developed by scientists from numerical optimization and, therefore, the proposed evolutionary computation approaches are in most of the cases naïve. It is our belief that uncertainty models offer real challenges for proposing more sophisticated algorithms by the EC community.
[1] R.C. Smith, Uncertainty Quantification: Theory, Implementation, and Applications (Computational Science and Engineering), SIAM, 2014
[2] R.J. Villanueva, J. Ignacio Hidalgo, C.Cervigón, J. Villanueva-Oller, J.C. Cortés. Calibration of an agent-based simulation model to the data of women infected by Human Papillomavirus with uncertainty, Applied Soft Computing, Apr/2019.
[3] C. Burgos, J.C. Cortés, I.C.Lombana, D.Martínez-Rodríguez, R.J. Villanueva. Modeling the Dynamics of the Frequent Users of Electronic Commerce in Spain Using Optimization Techniques for Inverse Problems with Uncertainty, Journal of Optimization Theory and Applications, Aug/2018.
[4] J.C. Cortés, P. Martínez‐Rodríguez, J.A. Moraño, J.V. Romero, M.D Roselló, R.J. Villanueva. Probabilistic calibration and short‐term prediction of the prevalence herpes simplex type 2: A transmission dynamics modelling approach, Mathematical Methods in the Applied Sciences, Jul/2021.
[5] C. Burgos-Simón, J.C. Cortés, D.Martínez-Rodríguez, R.J. Villanueva. Modeling breast tumor growth by a randomized logistic model: A computational approach to treat uncertainties via probability densities, The European Physical Journal Plus, Oct/2020.
Authors are invited to submit their original and unpublished work with evolutionary computation optimization in the areas below, but not limited to:
It is noteworthy to mention that the absence of evolutionary computation strategies within the submissions is not reason for exclusion from the workshop as the proposition of challenging optimization problems of the field is still interesting for the audience of the workshop and GECCO2022.