  Mathematical models simulate various events under different conditions,
enabling an early overview of the system to be implemented in practice,
reducing the waste of resources and in less time. In project optimization,
these models play a fundamental role, allowing to obtain parameters and
attributes capable of enhancing product performance, reducing costs and
operating time. These enhancements depend on several factors, including an
accurate computational modeling of the inherent characteristics of the system.
In general, such models include uncertainties in their mathematical
formulations, which affect the feasibility of the results and their practical
implementation. In this work, two different approaches capable of quantifying
uncertainties during the optimization of mathematical models are considered. In
the first, robust optimization, the sensitivity of decision variables in
relation to deviations caused by external factors is evaluated. Robust
solutions tend to reduce deviations due to possible system changes. The second
approach, reliability-based optimization, measures the probability of system
failure and obtains model parameters that ensures an established level of
reliability. Overall, the fundamental objective is to formulate a
multi-objective optimization problem capable of handling robust and
reliability-based optimizations, to obtain solutions that are least sensitive
to external noise and that satisfy prescribed reliability levels. The proposed
formulation is analyzed by solving benchmark and chemical engineering problems.
The results show the influence of both methodologies for the analysis of
uncertainties, the multi-objective approach provides a variety of feasible
optimizers, and the formulation proves to be flexible, so that the
uncertainties can be incorporated into the problem considering the needs of
each project.
