ABSTRACT
Mathematical optimization can be used to solve a variety of modeling, design, control, and decision-making challenges. The minimizing (or maximizing) of the objectives, given the constraints for the issue to be solved, is the traditional framework for optimization. Many design issues, on the other hand, are characterized by many objectives, which need a trade-off between various purposes, resulting in under- or over-achievement of various objectives. It is not always possible or required to precisely quantify numerous system performance criteria, parameters, and decision variables. Variables are said to be uncertain or fuzzy when their values cannot be properly determined. Probability distributions can be used to quantify values that are uncertain. It is an important class because many aspects of real-world situations may be modeled as networks, and the representation of the model is much more condensed than that of a general linear program.
