Overview of nonlinear interval optimization problems

Variables and parameters in natural systems are often associated with uncertainty. There are broadly three approaches to tackle the uncertainty of such systems, i.e., stochastic, fuzzy, and interval/gray/inexact programming. Uncertainty is modeled as a probability distribution function in stochastic approach. In fuzzy programming, variables and parameters are governed by the membership functions. In many realistic data scarce scenarios, adequate data are not available to define a probabilistic or membership function. The model has to be developed and solved with only information of the extreme values of variables and parameters. Under such situations, interval analysis-based approaches pave the way for efficient model development and solutions. Nonlinearity in the modeling process is conspicuous in recent years due to multidisciplinary driven complexities. Therefore, decision makers have to address interval uncertainties of the models along with nonlinear objective function and constraints. Many techniques have been developed in recent past to solve such nonlinear interval optimization problem (NLIOP). In this chapter, we provide an overview of such techniques to solve NLIOP including nature inspired swarm algorithms.