Robust optimization

Robust optimization is a field of optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the parameters of the problem itself and/or its solution.

History

The origins of robust optimization date back to the establishment of modern decision theory in the 1950s and the use of worst case analysis and Wald's maximin model  as a tool for the treatment of severe uncertainty.  It became a discipline of its own in the 1970s with parallel developments in several scientific and technological fields. Over the years, it has been applied in statistics,  but also in operations research,electrical engineering, control theory, finance, portfolio management logistics, manufacturing engineering, chemical engineering,  medicine, and computer science. In engineering problems, these formulations often take the name of "Robust Design Optimization", RDO or "Reliability Based Design Optimization", RBDO.

Classification

There are a number of classification criteria for robust optimization problems/models. In particular, one can distinguish between problems dealing with local and global models of robustness; and between probabilistic and non-probabilistic models of robustness. Modern robust optimization deals primarily with non-probabilistic models of robustness that are worst case oriented and as such usually deploy Wald's maximin models.

Probabilistically robust optimization models

These models quantify the uncertainty in the "true" value of the parameter of interest by probability distribution functions. They have been traditionally classified as stochastic programming and stochastic optimization models. Recently, probabilistically robust optimization has gained popularity by the introduction of rigorous theories such as scenario optimization able to quantify the robustness level of solutions obtained by randomization. These methods are also relevant to data-driven optimization methods.

Robust counterpart

The solution method to many robust program involves creating a deterministic equivalent, called the robust counterpart. The practical difficulty of a robust program depends on if its robust counterpart is  computationally tractable.