Robust optimization is a rather new modeling methodology for decision making under uncertainty. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems:
to operate under lack of full information on the nature of uncertainty,
to model the problem in a form that can be solved efficiently, and
to provide guarantees about the performance of the solution.
Robustness of decisions is defined in terms of the best performance in the worst case possible state-of-the-world (min-max optimization). A more in-depth discussion of robust optimization can be found, for instance, in [BTGN09].
Robust optimization in AIMMS
In this chapter, you will find a description of the facilities built into AIMMS for creating and solving robust optimization models. From any existing deterministic linear program (LP) or mixed-integer program (MIP), AIMMS is able to automatically create a robust optimization model as well, without the need for you to reformulate any of the constraint definitions. The only steps necessary to create a robust optimization model are
to indicate which parameters in your deterministic model are to become uncertain in a declarative manner,
to indicate which variables in your deterministic model are to become adjustable to the uncertain parameters (if any), and
to specify possible realizations of the uncertain parameters.
Being able to generate both a deterministic and robust optimization model from an identical symbolic formulation allows for any changes you make in the deterministic formulation to automatically propagate to the robust optimization model. This significantly reduces the effort involved with maintaining a robust optimization model associated with a given deterministic model.
Robust Optimization Add-On required
To be able to run an robust optimization model, you need to make sure you have the Robust Optimization Add-On licensed. Without the RO Add-On, you can still define your robust optimization models, but will be unable to solve them (an execution error will occur).
The Robust Optimization Add-On in AIMMS has been developed in close cooperation with Professor Aharon Ben-Tal and Boris Bachelis of the Technion, Israel Institute of Technology. We would like to express our gratitude for our partnership in developing the Robust Optimization Add-On in AIMMS and for their continuous support to get the details right, which allowed us to make Robust Optimization a natural and intuitive extension to our existing functionality.
Basic Concepts discusses a number of basic concepts in robust optimization. These provide a common understanding necessary for the introduction of the robust optimization features of AIMMS discussed in the sections to follow. Uncertain Parameters and Uncertainty Constraints describes the facilities available in AIMMS for specifying uncertain parameters, while Chance Constraints discusses chance constraints as another means to introduce uncertainty into your robust optimization model. Adjustable Variables discusses the facilities available to declare variables to be adjustable to uncertain parameters. Solving Robust Optimization Models, finally, describes the steps how to actually solve a robust optimization model.