Robust Optimization & Robust Programming software

The mathematical programming types linear programming, mixed integer programming, nonlinear programming etc. have a common assumption that all the input data used in the formulation of the mathematical program is known with certainty. This is known as decision making under certainty, and the corresponding models are called deterministic models.

A specific class of models that account for uncertainty in the input data using uncertainty ranges for the input data, are called robust optimization models.

Robust Optimization and dealing with uncertainty

The current set-up within AIMMS allows you to solve linear and mixed integer programming (LP/MIP)models with uncertainty to optimality and create robust solutions without changing the actual structure of the models. In general, any LP/MIP solver can be used for solving RO models. However, for a specific class (i.e. when the uncertainty is defined as an ellipsoid), CPLEX or MOSEK are required as the so-called robust counterpart becomes a Second Order Cone Program (SOCP).

Partnership with professor Ben-Tal of Technion

AIMMS has a partnership with Technion and is working with Professor A. Ben-Tal, who developed the robust optimization Methodology with Professor A. Nemirovski, to assure AIMMS users can apply robust optimization to their models successfully.

Professor A. Ben-Tal: "I am very excited about the partnership with Paragon to make robust optimization available in AIMMS. The extension is very natural and intuitive and will enable optimization specialists to solve realistic large scale linear Optimization problems affected by uncertainty without imposing on the end-users the need to provide full information on the nature of the uncertainty. A major advantage of the robust optimization add-on of AIMMS is the ability of handling with ease meaningful dynamic (multi-periods) optimization problems without falling into the trap of 'the curse of dimensionality'."

Robust Optimization Functional Examples

Chance Constraints

This example implements a portfolio selection model with uncertain investment returns, covering a single time period. The goal is to distribute a certain amount of money between a set of assets to maximize the value-at-risk of the resulting portfolio. Using this example it is illustrated how AIMMS supports handling uncertainty in input data through the safe approximation of chance constraints using a suitably chosen robust optimization counterpart. In a robust optimization model certain constraints are required to hold for every realization of the data within a specified uncertainty set. When a Robust Counterpart (RC) is used as a safe approximation of a chance constraint, an uncertainty set is considered based on the chance level and on the (partial) information known on the randomly distributed data.