March 2, 2009

Plans for Robust Optimization and AIMMS

Paragon has signed an agreement to develop Robust Optimization support for AIMMS. For this, we are going to work together with Prof. Aharon Ben-Tal of the Technion Israel Institute of Technology, foremost authority in the field of Robust Optimization and its applications. Prof. Ben-Tal developed the Robust Optimization methodology together with efficient computational methods for solving large-scale optimization problems with uncertain data.

Robust Optimization is a rather new modeling methodology for decision making under uncertainty. It aims at solving optimization problems where the description of uncertainty is crude (and not necessarily of a stochastic nature), yet feasibility must be satisfied. In this optimization paradigm, certain constraints are hard, i.e. they are required to hold for all possible outcomes of the uncontrollable parameters, within a prescribed uncertainty set. Robustness of decisions is defined in terms of the best performance against the worst possible realization of the parameters values within the uncertainty set. Robust Optimization is also capable of solving efficiently multi-stage (dynamic) linear optimization problems, without being faced with “the curse of dimensionality”.

Robust Optimization provides the modeling framework of choice for optimization problems in which the uncertain data may be naturally thought of as belonging to certain “ranges” or “regions”. Therefore it is particularly useful in cases where:

  • entries in the data vector may not be known at the moment the problem should be processed (e.g., hierarchical decision making)
  • entries in the data vector may be impossible to measure exactly (e.g. physical parameters at remote places)
  • after a solution is implemented, data entries may drift around their original values (e.g., it can not be predicted exactly what will be a load affecting a construction)
  • it is oftentimes impossible to implement the computed solution exactly. Normally, the implementation errors are equivalent to data uncertainty.

Potential areas of application for Robust Optimization are, among others:

  • Finance (e.g., portfolio management, capital allocation)
  • Engineering (e.g., truss topology design, chip design, signal processing, chemical process control)
  • Energy (e.g., wind energy models)
  • Supply Chain Management (e.g., operation, inventory)
  • Networks (e.g., network design, network capacity expansion)
  • Medicine (e.g., Intensive Modulated Radiation Therapy)

You may find more information about Robust Optimization through the following links:

The Robust Optimization support for AIMMS will provide AIMMS users with a powerful framework for dealing with uncertainty in a tractable manner in their optimization models. We will start the research and development activities for Robust Optimization support for AIMMS in March 2009. We will keep you informed about our progress and the expected release date of the Robust Optimization add-on module for AIMMS. Meanwhile, we invite you to share your needs and cases as input for this development. 


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