A Scenario-Based Approach for Robust Linear Optimization

Finding robust solutions of an optimization problem is an important issue in practice. The established concept of Ben-Tal et al. [2] requires that a robust solution is feasible for all possible scenarios. However, this concept is very conservative and hence may lead to solutions with a bad objective value and is in many cases hard to solve. Thus it is not suitable for most practical applications. In this paper we suggest an algorithm for calculating robust solutions that is easy to implement and not as conservative as the strict robustness approach. We show some theoretical properties of our approach and evaluate it using linear programming problems from NetLib.

[1]  Melvyn Sim,et al.  The Price of Robustness , 2004, Oper. Res..

[2]  Martin W. P. Savelsbergh,et al.  Robust Optimization for Empty Repositioning Problems , 2009, Oper. Res..

[3]  Robert F. Love,et al.  Hull properties in location problems , 1983 .

[4]  A Gerodimos,et al.  Robust Discrete Optimization and its Applications , 1996, J. Oper. Res. Soc..

[5]  Matteo Fischetti,et al.  Light Robustness , 2009, Robust and Online Large-Scale Optimization.

[6]  Arkadi Nemirovski,et al.  Robust solutions of Linear Programming problems contaminated with uncertain data , 2000, Math. Program..

[7]  Frank Plastria,et al.  Localization in single facility location , 1984 .

[8]  Anita Schöbel,et al.  An Empirical Analysis of Robustness Concepts for Timetabling , 2010, ATMOS.

[9]  Allen L. Soyster,et al.  Technical Note - Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming , 1973, Oper. Res..

[10]  Rolf H. Möhring,et al.  The Concept of Recoverable Robustness, Linear Programming Recovery, and Railway Applications , 2009, Robust and Online Large-Scale Optimization.

[11]  Daniele Frigioni,et al.  Recoverable Robustness in Shunting and Timetabling , 2009, Robust and Online Large-Scale Optimization.

[12]  Laurent El Ghaoui,et al.  Robust Solutions to Least-Squares Problems with Uncertain Data , 1997, SIAM J. Matrix Anal. Appl..

[13]  Rolf H. Möhring,et al.  Robust and Online Large-Scale Optimization: Models and Techniques for Transportation Systems , 2009, Robust and Online Large-Scale Optimization.

[14]  Sebastian Stiller,et al.  Extending Concepts of Reliability - Network Creation Games, Real-time Scheduling, and Robust Optimization , 2009 .

[15]  Arkadi Nemirovski,et al.  Robust Convex Optimization , 1998, Math. Oper. Res..

[16]  A. Ben-Tal,et al.  Adjustable robust solutions of uncertain linear programs , 2004, Math. Program..