ROBUST OPTIMIZATION OF LARGE-SCALE SYSTEMS

Mathematical programming models with noisy, erroneous, or incomplete d ata are common in operations research applications. Difficulties with such data are typically dealt with reactively-through sensitivity anal ysis-or proactively-through stochastic programming formulations. In th is paper, we characterize the desirable properties of a solution to mo dels, when the problem data are described by a set of scenarios for th eir value, instead of using point estimates. A solution to an optimiza tion model is defined as: solution robust if it remains ''close'' to o ptimal for all scenarios of the input data, and model robust if it rem ains ''almost'' feasible for all data scenarios. We then develop a gen eral model formulation, called robust optimization (RO), that explicit ly incorporates the conflicting objectives of solution and model robus tness. Robust optimization is compared with the traditional approaches of sensitivity analysis and stochastic linear programming. The classi cal diet problem illustrates the issues. Robust optimization models ar e then developed for several real-world applications: power capacity e xpansion; matrix balancing and image reconstruction; air-force airline scheduling; scenario immunization for financial planning; and minimum weight structural design. We also comment on the suitability of paral lel and distributed computer architectures for the solution of robust optimization models.