Robust Optimization II: applications and theory

Real applications are intrinsically characterized by some degrees of uncertainty in the input data. Typically, this uncertainty depends either on the difficulty to have accurate estimations for some of the quantities involved, or on unpredictable events that change some quantities, or both. The aim of robust optimization is to extend the classic combinatorial optimization theory in such a way that uncertainty about data can be directly considered while carrying out the optimization itself. The majority of the results available in the robust optimization academic literature are theoretical results aiming at extending the classic theoretical optimization tools in such a way that uncertainty is taken into account in some (often over-simplified) way. During our previous FNS project on robust optimization, we have developed some successful robust optimization methods that we have called application-driven, since they have been developed starting from the observation of real problems, the solutions produced by classic optimization, and the real needs and requirements of practitioners in presence of uncertainty. The aim of the present project is to extend the scope of the work done in the following directions. First, we would like to abstract the application-driven robust methodologies developed so far, in order to produce a general theory that can be easily specialized to produce methods for large classes of practical optimization problems. Second, we want to enlarge the number of applications considered by including vehicle routing problems and scheduling problems. Notice that these families of applications probably represent the most important and successful domains in terms of application of the classic optimization theory. Third, we will develop some further new application-driven robust algorithms (notice that considering other real problems will give us some new viewpoints that will likely turn into new ideas). Ideally, the new tools will be based on matheuristic ideas. Matheuristic is an emerging field of research where mathematical programming ideas are mixed with metaheuristic algorithms. Notice that since most of the robust optimization theory developed so far is based on mathematical programming, while our previous FNS project was mostly based on metaheuristics, matheuristic methods is a promising way for making the different results available converging towards a common, wider framework. Finally, we will investigate how probabilistic information can be used to contaminate the pure robust optimization models developed so far. Our aim is to close the gap between robust optimization and probabilistic/stochastic optimization. Notice that up to now robust optimization and probabilistic/stochastic optimization have (almost) always treated separately by the academic community, and a contamination of the two fields would be a major research result.