New results about multi-band uncertainty in Robust Optimization

"The Price of Robustness" by Bertsimas and Sim represented a breakthrough in the development of a tractable robust counterpart of Linear Programming Problems. However, the central modeling assumption that the deviation band of each uncertain parameter is single may be too limitative in practice: experience indeed suggests that the deviations distribute also internally to the single band, so that getting a higher resolution by partitioning the band into multiple sub-bands seems advisable. The critical aim of our work is to close the knowledge gap about the adoption of a multi-band uncertainty set in Robust Optimization: a general definition and intensive theoretical study of a multi-band model are actually still missing. Our new developments have been also strongly inspired and encouraged by our industrial partners, which have been interested in getting a better modeling of arbitrary distributions, built on historical data of the uncertainty affecting the considered real-world problems. In this paper, we study the robust counterpart of a Linear Programming Problem with uncertain coefficient matrix, when a multi-band uncertainty set is considered. We first show that the robust counterpart corresponds to a compact LP formulation. Then we investigate the problem of separating cuts imposing robustness and we show that the separation can be efficiently operated by solving a min-cost flow problem. Finally, we test the performance of our new approach to Robust Optimization on realistic instances of a Wireless Network Design Problem subject to uncertainty.Comment: 15 pages. The present paper is a revised version of the one appeared in the Proceedings of SEA 201

Attack-Surface Metrics, OSSTMM and Common Criteria Based Approach to “Composable Security” in Complex Systems

In recent studies on Complex Systems and Systems-of-Systems theory, a huge effort has been put to cope with behavioral problems, i.e. the possibility of controlling a desired overall or end-to-end behavior by acting on the individual elements that constitute the system itself. This problem is particularly important in the “SMART” environments, where the huge number of devices, their significant computational capabilities as well as their tight interconnection produce a complex architecture for which it is difficult to predict (and control) a desired behavior; furthermore, if the scenario is allowed to dynamically evolve through the modification of both topology and subsystems composition, then the control problem becomes a real challenge. In this perspective, the purpose of this paper is to cope with a specific class of control problems in complex systems, the “composability of security functionalities”, recently introduced by the European Funded research through the pSHIELD and nSHIELD projects (ARTEMIS-JU programme). In a nutshell, the objective of this research is to define a control framework that, given a target security level for a specific application scenario, is able to i) discover the system elements, ii) quantify the security level of each element as well as its contribution to the security of the overall system, and iii) compute the control action to be applied on such elements to reach the security target. The main innovations proposed by the authors are: i) the definition of a comprehensive methodology to quantify the security of a generic system independently from the technology and the environment and ii) the integration of the derived metrics into a closed-loop scheme that allows real-time control of the system. The solution described in this work moves from the proof-of-concepts performed in the early phase of the pSHIELD research and enrich es it through an innovative metric with a sound foundation, able to potentially cope with any kind of pplication scenarios (railways, automotive, manufacturing, ...)