Data-driven satisficing measure and ranking

We propose an computational framework for real-time risk assessment and prioritizing for random outcomes without prior information on probability distributions. The basic model is built based on satisficing measure (SM) which yields a single index for risk comparison. Since SM is a dual representation for a family of risk measures, we consider problems constrained by general convex risk measures and specifically by Conditional value-at-risk. Starting from offline optimization, we apply sample average approximation technique and argue the convergence rate and validation of optimal solutions. In online stochastic optimization case, we develop primal-dual stochastic approximation algorithms respectively for general risk constrained problems, and derive their regret bounds. For both offline and online cases, we illustrate the relationship between risk ranking accuracy with sample size (or iterations).Comment: 26 Pages, 6 Figure

A Posteriori Probabilistic Bounds of Convex Scenario Programs with Validation Tests

Scenario programs have established themselves as efficient tools towards decision-making under uncertainty. To assess the quality of scenario-based solutions a posteriori, validation tests based on Bernoulli trials have been widely adopted in practice. However, to reach a theoretically reliable judgement of risk, one typically needs to collect massive validation samples. In this work, we propose new a posteriori bounds for convex scenario programs with validation tests, which are dependent on both realizations of support constraints and performance on out-of-sample validation data. The proposed bounds enjoy wide generality in that many existing theoretical results can be incorporated as particular cases. To facilitate practical use, a systematic approach for parameterizing a posteriori probability bounds is also developed, which is shown to possess a variety of desirable properties allowing for easy implementations and clear interpretations. By synthesizing comprehensive information about support constraints and validation tests, improved risk evaluation can be achieved for randomized solutions in comparison with existing a posteriori bounds. Case studies on controller design of aircraft lateral motion are presented to validate the effectiveness of the proposed a posteriori bounds

Limited Visibility and Uncertainty Aware Motion Planning for Automated Driving

Adverse weather conditions and occlusions in urban environments result in impaired perception. The uncertainties are handled in different modules of an automated vehicle, ranging from sensor level over situation prediction until motion planning. This paper focuses on motion planning given an uncertain environment model with occlusions. We present a method to remain collision free for the worst-case evolution of the given scene. We define criteria that measure the available margins to a collision while considering visibility and interactions, and consequently integrate conditions that apply these criteria into an optimization-based motion planner. We show the generality of our method by validating it in several distinct urban scenarios

Solution Repair/Recovery in Uncertain Optimization Environment

Operation management problems (such as Production Planning and Scheduling) are represented and formulated as optimization models. The resolution of such optimization models leads to solutions which have to be operated in an organization. However, the conditions under which the optimal solution is obtained rarely correspond exactly to the conditions under which the solution will be operated in the organization.Therefore, in most practical contexts, the computed optimal solution is not anymore optimal under the conditions in which it is operated. Indeed, it can be "far from optimal" or even not feasible. For different reasons, we hadn't the possibility to completely re-optimize the existing solution or plan. As a consequence, it is necessary to look for "repair solutions", i.e., solutions that have a good behavior with respect to possible scenarios, or with respect to uncertainty of the parameters of the model. To tackle the problem, the computed solution should be such that it is possible to "repair" it through a local re-optimization guided by the user or through a limited change aiming at minimizing the impact of taking into consideration the scenarios

Efficient Robust Optimization of Metal Forming Processes using a Sequential Metamodel Based Strategy

The coupling of Finite Element (FE) simulations to mathematical optimization techniques has contributed significantly to product improvements and cost reductions in the metal forming industries. The next challenge is to bridge the gap between deterministic optimization techniques and the industrial need for robustness. This paper introduces a new and generally applicable structured methodology for modeling and solving robust optimization problems. Stochastic design variables or noise variables are taken into account explicitly in the optimization procedure. The metamodel-based strategy is combined with a sequential improvement algorithm to efficiently increase the accuracy of the objective function prediction. This is only done at regions of interest containing the optimal robust design. Application of the methodology to an industrial V-bending process resulted in valuable process insights and an improved robust process design. Moreover, a significant improvement of the robustness (> 2s ) was obtained by minimizing the deteriorating effects of several noise variables. The robust optimization results demonstrate the general applicability of the robust optimization strategy and underline the importance of including uncertainty and robustness explicitly in the numerical optimization procedure

Risk-Aware Management of Distributed Energy Resources

High wind energy penetration critically challenges the economic dispatch of current and future power systems. Supply and demand must be balanced at every bus of the grid, while respecting transmission line ratings and accounting for the stochastic nature of renewable energy sources. Aligned to that goal, a network-constrained economic dispatch is developed in this paper. To account for the uncertainty of renewable energy forecasts, wind farm schedules are determined so that they can be delivered over the transmission network with a prescribed probability. Given that the distribution of wind power forecasts is rarely known, and/or uncertainties may yield non-convex feasible sets for the power schedules, a scenario approximation technique using Monte Carlo sampling is pursued. Upon utilizing the structure of the DC optimal power flow (OPF), a distribution-free convex problem formulation is derived whose complexity scales well with the wind forecast sample size. The efficacy of this novel approach is evaluated over the IEEE 30-bus power grid benchmark after including real operation data from seven wind farms.Comment: To appear in Proc. of 18th Intl. Conf. on DSP, Santorini Island, Greece, July 1-3, 201