Invited Session Tue.2.MA 004

Tuesday, 13:15 - 14:45 h, Room: MA 004

Cluster 20: Robust optimization [...]

Applications of robust optimization I

 

Chair: Dick Den Hertog

 

 

Tuesday, 13:15 - 13:40 h, Room: MA 004, Talk 1

ihsan Yanikoglu
Robust simulation-based optimization with Taguchian regression models

Coauthor: Dick Den Hertog

 

Abstract:
A Taguchian way to deal with uncertain environmental parameters in simulation-based optimization is to create a regression model in both the optimization variables and the uncertain parameters, and then formulate the explicit optimization problem in terms of expectations and variances, or chance constraints. The disadvantages of this approach are that one has to assume that the distribution function for the uncertain parameters is normally distributed, and that both the mean and variance are known. The final solution may be very sensitive to these assumptions. We propose a Robust Optimization approach that do not need these assumptions. Based on historical data, uncertainty regions for the distribution is generated, and tractable robust counterparts are generated. This approach can be used for many types of regression models: polynomials, Kriging, etc. The novel approach is illustrated through numerical examples. Finally, for those simulation-based optimization problems that contain `wait-and-see' variables, we describe how to apply Adjustable Robust Optimization.

 

 

Tuesday, 13:45 - 14:10 h, Room: MA 004, Talk 2

Yudong Chen
Robust sparse regression and orthogonal matching pursuit

Coauthors: Constantine Caramanis, Shie Mannor

 

Abstract:
We consider support recovery in sparse regression, when some number n1 out of n+n1 total covariate/response pairs are arbitrarily corrupted. We are interested in understanding how many outliers, n1, we can tolerate, while identifying the correct support. As far as we know, neither standard outlier rejection techniques, nor recently developed robust regression algorithms (that focus only on corrupted response variables) provide guarantees on support recovery. Perhaps surprisingly, we also show that the natural brute force algorithm that searches over all subsets of n covariate/response pairs, and all subsets of possible support coordinates in order to minimize regression error, is remarkably poor, unable to correctly identify the support with even n1 = O(n/k) corrupted points, where k is the sparsity, and p is the dimension of the signal to be recovered. In this setting, we provide a simple algorithm that gives stronger performance guarantees, recovering the support with up to n1 = O(n/(√k log p)) corrupted points. Moreover, we compare our formulation with robust optimization, and demonstrate interesting connection and difference between them.

 

 

Tuesday, 14:15 - 14:40 h, Room: MA 004, Talk 3

Tsan Sheng Adam Ng
Target-oriented robust optimization for gas field development planning

Coauthors: Sy Charlle, Myun-Seok Cheon, Melvyn Sim, Lu Xu

 

Abstract:
Gas field development projects involve both investment and operation decisions, including field infrastructure installation, capacity expansions, and gas extraction planning. Many of these decisions are very expensive, difficult to reverse, and can impact the company's profitability. In this work we consider an offshore gas field development planning problem to achieve a target net present value at the end of the planning horizon as well as possible. This problem is also plagued by endogenous uncertainty that is found in the efficacy of gas well reserves. Inspired by robust optimization, we develop a model that maximizes the robustness of the development plan against uncertainty. The characteristics of the problem lead us to identify an equivalent deterministic mixed integer programming model of polynomial size, which enables us to obtain solutions to realistic size problems. Our computational tests show that the proposed model significantly improves target attainment and performs favourably in different problem instances.

 

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