Multi-stage Adjustable Robust Mixed-Integer Optimization via Iterative Splitting of the Uncertainty set

In this paper we propose a methodology for constructing decision rules for in- teger and continuous decision variables in multiperiod robust linear optimization problems. This type of problems finds application in, for example, inventory management, lot sizing, and manpower management. We show that by iteratively splitting the uncertainty set into subsets one can differentiate the later-period decisions based on the revealed uncertain parameters. At the same time, the problem’s computational complexity stays at the same level as for the static robust problem. This holds also in the non-fixed recourse situation. In the fixed recourse situation our approach can be combined with linear decision rules for the continuous decision variables. We provide theoretical results how to split the uncertainty set by identifying sets of uncertain parameter scenarios to be divided for an improvement in the worst-case objective value. Based on this theory, we propose several splitting heuristics. Numerical examples entailing a capital budgeting and a lot sizing problem illustrate the advantages of the proposed approach

Multi-stage Adjustable Robust Mixed-Integer Optimization via Iterative Splitting of the Uncertainty set (Revision of CentER Discussion Paper 2014-056)

In this paper we propose a methodology for constructing decision rules for integer and continuous decision variables in multi period robust linear optimization problems. This type of problems finds application in, for example, inventory management, lot sizing, and manpower management. We show that by iteratively splitting the uncertainty set into subsets one can differentiate the later-period decisions based on the revealed uncertain parameters. At the same time, the problem’s computational complexity stays at the same level as for the static robust problem. This holds also in the non-fixed recourse situation. In the fixed recourse situation our approach can be combined with linear decision rules for the continuous decision variables. We provide theoretical results how to split the uncertainty set by identifying sets of uncertain parameter scenarios to be divided for an improvement in the worst-case objective value. Based on this theory, we propose several splitting heuristics. Numerical examples entailing a capital budgeting and a lot sizing problem illustrate the advantages of the proposed approach

Adaptive Robust Optimization with Dynamic Uncertainty Sets for Multi-Period Economic Dispatch under Significant Wind

The exceptional benefits of wind power as an environmentally responsible renewable energy resource have led to an increasing penetration of wind energy in today's power systems. This trend has started to reshape the paradigms of power system operations, as dealing with uncertainty caused by the highly intermittent and uncertain wind power becomes a significant issue. Motivated by this, we present a new framework using adaptive robust optimization for the economic dispatch of power systems with high level of wind penetration. In particular, we propose an adaptive robust optimization model for multi-period economic dispatch, and introduce the concept of dynamic uncertainty sets and methods to construct such sets to model temporal and spatial correlations of uncertainty. We also develop a simulation platform which combines the proposed robust economic dispatch model with statistical prediction tools in a rolling horizon framework. We have conducted extensive computational experiments on this platform using real wind data. The results are promising and demonstrate the benefits of our approach in terms of cost and reliability over existing robust optimization models as well as recent look-ahead dispatch models.Comment: Accepted for publication at IEEE Transactions on Power System

Data-Driven Robust Optimization

The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee. \edit{We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Computational evidence in portfolio management and queuing confirm that our data-driven sets significantly outperform traditional robust optimization techniques whenever data is available.Comment: 38 pages, 15 page appendix, 7 figures. This version updated as of Oct. 201

Dynamic Robust Transmission Expansion Planning

Recent breakthroughs in Transmission Network Expansion Planning (TNEP) have demonstrated that the use of robust optimization, as opposed to stochastic programming methods, renders the expansion planning problem considering uncertainties computationally tractable for real systems. However, there is still a yet unresolved and challenging problem as regards the resolution of the dynamic TNEP problem (DTNEP), which considers the year-by-year representation of uncertainties and investment decisions in an integrated way. This problem has been considered to be a highly complex and computationally intractable problem, and most research related to this topic focuses on very small case studies or used heuristic methods and has lead most studies about TNEP in the technical literature to take a wide spectrum of simplifying assumptions. In this paper an adaptive robust transmission network expansion planning formulation is proposed for keeping the full dynamic complexity of the problem. The method overcomes the problem size limitations and computational intractability associated with dynamic TNEP for realistic cases. Numerical results from an illustrative example and the IEEE 118-bus system are presented and discussed, demonstrating the benefits of this dynamic TNEP approach with respect to classical methods.Comment: 10 pages, 2 figures. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPWRS.2016.2629266, IEEE Transactions on Power Systems 201