On robust optimization of two-stage systems
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In order to protect the environment and address fossil fuel scarcity, renewable energy is increasingly used for power generation. However, due to the uncertainties it brings to electricity production, deterministic optimization is no longer sufficient for operational needs. Therefore, a large number of optimization techniques under uncertainty have been proposed, which provide good ways to address uncertainties. This paper selects three of the more important optimization techniques under uncertainty to introduce: stochastic programming (SP), robust optimization (RO), and a novel approach named distributionally robust optimization (DRO) based on the first two. We explain the basic framework and general process of each approach using specific examples. The focus is on how each method addresses the uncertainties. In addition, we also compare their strengths and weaknesses and discuss future research directions.
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Summary Reservoir simulation is a valuable tool for performance prediction, production optimization, and field-development decision making. In recent years, significant progress has been made in developing automated workflows for optimization of production and field development by combining reservoir simulation with numerical optimization schemes. Although optimization under geologic uncertainty has received considerable attention, the uncertainty associated with future development activities has not yet been considered in field-development optimization. In practice, reservoirs undergo extensive development activities throughout their life cycle. Disregarding the possibility of future developments can lead to field-performance predictions and optimization results that might be far from optimal. This paper presents a stochastic optimization formulation to account for the uncertainty in future development activities while optimizing current decision variables (e.g., well controls and locations). A motivating example is presented first to demonstrate the significance of including the uncertainty in future drilling plans in oilfield-development optimization. Because future decisions might not be implemented as planned, a stochastic optimization framework is developed to incorporate future drilling activities as uncertain (random) variables. A multistage stochastic programming framework is introduced, in which the decision maker selects an optimal strategy for the current stage decisions while accounting for the uncertainty in future development activities. For optimization, a sequential approach is adopted whereby well locations and controls are repeatedly optimized until improvements in the objective function fall below a threshold. Case studies are presented to demonstrate the advantages of treating future field-development activities as uncertain events in the optimization of current decision variables. In developing real fields, where various unpredictable external factors can cast uncertainty regarding future drilling activities, the proposed approach provides solutions that are more robust and can hedge against changes/uncertainty in future development plans better than conventional workflows.
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In this paper a multi-stage multi-item production/inventory system with limited production capacity in stochastic demand environment is considered. We proposed a robust optimization model to deal with the uncertain market demands that are denoted as a number of discrete scenarios with known probabilities. An effective genetic algorithm is designed. The result of a simulation example shows that robust optimization is possible. By choice of proper programming weightω, we can meet the stochastic demand with little error and very little cost.
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Robust linear programming is a method of modeling.Combining calculate implement,optimization with uncertainty data and only uncertainty sets was carried out.This paper discuss ed the theory and method of robust linear optimization problem of linear optimization problem.
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This letter presents a stochastic robust framework for two-stage power system optimization problems with uncertainty. The model optimizes the probabilistic expectation of different worst-case scenarios with different uncertainty sets. A case study of unit commitment shows the effectiveness of the proposed model and algorithms.
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This chapter reviews the main ideas behind dynamic programming, stochastic programming, and robust optimization, and illustrates the techniques with examples. It provides taxonomy of methods for optimization when the input parameters are uncertain. Dynamic programming solves a large multistage optimization problem sequentially, starting at the last stage and proceeding backward, thus keeping track only of the optimal paths from any given time period onward. The stochastic programming can be used to address the presence of uncertain input data in three types of optimization problems: expected value for single-stage and multistage models; models involving risk measures; and chance-constrained models. A major problem with dynamic and stochastic programming formulations is that in practice it is often difficult to obtain detailed information about the probability distributions of the uncertainties in the model. Robust optimization formulations can be used also in multistage settings to replace dynamic programming or stochastic programming algorithms.
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