Data-driven Adaptive Robust Optimization Research Articles

A data-driven strategy for industrial cracking furnace system scheduling under uncertainty

Cyclic scheduling of ethylene cracking furnace system (CSECFS) has a significant impact on raising economic performance of ethylene plants. However, in actual plants, optimal results of deterministic models may be suboptimal or ineffective because of various uncertainties. This paper proposes a novel data-driven adaptive robust optimization (DDARO) strategy that effectively bridges robust optimization and machine learning methods. A mixed-integer nonlinear programming (MINLP) model for CSECFS is developed initially. Second, data-driven uncertainty sets are generated using the historical data of processing flow rates: maximally correlated principal component analysis (MCPCA) is employed to partition the data into two subspaces, which are then delineated by support vector clustering (SVC) and generalized norm approaches, respectively. Third, a multi-stage DDARO model is established using the derived uncertainty sets and afterward transformed as a tractable single-stage model. Finally, a real-world case is performed to exemplify the effectiveness of the proposed framework.

Data-driven adaptive robust optimization for energy systems in ethylene plant under demand uncertainty

The operational optimization of energy systems is of great significance for improving the overall efficiency of industrial processes. Facing new challenges brought by widespread uncertainties, a data-driven adaptive robust industrial multi-type energy systems optimization framework was proposed by bridging robust optimization and machine learning methods in this paper. The industrial data were used to capture the demand uncertainty of the actual process. Hybrid models of units were first developed considering the operational characteristics, and the energy system optimization model was then formed as a mixed-integer nonlinear programming problem. The uncertain parameter set of process power demands was formed by the process models using historical data of a whole operating period. Afterward, the uncertainty set was constructed by applying the robust kernel density estimation method, which can reduce conservatism by considering the distributional information. By integrating the derived data-driven uncertainty set, a two-stage adaptive robust optimization model aiming at minimizing the weighted total energy consumption was developed. The multi-level robust optimization model was reformulated as a tractable single-level model by employing the affine decision rule. A case study on a plant-wide industrial energy system in the ethylene plant was performed, and the minimum optimal energy consumption was 25,350 kg/h, whose price of robustness was only 2.18%. The robust optimization results can guide the operational optimization of energy systems under uncertainty for the operators of the ethylene plant.

Data-Driven Adaptive Robust Unit Commitment Under Wind Power Uncertainty: A Bayesian Nonparametric Approach

This paper proposes a novel data-driven adaptive robust optimization (ARO) framework for the unit commitment (UC) problem integrating wind power into smart grids. By leveraging a Dirichlet process mixture model, a data-driven uncertainty set for wind power forecast errors is constructed as a union of several basic uncertainty sets. Therefore, the proposed uncertainty set can flexibly capture a compact region of uncertainty in a nonparametric fashion. Based on this uncertainty set and wind power forecasts, a data-driven adaptive robust UC problem is then formulated as a four-level optimization problem. A decomposition-based algorithm is further developed. Compared to conventional robust UC models, the proposed approach does not presume single mode, symmetry, or independence in uncertainty. Moreover, it not only substantially withstands wind power forecast errors, but also significantly mitigates the conservatism issue by reducing operational costs. We also compare the proposed approach with the state-of-the-art data-driven ARO method based on principal component analysis and kernel smoothing to assess its performance. The effectiveness of the proposed approach is demonstrated with the six-bus and IEEE 118-bus systems. Computational results show that the proposed approach scales gracefully with problem size and generates solutions that are more cost effective than the existing data-driven ARO method.

Adaptive robust unit commitment considering distributional uncertainty

To reduce the conservativeness of robust optimization-based unit commitment methods, an uncertainty set is usually prespecified with respect to the distributions of uncertain renewable resources, i.e., wind power. However, since the law of large numbers does not always work in practice, the obtained probability distribution may be unreliable. In this paper, a data-driven adaptive robust optimization method for the unit commitment of bulk power systems with high-level wind power integration is proposed. Different from the conventional robust unit commitment methods, the distributional uncertainty of wind power is well respected in the proposed approach. An imprecise-Dirichlet-model-based method is developed to construct the ambiguity set of wind power, which incorporates all possible probability distributions confirmed by historical data. The set can dynamically change with the data, i.e., the more valid data we have, the smaller the ambiguity set will become. With respect to the bounds of the ambiguity set, a polyhedron uncertainty set of wind power is constructed. By tuning the parameters of the uncertainty set, a balance between operational efficiency and risk can be achieved. An adaptive, robust unit commitment model is constructed based on the uncertainty set. By using the duality principle and big-M method, the formulations are converted into a mixed integer linear programming problem and solved using a column and constraint generation algorithm. Case studies on two benchmark systems illustrate the effectiveness and efficiency of the proposed method.