A deep learning-based robust optimization approach for refinery planning under uncertainty
Introduction
Crude oil is a vital energy resource, and refinery is the core of production, which converts crude oil into valuable products such as gasoline, diesel, and fuel oil. However, recent years have witnessed a fluctuating price of crude oil and a severer shortage of crude oil resources (Abdollahi, 2020). Therefore, refinery planning optimization has received increasing attention in academia and industry to process crude oil appropriately (Nicoletti and You, 2020; Zhang, 2015).
A variety of methods have been developed for modeling refinery planning (Khor and Varvarezos, 2016; Karuppiah et al., 2008). It is challenging to construct processing models, and a recent streamline is to employ nonlinear models to capture the nonlinear nature in the optimization framework (Li et al., 2005; Kelly, 2004; Mahalec and Sanchez, 2012). A general mixed-integer nonlinear programming (MINLP) model described general refinery topology with nonlinear processing and blending models (Pinto et al., 2000). Two different nonlinear models for the distillation units were employed in refinery-wide planning to develop more accurate processing models (Siamizade, 2019). Aiming at integrating production systems and energy systems, a multi-period MINLP model was developed (Zhang, 2015). Due to the enormous amount of industrial historical data, Li proposed a data-driven method based on process knowledge to predict yields and products properties (Li, 2016). A piecewise linear model of the nonlinear processing unit was derived for reducing the computational cost. The resultant large-scale MINLP optimization problem can be transformed into a MILP problem (Gao, 2015). Despite the strict nonlinear processing models and optimization algorithms were developed, none of them account for uncertainties at the system level.
Uncertainties spread over the refinery planning (Li, 2004), such as product demands, supply of crude oil, and device efficiency. The existence of these uncertainties may render the solution obtained by the deterministic method suboptimal or even infeasible (Bertsimas and Sim, 2004). Thus, there is a strong desire to tackle these uncertainties in the industrial process. Stochastic programming (Birge, 1997), robust optimization (Ben-Tal and Nemirovski, 2000), and other optimization methods have been developed in refinery planning optimization (Li et al., 2008; Grossmann, 2016). Due to its broad applicability, stochastic programming has been successfully applied to model uncertainty in refinery planning. The term loss function was proposed to deal with demand uncertainty by calculating the expectation of profit (Li, 2004). Account for the uncertainty in crude oil property, a two-stage stochastic programming approach was presented by combining crude oil purchase and planning optimization (Yang and Barton, 2016). The Markov property was used to describe the production rate fluctuation caused by the switching of processing schemes, and a chance-constrained programming model was further established (Yang et al., 2017). A stochastic programming model was proposed to deal with multi-period planning and scheduling under component uncertainty (Jalanko and Mahalec, 2018). Awudu investigated a stochastic programming approach for biofuel supply chain under demand and price uncertainty (Awudu and Zhang, 2013). In Panda's work, a structural adaptive algorithm was developed in crude oil scheduling (Panda and Ramteke, 2019).
Stochastic programming assumes that the probability distribution of uncertain parameters is known in advance, which is hard to fulfill in industrial practice. Furthermore, the assumed probability distribution deviates from the true distribution, which could get an infeasible solution. As another powerful optimization method under uncertainty, robust optimization does not require probability distributions of uncertain parameters but only models possible values of parameters utilizing an uncertainty set (Grossmann, 2016). The construction of uncertainty sets is a crucial ingredient in robust optimization (Bertsimas et al., 2018), and thus special care shall be taken while designing the structure and size of uncertainty sets. Conventional uncertainty sets such as the ellipsoidal uncertainty set, budget uncertainty set (Bertsimas and Sim, 2004), and the combined uncertainty set (Li et al., 2011) are overly conservative and lead to a pessimistic solution.
Recent years have witnessed a rapid development of data-driven robust optimization where machine learning methods are applied to construct uncertainty sets (Guevara, 2020). Ning and You reviewed recent advances for data-driven optimization integrating machine learning while pointing out potential research opportunities (Ning and You, 2019). A method of constructing the polyhedral uncertainty set based on principal component analysis and kernel density estimation was proposed to capture asymmetric distributions, where forward and backward deviation vectors were considered (Ning and You, 2018). The Dirichlet process mixture model was successfully employed for modeling high-dimensional uncertainty (Campbell and How, 2015; Ning and You, 2017). To maintain tractability with multi-mode uncertainty data, a data-driven stochastic robust optimization framework was further proposed (Ning and You, 2018). The support vector clustering (SVC) method with a piecewise linear kernel was used to handle the correlated uncertainty data (Shang et al., 2017). Shang and You analyzed the knowledge gap between the theoretical model and practical requirements. Then, they suggested that these data-driven methods should incorporate a priori knowledge of processes in practice (Shang and You, 2019). These methods are applied widely in energy systems (Zhao et al., 2018; Rong, 2018), planning, and scheduling (Shang and You, 2018; Zhang et al., 2018; Zhang, 2018). To avoid harm caused by excessive sulfur content, a novel data-driven robust optimization model based on principal component analysis was applied for recipe optimization of crude oil blending (Dai, 2020). A robust MINLP framework for utility system optimization under device efficiency uncertainty was proposed, where the SVC method was utilized for constructing an uncertainty set (Shen, 2020). Furthermore, the combination of data-driven robust optimization and refinery planning should be further studied to hedge against the uncertainty.
To address refinery planning under uncertainty, an unsupervised deep learning method is proposed to model uncertainty set, given by the union of convex subsets (Goerigk and Kurtz, 2020). Due to the non-convexity of the proposed uncertainty set, the classical dual transformation is not suitable for this issue. An iterative constraint generation approach is further employed to solve the proposed data-driven problem. Compared with the data-driven SVC method, the deep neural networks for support vector data description (denoted as Deep-SVDD in the following) method performs better. The main contributions of this paper are as follows.
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A deep learning-based robust optimization framework is employed for refinery planning under uncertainty.
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A data-driven price uncertainty set is constructed using historical data for refinery planning by Deep-SVDD.
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An activation pattern is calculated by all scenarios to solve the adversarial problem for refinery planning.
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An industrial case study of refinery planning optimization is presented to illustrate the effectiveness of the proposed method.
The rest of this paper is organized as follows. The problem statement is presented in Section 2. The deterministic refinery planning model and the data-driven robust model are formulated in Section 3. Case studies from an actual refinery are discussed in Section 4. Conclusions are presented in Section 5.
Section snippets
Problem Statements
The problem studied in this work pertains to refinery planning optimization under uncertainty over a planning time horizon. Fig. 1 illustrates a general representation of streamflow in typical refinery planning. Three processes are involved in the refinery planning operation, crude oil blending and processing, production operations, and product blending. The set denotes crude oils, which means crude oils with different properties and prices are mixed and sent to crude
Deterministic and data-driven robust optimization models for refinery planning
In this section, a deterministic optimization model for refinery planning is first developed. Based on that, the data-driven robust optimization model is further formulated by utilizing the deep neural network. The flowchart of the proposed data-driven robust optimization framework is presented in Fig. 2.
Case study
A case study on refinery planning of an actual plant is carried out to demonstrate the effectiveness of the proposed data-driven robust optimization model. The detailed flowchart of the refinery is shown in Fig. 3. A horizon of refinery planning is set as 10 days. Note that there are five types of crude oils available to the CDU, and mixed crude oils are separated into different intermediate products according to boiling points. There are four hydrogenation units (kerosene hydrogenation unit,
Conclusions
In this work, a novel framework combined deep learning and robust optimization was presented for refinery planning under prices uncertainty. The prices uncertain parameters were collected from an actual refinery, and the data-driven uncertainty set can be constructed by a deep support vector data description method. Base on this, the data-driven MILP model with uncertain parameters was formulated. Since the data-driven MILP problem cannot be reformulated into a tractable counterpart using
CRediT authorship contribution statement
Cong Wang: Software, Investigation, Resources, Writing – original draft, Visualization, Writing – review & editing. Xin Peng: Software, Investigation, Resources, Writing – original draft, Visualization, Writing – review & editing, Formal analysis, Data curation. Chao Shang: Software, Investigation, Resources, Writing – original draft, Visualization, Writing – review & editing, Methodology, Software, Formal analysis. Chen Fan: Software, Investigation, Resources, Writing – original draft,
Declaration of Competing Interest
We have already confirmed that this manuscript (Manuscript name: ``A deep learning-based robust optimization approach for refinery planning optimization under uncertainty'') has been approved by all authors for publication and no conflict of interest is declared in this manuscript. The work described in this paper was an original research which has not been published before and not going to be published elsewhere, neither in whole nor in part.
Acknowledgments
The authors acknowledge the supports from National Science and Technology Innovation 2030 Major Project of the Ministry of Science and Technology of China under Grant 2018AAA0101602, National Natural Science Foundation of China (Major Program: 61890930-3), International (Regional) Cooperation and Exchange Project (61720106008) and National Natural Science Fund for Distinguished Young Scholars (61925305).
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2023, Computers and Operations ResearchCitation Excerpt :By scaling the radius of our derived set, we can additionally control the conservativeness of the robust solution. While this work was under review, our method has been applied to a real-world refinery planning problem under uncertainty in Wang et al. (2021). The results reported in that paper give further evidence that our method performs well in practice.
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2022, Computers and Chemical EngineeringCitation Excerpt :This applies particularly to global optimization relying on MINLP solvers such as Baron (Castillo Castillo et al., 2017; Kolodziej et al., 2013; Sua et al., 2021). Recent applications of emerging technologies such as machine learning (Ning and You, 2019; Wang et al., 2021), data-driven method (Beykal et al., 2022), and quantum computing (Ossorio-Castillo and Pena-Brage, 2021) to scheduling and general mixed-integer programming problems hint potential ways of accelerating the solution speed. At present, however, scheduling optimization in industrial refineries often comes from know-how and from the planification step (LP model).
Machine learning-based data-driven robust optimization approach under uncertainty
2022, Journal of Process ControlCitation Excerpt :For example, many unsupervised learning models have been employed to construct the data-driven uncertainty set, which can obtain lower conservative optimal solutions. Among them, support vector clustering, principal component analysis (PCA), and kernel density estimation (KDE) have been used to construct data-driven uncertainty sets defined by several linear inequalities [19,34–37], whereas fuzzy C-means clustering and neuro fuzzy C-means clustering have been adopted to design flexible data-driven uncertainty sets with irregular boundaries [30,38,39]. However, there are still some limitations in data-driven RO methods.