scholarly journals Data-Driven Robust Optimization for Steam Systems in Ethylene Plants under Uncertainty

Processes ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 744 ◽  
Author(s):  
Liang Zhao ◽  
Weimin Zhong ◽  
Wenli Du
Keyword(s):  
Robust Optimization ◽  
Dirichlet Process ◽  
Programming Model ◽  
Operating Cost ◽  
Data Driven ◽  
Mixed Integer ◽  
Ethylene Plant ◽  
Uncertainty Set ◽  
Quadratic Mixed Integer Programming ◽  
Steam System

In an ethylene plant, steam system provides shaft power to compressors and pumps and heats the process streams. Modeling and optimization of a steam system is a powerful tool to bring benefits and save energy for ethylene plants. However, the uncertainty of device efficiencies and the fluctuation of the process demands cause great difficulties to traditional mathematical programming methods, which could result in suboptimal or infeasible solution. The growing data-driven optimization approaches offer new techniques to eliminate uncertainty in the process system engineering community. A data-driven robust optimization (DDRO) methodology is proposed to deal with uncertainty in the optimization of steam system in an ethylene plant. A hybrid model of extraction–exhausting steam turbine is developed, and its coefficients are considered as uncertain parameters. A deterministic mixed integer linear programming model of the steam system is formulated based on the model of the components to minimize the operating cost of the ethylene plant. The uncertain parameter set of the proposed model is derived from the historical data, and the Dirichlet process mixture model is employed to capture the features for the construction of the uncertainty set. In combination with the derived uncertainty set, a data-driven conic quadratic mixed-integer programming model is reformulated for the optimization of the steam system under uncertainty. An actual case study is utilized to validate the performance of the proposed DDRO method.

scholarly journals Data Driven Robust Energy and Reserve Dispatch Based on a Nonparametric Dirichlet Process Gaussian Mixture Model

Energies ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4642
Author(s):  
Li Dai ◽  
Dahai You ◽  
Xianggen Yin
Keyword(s):  
Robust Optimization ◽  
Dirichlet Process ◽  
Forecast Error ◽  
Optimization Methods ◽  
Optimization Method ◽  
Gaussian Mixture ◽  
Data Driven ◽  
Uncertainty Sets ◽  
Uncertainty Set ◽  
Simulation Results

Traditional robust optimization methods use box uncertainty sets or gamma uncertainty sets to describe wind power uncertainty. However, these uncertainty sets fail to utilize wind forecast error probability information and assume that the wind forecast error is symmetrical and independent. This assumption is not reasonable and makes the optimization results conservative. To avoid such conservative results from traditional robust optimization methods, in this paper a novel data driven optimization method based on the nonparametric Dirichlet process Gaussian mixture model (DPGMM) was proposed to solve energy and reserve dispatch problems. First, we combined the DPGMM and variation inference algorithm to extract the GMM parameter information embedded within historical data. Based on the parameter information, a data driven polyhedral uncertainty set was proposed. After constructing the uncertainty set, we solved the robust energy and reserve problem. Finally, a column and constraint generation method was employed to solve the proposed data driven optimization method. We used real historical wind power forecast error data to test the performance of the proposed uncertainty set. The simulation results indicated that the proposed uncertainty set had a smaller volume than other data driven uncertainty sets with the same predefined coverage rate. Furthermore, the simulation was carried on PJM 5-bus and IEEE-118 bus systems to test the data driven optimization method. The simulation results demonstrated that the proposed optimization method was less conservative than traditional data driven robust optimization methods and distributionally robust optimization methods.

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

2021 ◽  
pp. 118148
Author(s):  
Feifei Shen ◽  
Liang Zhao ◽  
Meihong Wang ◽  
Wenli Du ◽  
Feng Qian
Keyword(s):  
Robust Optimization ◽  
Demand Uncertainty ◽  
Energy Systems ◽  
Data Driven ◽  
Ethylene Plant

scholarly journals A Data-Driven Hybrid Three-Stage Framework for Hospital Bed Allocation: A Case Study in a Large Tertiary Hospital in China

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Li Luo ◽  
Jialing Li ◽  
Xueru Xu ◽  
Wenwu Shen ◽  
Lin Xiao
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Programming Model ◽  
Tertiary Hospital ◽  
Data Driven ◽  
Mixed Integer ◽  
Hospital Bed ◽  
Tertiary Hospitals ◽  
Bed Allocation

Beds are key, scarce medical resources in hospitals. The bed occupancy rate (BOR) amongst different departments within large tertiary hospitals is very imbalanced, a situation which has led to problems between the supply of and the demand for bed resources. This study aims to balance the utilization of existing beds in a large tertiary hospital in China. We developed a data-driven hybrid three-stage framework incorporating data analysis, simulation, and mixed integer programming to minimize the gaps in BOR among different departments. The first stage is to calculate the length of stay (LOS) and BOR of each department and identify the departments that need to be allocated beds. In the second stage, we used a fitted arrival distribution and median LOS as the input to a generic simulation model. In the third stage, we built a mixed integer programming model using the results obtained in the first two stages to generate the optimal bed allocation strategy for different departments. The value of the objective function, Z, represents the severity of the imbalance in BOR. Our case study demonstrated the effectiveness of the proposed data-driven hybrid three-stage framework. The results show that Z decreases from 0.7344 to 0.0409 after re-allocation, which means that the internal imbalance has eased. Our framework provides hospital bed policy makers with a feasible solution for bed allocation.

Radius of Robust Feasibility for Mixed-Integer Problems

2021 ◽  
Author(s):  
Frauke Liers ◽  
Lars Schewe ◽  
Johannes Thürauf
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Mixed Integer ◽  
Lp Relaxation ◽  
Maximal Size ◽  
Uncertainty Sets ◽  
Uncertainty Set ◽  
New Methodologies ◽  
Continuous Optimization Problems

For a mixed-integer linear problem (MIP) with uncertain constraints, the radius of robust feasibility (RRF) determines a value for the maximal size of the uncertainty set such that robust feasibility of the MIP can be guaranteed. The approaches for the RRF in the literature are restricted to continuous optimization problems. We first analyze relations between the RRF of a MIP and its continuous linear (LP) relaxation. In particular, we derive conditions under which a MIP and its LP relaxation have the same RRF. Afterward, we extend the notion of the RRF such that it can be applied to a large variety of optimization problems and uncertainty sets. In contrast to the setting commonly used in the literature, we consider for every constraint a potentially different uncertainty set that is not necessarily full-dimensional. Thus, we generalize the RRF to MIPs and to include safe variables and constraints; that is, where uncertainties do not affect certain variables or constraints. In the extended setting, we again analyze relations between the RRF for a MIP and its LP relaxation. Afterward, we present methods for computing the RRF of LPs and of MIPs with safe variables and constraints. Finally, we show that the new methodologies can be successfully applied to the instances in the MIPLIB 2017 for computing the RRF. Summary of Contribution: Robust optimization is an important field of operations research due to its capability of protecting optimization problems from data uncertainties that are usually defined via so-called uncertainty sets. Intensive research has been conducted in developing algorithmically tractable reformulations of the usually semi-infinite robust optimization problems. However, in applications it also important to construct appropriate uncertainty sets (i.e., prohibiting too conservative, intractable, or even infeasible robust optimization problems due to the choice of the uncertainty set). In doing so, it is useful to know the maximal “size” of a given uncertainty set such that a robust feasible solution still exists. In this paper, we study one notion of “size”: the radius of robust feasibility (RRF). We contribute on the theoretical side by generalizing the RRF to MIPs as well as to include “safe” variables and constraints (i.e., where uncertainties do not affect certain variables or constraints). This allows to apply the RRF to many applications since safe variables and constraints exist in most applications. We also provide first methods for computing the RRF of LPs as well as of MIPs with safe variables and constraints. Finally, we show that the new methodologies can be successfully applied to the instances in the MIPLIB 2017 for computing the RRF.

scholarly journals Reduction of Annual Operational Costs in Power Systems through the Optimal Siting and Sizing of STATCOMs

2021 ◽  
Vol 11 (10) ◽  
pp. 4634
Author(s):  
Oscar Danilo Montoya ◽  
Jose Eduardo Fuentes ◽  
Francisco David Moya ◽  
José Ángel Barrios ◽  
Harold R. Chamorro
Keyword(s):  
Power Systems ◽  
Power System ◽  
Reactive Power ◽  
Programming Model ◽  
Operating Cost ◽  
Mathematical Optimization ◽  
System Optimization ◽  
Point Of View ◽  
Mixed Integer ◽  
Annual Operating Cost

The problem of the optimal siting and placement of static compensates (STATCOMs) in power systems is addressed in this paper from an exact mathematical optimization point of view. A mixed-integer nonlinear programming model to present the problem was developed with the aim of minimizing the annual operating costs of the power system, which is the sum of the costs of the energy losses and of the installation of the STATCOMs. The optimization model has constraints regarding the active and reactive power balance equations and those associated with the devices’ capabilities, among others. To characterize the electrical behavior of the power system, different load profiles such as residential, industrial, and commercial are considered for a period of 24 h of operation. The solution of the proposed model is reached with the general algebraic modeling system optimization package. The numerical results indicate the positive effect of the dynamic reactive power injections in the power systems on annual operating cost reduction. A Pareto front was built to present the multi-objective behavior of the studied problem when compared to investment and operative costs. The complete numerical validations are made in the IEEE 24-, IEEE 33-, and IEEE 69-bus systems, respectively.

Modeling Defender-Attacker Problems as Robust Linear Programs with Mixed-Integer Uncertainty Sets

2021 ◽  
Author(s):  
Juan S. Borrero ◽  
Leonardo Lozano
Keyword(s):  
Robust Optimization ◽  
Convex Sets ◽  
Optimization Problems ◽  
Computational Study ◽  
Mixed Integer ◽  
Computational Time ◽  
Point Problem ◽  
Solution Algorithms ◽  
Uncertainty Sets ◽  
Uncertainty Set

We study a class of sequential defender-attacker optimization problems where the defender’s objective is uncertain and depends on the operations of the attacker, which are represented by a mixed-integer uncertainty set. The defender seeks to hedge against the worst possible data realization, resulting in a robust optimization problem with a mixed-integer uncertainty set, which requires the solution of a challenging mixed-integer problem, which can be seen as a saddle-point problem over a nonconvex domain. We study two exact solution algorithms and present two feature applications for which the uncertainty is naturally modeled as a mixed-integer set. Our computational experiments show that the considered algorithms greatly outperform standard algorithms both in terms of computational time and solution quality. Moreover, our results show that modeling uncertainty with mixed-integer sets, instead of approximating the data using convex sets, results in less conservative solutions, which translates to a lower cost for the defender to protect from uncertainty. Summary of Contribution: We consider a class of defender-attacker problems where the defender has to make operational decisions that depend on uncertain actions from an adversarial attacker. Due to the type of information available to the defender, neither probabilistic modeling, nor robust optimization methods with convex uncertainty sets, are well suited to address the defender’s decision-making problem. Consequently, we frame the defender’s problem as a class of robust optimization problems with a mixed-integer uncertainty sets, and devise two exact algorithms that solve this class of problems. A comprehensive computational study shows that for the considered applications, our algorithms improves the performance of existing robust optimization approaches that can be adapted to solve this class of problems. Moreover, we show how mixed-integer uncertainty sets can reduce the level of over-conservatism that is a known issue of robust optimization approaches.

Sign in / Sign up

Export Citation Format

Share Document