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.

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.

The Effect of Different Optimization Methods on Robustness for Robust Optimization Design

2014 ◽  
Vol 721 ◽  
pp. 464-467
Author(s):  
Tao Fu ◽  
Qin Zhong Gong ◽  
Da Zhen Wang
Keyword(s):  
Robust Optimization ◽  
Objective Function ◽  
Robust Design ◽  
Optimization Design ◽  
Optimization Methods ◽  
Optimization Method ◽  
Design Parameters ◽  
Hybrid Particle Swarm Optimization ◽  
Design Variables ◽  
Robust Optimization Design

In view of robustness of objective function and constraints in robust design, the method of maximum variation analysis is adopted to improve the robust design. In this method, firstly, we analyses the effect of uncertain factors in design variables and design parameters on the objective function and constraints, then calculate maximum variations of objective function and constraints. A two-level optimum mathematical model is constructed by adding the maximum variations to the original constraints. Different solving methods are used to solve the model to study the influence to robustness. As a demonstration, we apply our robust optimization method to an engineering example, the design of a machine tool spindle. The results show that, compared with other methods, this method of HPSO(hybrid particle swarm optimization) algorithm is superior on solving efficiency and solving results, and the constraint robustness and the objective robustness completely satisfy the requirement, revealing that excellent solving method can improve robustness.

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 Selection of settings of PID regulators for quadrocopter with the use of optimization methods in the Wolfram MATHEMATICA software

2018 ◽  
Vol 19 (6) ◽  
pp. 780-785
Author(s):  
Krzysztof Wieczorkowski ◽  
Leszek Cedro
Keyword(s):  
Optimization Methods ◽  
Optimization Method ◽  
Lagrange Equations ◽  
Wolfram Mathematica ◽  
Simulation Results ◽  
Mathematica Software ◽  
Selection Of

The article presents the method of modeling the dynamics of a quadrocopter and presents a method for the selection of PID regulators. The quadrocopter's dynamics were derived based on the Lagrange equations of the second type. In the form of graphs, the simulation results were presented for the settings selected using the optimization method using the Wolfram Mathematica package

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.

scholarly journals HyAdamC: A New Adam-Based Hybrid Optimization Algorithm for Convolution Neural Networks

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4054
Author(s):  
Kyung-Soo Kim ◽  
Yong-Suk Choi
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Robust Optimization ◽  
Image Classification ◽  
Large Scale ◽  
Optimization Methods ◽  
Optimization Method ◽  
Hybrid Optimization ◽  
Computation Method ◽  
Convolution Neural Networks

As the performance of devices that conduct large-scale computations has been rapidly improved, various deep learning models have been successfully utilized in various applications. Particularly, convolution neural networks (CNN) have shown remarkable performance in image processing tasks such as image classification and segmentation. Accordingly, more stable and robust optimization methods are required to effectively train them. However, the traditional optimizers used in deep learning still have unsatisfactory training performance for the models with many layers and weights. Accordingly, in this paper, we propose a new Adam-based hybrid optimization method called HyAdamC for training CNNs effectively. HyAdamC uses three new velocity control functions to adjust its search strength carefully in term of initial, short, and long-term velocities. Moreover, HyAdamC utilizes an adaptive coefficient computation method to prevent that a search direction determined by the first momentum is distorted by any outlier gradients. Then, these are combined into one hybrid method. In our experiments, HyAdamC showed not only notable test accuracies but also significantly stable and robust optimization abilities when training various CNN models. Furthermore, we also found that HyAdamC could be applied into not only image classification and image segmentation tasks.

scholarly journals A Novel Graph and Safety Potential Field Theory-Based Vehicle Platoon Formation and Optimization Method

2021 ◽  
Vol 11 (3) ◽  
pp. 958
Author(s):  
Linheng Li ◽  
Jing Gan ◽  
Xu Qu ◽  
Peipei Mao ◽  
Ziwei Yi ◽  
...  
Keyword(s):  
Traffic Safety ◽  
Potential Field ◽  
Control Method ◽  
Control Strategies ◽  
Optimization Methods ◽  
Optimization Method ◽  
Optimization Strategy ◽  
Transmission Method ◽  
Optimization Control ◽  
Simulation Results

Platooning is considered to be a very effective method for improving traffic efficiency, traffic safety and fuel economy under the connected and automated environment. The prerequisite for realizing these advantages is how to form a platoon without any collisions and how to maintain and optimize the car-following behavior after platoon formation. However, most of the existing studies focus on the platoon configuration and information transmission method, while only a few attempt to address the issue of platoon formation and optimization methods. To this end, this study proposes a novel platoon formation and optimization model combining graph theory and safety potential field (G-SPF) theory for connected and automated vehicles (CAVs) under different vehicle distributions. Compared to previous studies, we innovatively incorporate the concept of the safety potential field to better describe the actual driving risk of vehicles and ensure their absolute safety. A four-step platoon formation and optimization strategy is developed to achieve platoon preliminary formation and platoon driving optimization control. Three traffic scenarios with different CAVs distributions are designed to verify the effectiveness of our proposed platoon formation method based on G-SPF theory, and the simulation results indicate that a collision-free platoon can be formed in a short time. Additionally, the G-SPF-based platoon driving optimization control method is demonstrated by comparing it with two typical control strategies. Compared with the constant spacing and constant time headway control strategies, the simulation results show that our proposed method can improve the traffic capacity by approximately 48.8% and 26.6%, respectively.

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