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A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs

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arXiv 2018年

作者： Ogbe, Emmanuel Li, Xiang Department of Chemical Engineering Queen's University KingstonONK7L 3N6 Canada

This paper proposes a joint decomposition method that combines Lagrangian decomposition and generalized Benders decomposition, to eficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global optimality, without the need for explicit branch and bound search. In this approach, we view the variables coupling the scenario dependent variables and those causing nonconvexity as complicating variables. We systematically solve the Lagrangian decomposition subproblems and the generalized Benders decomposition subproblems in a unified framework. The method requires the solution of a di_cult relaxed master problem, but the problem is only solved when necessary. Enhancements to the method are made to reduce the number of the relaxed master problems to be solved and ease the solution of each relaxed master problem. We consider two scenario-based, two-stage stochastic nonconvex MINLP problems that arise from integrated design and operation of process networks in the case study, and we show that the proposed method can solve the two problems significantly faster than stateof-the-art global optimization solvers. Copyright © 2018, The Authors. All rights reserved.

关键词： stochastic programming

Index-based policy for risk-averse multi-armed bandit

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arXiv 2018年

作者： Xu, Jianyu Haskell, William B. Ye, Zhisheng Department of Industrial Systems Engineering and Management National University of Singapore 1 Engineering Drive 2 Singapore

The multi-armed bandit (MAB) is a classical online optimization model for the trade-off between exploration and exploitation. The traditional MAB is concerned with finding the arm that minimizes the mean cost. However, minimizing the mean does not take the risk of the problem into account. We now want to accommodate risk-averse decision makers. In this work, we introduce a coherent risk measure as the criterion to form a risk-averse MAB. In particular, we derive an index-based online sampling framework for the risk-averse MAB. We develop this framework in detail for three specific risk measures, i.e. the conditional value-at-risk, the mean-deviation and the shortfall risk measures. Under each risk measure, the convergence rate for the upper bound on the pseudo regret, defined as the difference between the expectation of the empirical risk based on the observation sequence and the true risk of the optimal arm, is established. Copyright © 2018, The Authors. All rights reserved.

关键词： stochastic programming

Modeling and Optimizing of Assets and Liabilities Structure of Commercial Bank in Multi time Periods

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Modeling and Optimizing of Assets and Liabilities Structure ...

第37届中国控制会议

作者： Hali Pang Weilong Gao College of Information Science and Engineering Northeastern University

Considering uncertainty of the deposit flow, non-performing loan and allotted time matching of assets and liabilities, a multi time periods asset-liability optimizing problem of commercial banks is studied in this paper. A stochastic programming model with objective of maximum profit is established, and the constraints of loss of non-performing loan and mismatching limit of allotted time of assets and liabilities are used to control the loss of bad loan and mismatching degree. Genetic algorithm is used to solve the model and computation results illustrate the feasibility and the effectiveness of proposed model and algorithm. The conclusion that has management significance is obtained.

关键词： Uncertain environment Asset and liability management stochastic programming Genetic algorithm

Scenario Generation for Multi-objective stochastic Portfolio Selection

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Scenario Generation for Multi-objective Stochastic Portfolio...

International Conference on Modeling, Simulation and Applied Optimization

作者： El Fayedh Rimeh Ben Abdelaziz Fouad Aouni Belaid Lab. Larodec ISG Rouen Business School Mont Saint Angnan SCA Laurantian University

ISBN: (纸本)9781467358125

Scenario generation allows stochastic programming the expression of uncertainty. In fact scenarios allow the representation of stochastic elements by discrete distributions with many outcomes. In [15] authors proposed to use a nonlinear program to satisfy specified statistical properties. In this paper, we formulate a goal programming model for scenario generation for several random objectives. Scenarios generation help decision maker in solving stochastic goal programming model for portfolio selection problem. We applied our models on some Tunisian stock market security's data where we consider two random objectives that are the rate of return and liquidity.

关键词： Scenario generation stochastic programming Goal programming Portfolio selection

A distributionally robust self-scheduling under price uncertainty based on CVaR

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arXiv 2021年

作者： Yang, Linfeng Yang, Ying Chen, Guo Dong, Zhaoyang School of Computer Electronics and Information Guangxi University Nanning530004 China Guangxi Key Laboratory of Multimedia Communication and Network Technology Guangxi University School of Electrical Engineering and Tele-communications University of NSW SydneyNSW2052 Australia

To ensure a successful bid while maximizing of profits, generation companies (GENCOs) need a self-scheduling strategy that can cope with a variety of scenarios. So distributionally robust optimization (DRO) is a good choice because that it can provide an adjustable self-scheduling strategy for GENCOs in the uncertain environment, which can well balance robustness and economics compared to strategies derived from robust optimization (RO) and stochastic programming (SO). In this paper, a novel moment-based DRO model with conditional value-at-risk (CVaR) is proposed to solve the self-scheduling problem under electricity price uncertainty. Such DRO models are usually translated into semi-definite programming (SDP) for solution, however, solving large-scale SDP needs a lot of computational time and resources. For this shortcoming, two effective approximate models are proposed: one approximate model based on vector splitting and another based on alternate direction multiplier method (ADMM), both can greatly reduce the calculation time and resources, and the second approximate model only needs the information of the current area in each step of the solution and thus information private is guaranteed. Simulations of three IEEE test systems are conducted to demonstrate the correctness and effectiveness of the proposed DRO model and two approximate models. Copyright © 2021, The Authors. All rights reserved.

关键词： stochastic programming

Comparisons of Two-stage Models for Flood Mitigation of Electrical Substations

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arXiv 2023年

作者： Austgen, Brent Kutanoglu, Erhan Hasenbein, John J. Santoso, Surya The University of Texas at Austin Operations Research and Industrial Engineering Program United States The University of Texas at Austin Chandra Department of Electrical and Computer Engineering United States

We compare stochastic programming and robust optimization decision models for informing the deployment of ad hoc flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. In our models, the first stage captures the deployment of a fixed quantity of flood mitigation resources, and the second stage captures the operation of a potentially degraded power grid with the primary goal of minimizing load shed. To model grid operation, we introduce adaptations of the DC and LPAC power flow approximation models that feature relatively complete recourse by way of an indicator variable. We apply our models to a pair of geographically realistic flooding case studies, one based on Hurricane Harvey and the other on Tropical Storm Imelda. We investigate the effect of the mitigation budget, the choice of power flow model, and the uncertainty perspective on the optimal mitigation strategy. Our results indicate the mitigation budget and uncertainty perspective are impactful whereas choosing between the DC and LPAC power flow models is of little to no consequence. To validate our models, we assess the performance of the mitigation solutions they prescribe in an AC power flow model. © 2023, CC BY.

关键词： stochastic programming

PRAGMATIC DISTRIBUTIONALLY ROBUST OPTIMIZATION FOR SIMPLE INTEGER RECOURSE MODELS

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arXiv 2022年

作者： van Beesten, E. Ruben Romeijnders, Ward Morton, David P. Trondheim Norway Faculty of Economics and Business University of Groningen Groningen Netherlands Department of Industrial Engineering and Management Science Northwestern University Evan-ston IL United States

Inspired by its success for their continuous counterparts, the standard approach to deal with mixed-integer recourse (MIR) models under distributional uncertainty is to use distributionally robust optimization (DRO). We argue, however, that this modeling choice is not always justified, since DRO techniques are generally computationally extremely challenging when integer decision variables are involved. That is why we propose a fundamentally different approach for MIR models under distributional uncertainty aimed at obtaining models with improved computational tractability. For the special case of simple integer recourse (SIR) models, we show that tractable models can be obtained by pragmatically selecting the uncertainty set. Here, we consider uncertainty sets based on the Wasserstein distance and also on generalized moment conditions. We compare our approach with standard DRO and discuss potential generalizations of our ideas to more general MIR models. An important side-result of our analysis is the derivation of performance guarantees for convex approximations of SIR models. In contrast with the literature, these error bounds are not only valid for continuous distribution, but hold for any *** Codes 90C15 Copyright © 2022, The Authors. All rights reserved.

关键词： stochastic programming

An integrated market for electricity and natural gas systems with stochastic power producers

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arXiv 2018年

作者： Ordoudis, Christos Pinson, Pierre Morales, Juan M. Department of Electrical Engineering Technical University of Denmark Kgs. Lyngby2800 Denmark Department of Applied Mathematics University of Málaga Málaga Spain

In energy systems with high shares of weather-driven renewable power sources, gas-fired power plants can serve as a back-up technology to ensure security of supply and provide short-term flexibility. Therefore, a tighter coordination between electricity and natural gas networks is foreseen. In this work, we examine different levels of coordination in terms of system integration and time coupling of trading floors. We propose an integrated operational model for electricity and natural gas systems under uncertain power supply by applying two-stage stochastic programming. This formulation co-optimizes day-ahead and real-time dispatch of both energy systems and aims at minimizing the total expected cost. Additionally, two deterministic models, one of an integrated energy system and one that treats the two systems independently, are presented. We utilize a formulation that considers the linepack of the natural gas system, while it results in a tractable mixed-integer linear programming (MILP) model. Our analysis demonstrates the effectiveness of the proposed model in accommodating high shares of renewables and the importance of proper natural gas system modeling in short-term operations to reveal valuable flexibility of the natural gas system. Moreover, we identify the coordination parameters between the two markets and show their impact on the system’s operation and dispatch. Copyright © 2018, The Authors. All rights reserved.

关键词： stochastic programming

stochastic Model Predictive Control for Scheduling Charging of Electric Vehicle Fleets with Market Power

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Stochastic Model Predictive Control for Scheduling Charging ...

International Conference on Connected Vehicles and Expo (ICCVE)

作者： Arec L. Jamgochian Mykel J. Kochenderfer Stanford University Stanford CA

ISBN: (纸本)9781728101439

With the penetration of electric vehicles in local markets, vehicle-induced electricity demand can cause power grid instability. Collaborative smart charging can help stabilize grid demand and mitigate those issues. This paper formulates charge scheduling when connected vehicles constitute a large portion of instantaneous demand. Allowing coordinated charging to sway electricity price, we formulate a multi-objective stochastic optimization problem to minimize cost while maximizing charge in each car. We model stochastic base electricity demand using a Gaussian Mixture Model (GMM) and solve the certainty-equivalent stochastic optimization problem. We then implement a stochastic model predictive control (SMPC) algorithm and compare performance between a naive policy, a certainty-equivalent optimized policy, and SMPC on a dataset derived from California ISO-serviced demand.

关键词： stochastic programming Model predictive control Electric vehicles Charge scheduling Electric vehicles Predictive control stochastic models vehicle fleet SMPC distributed model predictive control nonlinear model predictive control CHARGING(ACCOUNTTNG) stochastic programming Model predictive control power markets