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An Overview of Uncertain Control Co-Design Formulations

JOURNAL OF MECHANICAL DESIGN 2023年第9期145卷 091709-091709页

作者： Azad, Saeed Herber, Daniel R. Colorado State Univ Dept Syst Engn Ft Collins CO 80523 USA

This article explores various uncertain control co-design (UCCD) problem formulations. While previous work offers formulations that are method-dependent and limited to only a handful of uncertainties (often from one discipline), effective application of UCCD to real-world dynamic systems requires a thorough understanding of uncertainties and how their impact can be captured. Since the first step is defining the UCCD problem of interest, this article aims at addressing some of the limitations of the current literature by identifying possible sources of uncertainties in a general UCCD context and then formalizing ways in which their impact is captured through problem formulation alone (without having to immediately resort to specific solution strategies). We first develop and then discuss a generalized UCCD formulation that can capture uncertainty representations presented in this article. Issues such as the treatment of the objective function, the challenge of the analysis-type equality constraints, and various formulations for inequality constraints are discussed. Then, more specialized problem formulations such as stochastic in expectation, stochastic chance-constrained, probabilistic robust, worst-case robust, fuzzy expected value, and possibilistic chance-constrained UCCD formulations are presented. Key concepts from these formulations, along with insights from closely-related fields, such as robust and stochastic control theory, are discussed, and future research directions are identified.

关键词： control co-design dynamics uncertainty stochastic programming fuzzy programming robust optimization

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A two-stage stochastic post-disaster humanitarian supply chain network design problem

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COMPUTERS & INDUSTRIAL ENGINEERING 2023年第1期183卷

作者： Daneshvar, Mohammad Jena, Sanjay Dominik Rei, Walter Univ Quebec Montreal Dept Analyt Operat & Technol Informat 315Sainte Catherine St East Montreal PQ H2X 3X2 Canada Univ Montreal CIRRELT 2920Chemin Tour Montreal PQ H3T 1J4 Canada

We consider the planning problem of designing and operating humanitarian supply chain networks (HSCN) after natural disasters. Specifically, we focus on the design of a three-layer network under demand and capacity uncertainty to support short-term recovery, i.e., to distribute critical supplies to the affected population. We aim to analyze the effect of unmet demand accumulating over the planning horizon in order to better understand and respond to natural disasters. To this end, we explicitly consider the impact of unmet demand through time under uncertain conditions by introducing a spread factor. We develop a two-stage stochastic model that retains the uncertainty pertaining to the demand along with the transportation and storage capacities of the HSCN. Then, we apply our model to a case study using real-world data from the 2018 earthquake in Indonesia. Various aspects of the problem are studied over a set of experiments, including the importance of modeling uncertainty, the effect of the budget on the solution performance, and the role of the spread factor in the accurate understanding of the crisis. According to the results obtained, considering lower values for the spread factor parameter can irreparably misguide the decision-makers by an inaccurate presentation of the crisis' depth and consequently increase the damage caused to people's health

关键词： stochastic programming Humanitarian relief network Tactical planning Humanitarian supply chain Post-disaster

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A Bilevel stochastic Optimization Framework for Market-Oriented Transmission Expansion Planning Considering Market Power

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ENERGIES 2023年第7期16卷 3256页

作者： Alnowibet, Khalid A. Alshamrani, Ahmad M. Alrasheedi, Adel F. King Saud Univ Coll Sci Stat & Operat Res Dept Riyadh 11451 Saudi Arabia

Market power, defined as the ability to raise prices above competitive levels profitably, continues to be a prime concern in the restructured electricity markets. Market power must be mitigated to improve market performance and avoid inefficient generation investment, price volatility, and overpayment in power systems. For this reason, involving market power in the transmission expansion planning (TEP) problem is essential for ensuring the efficient operation of the electricity markets. In this regard, a methodological bilevel stochastic framework for the TEP problem that explicitly includes the market power indices in the upper level is proposed, aiming to restrict the potential market power execution. A mixed-integer linear/quadratic programming (MILP/MIQP) reformulation of the stochastic bilevel model is constructed utilizing Karush-Kuhn-Tucker (KKT) conditions. Wind power and electricity demand uncertainty are incorporated using scenario-based two-stage stochastic programming. The model enables the planner to make a trade-off between the market power indices and the investment cost. Using comparable results of the IEEE 118-bus system, we show that the proposed TEP outperforms the existing models in terms of market power indices and facilitates open access to the transmission network for all market participants.

关键词： bilevel programming KKT conditions market power mixed-integer linear quadratic programming stochastic programming transmission expansion planning

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UV Mission Planning Under Uncertainty in Vehicles' Availability

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JOURNAL OF INTELLIGENT & ROBOTIC SYSTEMS 2023年第2期108卷 26-26页

作者： Chirala, Venkata Sirimuvva Venkatachalam, Saravanan Smereka, Jonathon M. Wayne State Univ Dept Ind & Syst Engn 4815 Fourth St Detroit MI 48202 USA US Army Ground Vehicle Robot GVR Team CCDC Ground Vehicle Syst Ctr GVSC 6305 E Eleven Mile Rd Warren MI USA

Heterogeneous unmanned vehicles (UVs) are used in various defense and civil applications. Some of the civil applications of UVs for gathering data and monitoring include civil infrastructure management, agriculture, public safety, law enforcement, disaster relief, and transportation. This paper presents a two-stage stochastic model for a fuel-constrained UV mission planning problem with multiple refueling stations under uncertainty in availability of UVs. Given a set of points of interests (POI), a set of refueling stations for UVs, and a base station where the UVs are stationed and their availability is random, the objective is to determine route for each UV starting and terminating at the base station such that overall incentives collected by visiting POIs is maximized. We present an outer approximation based decomposition algorithm and the skewed variable neighborhood search heuristic to solve large instances, and perform extensive computational experiments using random instances. Additionally, a data driven simulation study is performed using robot operating system (ROS) framework to corroborate the use of the stochastic programming approach.

关键词： Mission planning stochastic programming Two-stage stochastic model Orienteering UV ROS L-shaped method

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Vessel weather routing subject to sulfur emission regulation

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2023年第1期177卷

作者： Lee, Sang-Jeong Sun, Qinghe Meng, Qiang Natl Univ Singapore Dept Civil & Environm Engn Singapore 117576 Singapore Hong Kong Polytech Univ Fac Business Dept Logist & Maritime Studies Kowloon Hong Kong Peoples R China

The International Maritime Organization (IMO) rolled out a set of new regulations that limit the sulfur content in the fuel oil used by ships, which came into effect from 2020. This study aims to explore the operational decisions of vessels inside and outside emission control areas (ECAs) under uncertain weather conditions and scrutinizes the economics of two types of ships: fuel-switching and scrubber installation. Such operational decisions include speed, trim, and path decision. We construct a navigation grid system, in which each grid contains weather parameters and sea condition. This navigation grid system can be applied to other type of ships due to the well-established cost structure. To improve fuel consumption estimation, we train fuel consumption estimation functions with respect to weather parameters, sea conditions, and operational decisions. This study then develops a stochastic dynamic programming model to optimize the path decisions, vessel speed, and trim. To evaluate the efficiency of the developed stochastic dynamic programming model, we further conduct a case study on a Post-Panamax container vessel that operates westbound from Hamburg to Houston. We identify the path decision, speed and trim under ECAs and the uncertain weather conditions. Surprisingly, this case study demonstrates that the ship utilizing fuel-switching takes a detour trip;in contrast, the ship with a scrubber chooses the shortest path by maximizing the speed. Additionally, we observe a knock-on effect - scrubber installation lifts carbon dioxide emissions due to increased vessel speed outside the ECA region. Rich managerial insights and potential policy implications are discussed.

关键词： Speed Trim Weather routing Emission control area (ECA) stochastic programming

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stochastic FIRST- AND ZEROTH-ORDER METHODS FOR NONCONVEX stochastic programming

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SIAM JOURNAL ON OPTIMIZATION 2013年第4期23卷 2341-2368页

作者： Ghadimi, Saeed Lan, Guanghui Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

In this paper, we introduce a new stochastic approximation type algorithm, namely, the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method possesses a nearly optimal rate of convergence if the problem is convex. We discuss a variant of the algorithm which consists of applying a postoptimization phase to evaluate a short list of solutions generated by several independent runs of the RSG method, and we show that such modification allows us to improve significantly the large-deviation properties of the algorithm. These methods are then specialized for solving a class of simulation-based optimization problems in which only stochastic zeroth-order information is available.

关键词： stochastic approximation nonconvex optimization stochastic programming simulation-based optimization

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Water resources management under multi-parameter interactions: A factorial multi-stage stochastic programming approach

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2013年第3期41卷 559-573页

作者： Zhou, Yang Huang, Guo H. Yang, Boting Univ Regina Fac Engn Regina SK S4S 0A2 Canada Univ Regina Dept Comp Sci Regina SK S4S 0A2 Canada

The paper proposes a factorial multi-stage stochastic programming (FMSP) approach to support water resources management under uncertainty. This approach was developed based on the conventional inexact multi-stage stochastic programming method. Five alternative inexact multi-stage stochastic programming algorithms in addition to the conventional algorithm were introduced and bundled to offer multiple decision options that reflect decision makers' perspectives and the complexities in system uncertainties. More importantly, factorial analysis, a multivariate inference method, was introduced into the modeling framework to analyze the potential interrelationships among a variety of uncertain parameters and their impacts on system performance. The proposed approach was applied to a water resources management case. The desired water-allocation schemes were obtained to assist in maximizing the total net benefit of the system. Multiple uncertain parameters and their interactions were examined, and those that had significant influences on system performance were identified. For example, the medium flow in the third planning period was the system objective's most influential factor. Any variation of this factor would significantly influence the acquisition of the total net benefit in the community. The significant interactions were also identified, such as the interaction between the agricultural sector's penalty and the medium flow in the third planning period. Through the analysis of multi-parameter interactions, the interrelationships among the uncertain parameters could be further revealed. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： stochastic programming Multi-stage Factorial analysis Decision making Water resources management

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Progressive hedging for stochastic energy management systems The mixed-integer linear case

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2021年第1期12卷 1-29页

作者： Kaisermayer, Valentin Muschick, Daniel Horn, Martin Goelles, Markus BEST Bioenergy & Sustainable Technol GmbH Inffeldgasse 21-B A-8010 Graz Austria Graz Univ Technol Inst Automat & Control Inffeldgasse 21-B A-8010 Graz Austria

Energy systems have increased in complexity in the past years due to the ever-increasing integration of intermittent renewable energy sources such as solar thermal or wind power. Modern energy systems comprise different energy domains such as electrical power, heating and cooling which renders their control even more challenging. Employing supervisory controllers, so-called energy management systems (EMSs), can help to handle this complexity and to ensure the energy-efficient and cost-efficient operation of the energy system. One promising approach are optimization-based EMS, which can for example be modelled as stochastic mixed-integer linear programmes (SMILP). Depending on the problem size and control horizon, obtaining solutions for these in real-time is a difficult task. The progressive hedging (PH) algorithm is a practical way for splitting a large problem into smaller sub problems and solving them iteratively, thus possibly reducing the solving time considerably. The idea of the PH algorithm is to aggregate the solutions of subproblems, where artificial costs have been added. These added costs enforce that the aggregated solutions become non-anticipative and are updated in every iteration of the algorithm. The algorithm is relatively simple to implement in practice, re-using almost all of a possibly existing deterministic implementations and can be easily parallelized. Although it has no convergence guarantees in the mixed-integer linear case, it can nevertheless be used as a good heuristic for SMILPs. Recent theoretical results shown that for applying augmented Lagrangian functions in the context of mixed-integer programmes, any norm proofs to be a valid penalty function. This is not true for squared norms, like the squared L-2-norm that is used in the classical progressive hedging algorithm. Building on these theoretical results, the use of the L-1 and L-infinity-norm in the PH algorithm is investigated in this paper. In order to incorporate these into the

关键词： Energy management system stochastic programming Progressive hedging Mixed-integer linear programming

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stochastic Dynamic Cutting Plane for Multistage stochastic Convex Programs

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2021年第2期189卷 513-559页

作者： Guigues, Vincent Monteiro, Renato D. C. FGV Sch Appl Math Praia De Botafogo RJ Brazil Georgia Inst Technol Atlanta GA 30332 USA

We introduce stochastic Dynamic Cutting Plane (StoDCuP), an extension of the stochastic Dual Dynamic programming (SDDP) algorithm to solve multistage stochastic convex optimization problems. At each iteration, the algorithm builds lower bounding affine functions not only for the cost-to-go functions, as SDDP does, but also for some or all nonlinear cost and constraint functions. We show the almost sure convergence of StoDCuP. We also introduce an inexact variant of StoDCuP where all subproblems are solved approximately (with bounded errors) and show the almost sure convergence of this variant for vanishing errors. Finally, numerical experiments are presented on nondifferentiable multistage stochastic programs where Inexact StoDCuP computes a good approximate policy quicker than StoDCuP while SDDP and the previous inexact variant of SDDP combined with Mosek library to solve subproblems were not able to solve the differentiable reformulation of the problem.

关键词： stochastic programming Inexact cuts for value functions SDDP Inexact SDDP

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Distributionally robust day-ahead combined heat and power plants scheduling with Wasserstein Metric

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ENERGY 2023年第1期269卷

作者： Skalyga, Mikhail Amelin, Mikael Wu, Qiuwei Soder, Lennart Tech Univ Denmark DTU Ctr Elect Power & Energy Dept Elect Engn DK-2800 Lyngby Denmark KTH Royal Inst Technol Sch Elect Engn Div Elect Power & Energy Syst Teknikringen 33 S-10044 Stockholm Sweden Tsinghua Univ Tsinghua Berkeley Shenzhen Inst Tsinghua Shenzhen Int Grad Sch Shenzhen 518055 Peoples R China

Combined heat and power (CHP) plants are main generation units in district heating systems that produce both heat and electric power simultaneously. Moreover, CHP plants can participate in electricity markets, selling and buying the extra power when profitable. However, operational decisions have to be made with unknown electricity prices. The distribution of unknown electricity prices is also not known exactly and uncertain in practice. Therefore, the need of tools to schedule CHP units' production under distributional uncertainty is necessary for CHP producers. On top of that, a heating network could serve as a heat storage and an additional source of flexibility for CHP plants. In this paper, a distributionally robust short-term operational model of CHP plants in the day-ahead electricity market is developed. The model accounts for the heating network and considers temperature dynamics in the pipes. The problem is formulated in a data-driven manner, where the production decisions explicitly depend on the historical data for the uncertain day-ahead electricity prices. A case study is performed, and the resulting profit of the CHP producer is analyzed. The proposed operational strategy shows high reliability in the out-of-sample performance and a profit gain of the CHP producer, who is aware of the temperature dynamics in the heating network.

关键词： stochastic programming Combined heat and power District heating Distributionally robust optimization Electricity markets

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