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作者： Han, Jeongwoo University of Michigan

学位级别：Ph.D.

Decision-making under uncertainty is particularly challenging in the case of multi-disciplinary, multilevel system optimization problems. Subsystem interactions cause strong couplings, which may be amplified by uncertainty. Thus, effective coordination strategies can be particularly beneficial. Analytical target cascading (ATC) is a deterministic optimization method for multilevel hierarchical systems, which was recently extended to probabilistic design. Solving the optimization problem requires propagation of uncertainty, namely, evaluating or estimating output distributions given random input variables. This uncertainty propagation can be a challenging and computationally expensive task for nonlinear functions, but is relatively easy for linear ones. In order to overcome the difficulty in uncertainty propagation, this dissertation introduces the use of sequential linear programming (SLP) for solving ATC problems, and specifically extends this use for Probabilistic Analytical Target Cascading (PATC) problems. A new coordination strategy is proposed for ATC and PATC, which coordinates linking variables among subproblems using sequential lineralizations. By linearizing and solving a hierarchy of problems successively, the algorithm takes advantage of the simplicity and ease of uncertainty propagation for a linear system. linearity of subproblems is maintained using an L∞ norm to measure deviations between targets and responses. A subproblem suspension strategy is used to temporarily suspend inclusion of subproblems that do not need significant redesign, based on trust region and target value step size. A global convergence proof of the SLP-based coordination strategy is derived. Experiments with test problems show that, relative to standard ATC and PATC coordination, the number of subproblem evaluations is reduced considerably while maintaining accuracy. To demonstrate the applicability of the proposed strategies to problems of practical complexity, a hybrid electric

关键词： sequential linear programming Probabilistic Analytical Target Cascading Multi-disciplinary Design Optimization Under Uncertainty Thesis

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Mixed 0-1 sequential linear programming optimization of heat distribution in a district-heating system

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ENERGY AND BUILDINGS 2000年第3期32卷 309-317页

作者： Bojic, M Trifunovic, N Gustafsson, SI Hong Kong Polytech Univ Dept Bldg Serv Engn Kowloon Hong Kong Peoples R China

A district-heating system transports heat from the heat plant by using primary pipe network, via substation, to secondary pipe network where heat is finally distributed to buildings. When this system is designed its operational characteristics were selected to provide thermal comfort (TC) in all buildings served by this district heating system. After several years of operation, the system characteristics may change and TC in buildings deteriorates;some buildings are overheated and other buildings are underheated. The study investigates an optimum strategy to mitigate the problem caused by changes of three of system characteristics: hydraulic resistance of secondary pipe network, heat transmittance of radiators inside buildings, and heat transmittance of building envelope. A strategy of problem mitigation consists of the adjustment of hydraulic resistance of existing valves and retrofitting the local heating system with new substation heat exchanger and additional pumps. We used a steady state, bottom-up approach and mixed 0-1 sequential linear programming to find optimal mitigation strategy, i.e. optimum combination of valves' hydraulic resistances, new pumps placement and new size of substation heat exchanger. The results indicate that the calculated optimal strategy does not effectively improve TC in buildings only in cases when TC is deteriorated by higher than nominal values of heat transmittance of some building envelopes. (C) 2000 Elsevier Science S.A. All rights reserved.

关键词： heat distribution district-heating system sequential linear programming

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Efficient size and shape optimization of truss structures subject to stress and local buckling constraints using sequential linear programming

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2018年第1期58卷 171-184页

作者： Schwarz, Jonas Chen, Tian Shea, Kristina Stankovic, Tino Swiss Fed Inst Technol Dept Mech & Proc Engn Engn Design & Comp Lab Zurich Switzerland

The advance in digital fabrication technologies and additive manufacturing allows for the fabrication of complex truss structure designs but at the same time posing challenging structural optimization problems to capitalize on this new design freedom. In response to this, an iterative approach in which sequential linear programming (SLP) is used to simultaneously solve a size and shape optimization sub-problem subject to local stress and Euler buckling constraints is proposed in this work. To accomplish this, a first order Taylor expansion for the nodal movement and the buckling constraint is derived to conform to the SLP problem formulation. At each iteration a post-processing step is initiated to map a design vector to the exact buckling constraint boundary in order to facilitate the overall efficiency. The method is verified against an exact non-linear optimization problem formulation on a range of benchmark examples obtained from the literature. The results show that the proposed method produces optimized designs that are either close or identical to the solutions obtained by the non-linear problem formulation while significantly decreasing the computational time. This enables more efficient size and shape optimization of truss structures considering practical engineering constraints.

关键词： Truss structures linear programming sequential linear programming Shape optimization Local buckling

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A sequential linear programming algorithm for economic optimization of Hybrid Renewable Energy Systems

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JOURNAL OF PROCESS CONTROL 2019年 74卷 189-201页

作者： Vaccari, M. Mancuso, G. M. Riccardi, J. Cantu, M. Pannocchia, G. Univ Pisa Dept Civil & Ind Engn Largo L Lazzarino 2 I-56126 Pisa Italy Enel Green Power Innovat & Sustainabil Via Andrea Pisano 120 I-56120 Pisa Italy Enel Engn & Res Via Andrea Pisano 120 I-56120 Pisa Italy

Combining renewable energy sources, as photovoltaic arrays (PV), wind turbine (WT), biomass fuel generators (BM), with back-up units to form a Hybrid Renewable Energy System (HRES) can provide a more economic and reliable energy supply architecture compared to the separate usage of such units. In this work an optimization tool for a general HRES is developed: it generates an operating plan over a specified time horizon of the setpoints of each device to meet all electrical and thermal load requirements with possibly minimum operating costs. A large number of devices, such as conventional and renewable source generators, mandatory and deferrable adjustable electrical loads, batteries, combined heat and power configurations are modeled with high fidelity. The optimization tool is based on a sequential linear programming (SLP) algorithm, equipped with trust region, which is able to efficiently solve a general nonlinear program. A case study of a real HRES in Tuscany is presented to test the major functionalities of the developed optimization tool. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Energy systems Numerical optimization algorithms sequential linear programming Hybrid Renewable Energy Systems (HRES)

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Introducing the sequential linear programming level-set method for topology optimization

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2015年第3期51卷 631-643页

作者： Dunning, Peter D. Kim, H. Alicia Univ Bath Bath BA2 7AY Avon England

This paper introduces an approach to level-set topology optimization that can handle multiple constraints and simultaneously optimize non-level-set design variables. The key features of the new method are discretized boundary integrals to estimate function changes and the formulation of an optimization sub-problem to attain the velocity function. The sub-problem is solved using sequential linear programming (SLP) and the new method is called the SLP level-set method. The new approach is developed in the context of the Hamilton-Jacobi type level-set method, where shape derivatives are employed to optimize a structure represented by an implicit level-set function. This approach is sometimes referred to as the conventional level-set method. The SLP level-set method is demonstrated via a range of problems that include volume, compliance, eigenvalue and displacement constraints and simultaneous optimization of non-level-set design variables.

关键词： Level-set method Topology optimization Constraints sequential linear programming

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Upper bound sequential linear programming mesh adaptation scheme for collapse analysis of masonry vaults

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ADVANCES IN ENGINEERING SOFTWARE 2015年 79卷 91-110页

作者： Milani, G. Politecn Milan Dept Architecture Built Environm & Construct Engn I-20133 Milan Italy

The analysis of masonry double curvature structures by means of the kinematic theorem of limit analysis is traditionally the most diffused and straightforward method for an estimate of the load carrying capacity. However, the evaluation of the actual failure mechanism is not always trivial, especially for complex geometries and load conditions. Usually, the failure mechanism is simply hypothesized basing on previous experience, or - due to the complexity of the problem - FE rigid elements with interfaces are used. Both strategies may result in a wrong evaluation of the failure mechanism and hence, in the framework of the kinematic theorem of limit analysis, in an overestimation of the collapse load. In this paper, a simple discontinuous upper bound limit analysis approach with sequential linear programming mesh adaptation to analyze masonry double curvature structures is presented. The discretization of the vault is performed with infinitely resistant triangular elements (curved elements basing on a quadratic interpolation), with plastic dissipation allowed only at the interfaces for possible in- and out-of-plane jumps of velocities. Masonry is substituted with a fictitious material exhibiting an orthotropic behavior, by means of consolidated homogenization strategies. To progressively favor that the position of the interfaces coincide with the actual failure mechanism, an iterative mesh adaptation scheme based on sequential linear programming is proposed. Non-linear geometrical constraints on nodes positions are linearized with a first order Taylor expansion scheme, thus allowing to treat the NLP problem with consolidated LP routines. The choice of inequalities constraints on elements nodes coordinates turns out to be crucial on the algorithm convergence. The model performs poorly for coarse and unstructured meshes (i.e. at the initial iteration), but converges to the actual solution after few iterations. Several examples are treated, namely a straight circular and

关键词： Masonry Upper bound limit analysis Double curvature structures Rigid elements and interfaces sequential linear programming Mesh adaptation

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An interval sequential linear programming for nonlinear robust optimization problems

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APPLIED MATHEMATICAL MODELLING 2022年 107卷 256-274页

作者： Tang, Jiachang Fu, Chunming Mi, Chengji Liu, Haibo Hunan Univ Technol Dept Mech Engn Zhuzhou 412007 Peoples R China Univ South China Coll Mech Engn Hengyang 421001 Peoples R China Hunan Univ Sci & Technol Hunan Prov Key Lab Hlth Maintenance Mech Equipment Xiangtan 411201 Peoples R China

In this paper, interval sequential linear programming (ISLP) is proposed to solve nonlinear robust optimization (RO). The main idea of the programming is to transform the uncertain optimization into several possibility-sensitivity analyses and deterministic linear optimization problems that are sequentially solved. At each cycle, a possibility-sensitivity analysis method is proposed to obtain the approximate partial derivatives of the uncertain constraints at the current design point, based on which a deterministic linear optimization model is constructed and the design point is updated by solving the linear optimization. Moreover, an iterative mechanism is created to adaptively update the design space and improve the convergence rate. Finally, two numerical examples and two practical engineering problems are applied to verify the accuracy and efficiency of the proposed method.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Robust optimization Interval uncertainty Reliability-based possibility degree of interval (RPDI) Sensitivity analysis sequential linear programming

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An Exact sequential linear programming Algorithm for the Optimal Power Flow Problem

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IEEE TRANSACTIONS ON POWER SYSTEMS 2022年第1期37卷 666-679页

作者： Mhanna, Sleiman Mancarella, Pierluigi Univ Melbourne Elect & Elect Engn Dept Melbourne Sch Engn Melbourne Vic 3010 Australia

Despite major advancements in nonlinear programming (NLP) and convex relaxations, most system operators around the world still predominantly use some form of linear programming (LP) approximation of the AC power flow equations. This is largely due to LP technology's superior reliability and computational efficiency, especially in real-time market applications, security-constrained applications, and extensions involving integer variables, in addition to its ability to readily generate locational marginal prices (LMP) for market applications. In the aim of leveraging the advantages of LP while retaining the accuracy of NLP interior-point methods (IPMs), this paper proposes a sequential linear programming (SLP) approach consisting of a sequence of carefully constructed supporting hyperplanes and halfspaces. The algorithm is numerically demonstrated to converge on 138 test cases with up the 3375 buses to feasible high-quality solutions (i) without AC feasibility restoration (i.e., using LP solvers exclusively), (ii) in computation times generally within the same order of magnitude as those from a state-of-the-art NLP solver, and (iii) with robustness against the choice of starting point. In particular, the (relative) optimality gaps and the mean constraint violations are on average around 10(-3)% and 10(-7), respectively, under a single parameter setting for all the 138 test cases. To the best of our knowledge, the proposed SLP approach is the first to use LP exclusively to reach feasible and high-quality solutions to the nonconvex AC OPF in a reliable way, which paves the way for system and market operators to keep using their LP solvers but now with the ability to accurately capture transmission losses, price reactive power (Q-LMP), and obtain more accurate LMP.

关键词： sequential linear programming optimal power flow supporting hyperplanes locationalmarginal pricing reactive power pricing

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A trust-region based sequential linear programming approach for AC optimal power flow problems

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ELECTRIC POWER SYSTEMS RESEARCH 2018年 165卷 134-143页

作者： Sampath, L. P. M. I. Patil, Bhagyesh V. Gooi, H. B. Maciejowski, J. M. Ling, K. V. Nanyang Technol Univ Interdisciplinary Grad Sch Singapore Singapore Cambridge Ctr Adv Res & Educ Singapore CARES Singapore Singapore Nanyang Technol Univ Sch Elect & Elect Engn Singapore Singapore Univ Cambridge Dept Engn Cambridge England NTU ERI N Energy Res Inst Singapore Singapore

This study proposes a new trust-region based sequential linear programming algorithm to solve the AC optimal power flow (OPF) problem. The OPF problem is solved by linearizing the cost function, power balance and engineering constraints of the system, followed by a trust-region to control the validity of the linear model. To alleviate the problems associated with the infeasibilities of a linear approximation, a feasibility restoration phase is introduced. This phase uses the original nonlinear constraints to quickly locate a feasible point when the linear approximation is infeasible. The algorithm follows convergence criteria to satisfy the first order optimality conditions for the original OPF problem. Studies on standard IEEE systems and large-scale Polish systems show an acceptable quality of convergence to a set of best-known solutions and a substantial improvement in computational time, with linear scaling proportional to the network size.

关键词： Nonlinear programming Optimal power flow sequential linear programming Trust-region method

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sequential linear programming and particle swarm optimization for the optimization of energy districts

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ENGINEERING OPTIMIZATION 2019年第1期51卷 84-100页

作者： Riccietti, Elisa Bellavia, Stefania Sello, Stefano Univ Firenze Dipartimento Matemat & Informat Ulisse Dini Florence Italy Univ Firenze Dipartimento Ingn Ind Florence Italy Enel Ingn & Ric Pisa Italy IRIT Toulouse France

This article deals with the optimization of energy resource management of industrial districts, with the aim of minimizing customer energy expenses. A model of the district is employed, whose optimization gives rise to a nonlinear constrained optimization problem. Here the focus is on its numerical solution. Two different methods are considered: a sequential linear programming method and a particle swarm optimization method. Efficient implementations of both approaches are devised and the results of the tests performed on several energetic districts are reported, including a real case study.

关键词： Nonlinear optimization problems sequential linear programming particle swarm optimization energy districts penalty functions

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