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Hierarchical Distributed mixed-integer optimization for Reactive Power Dispatch

IFAC-PapersOnLine 2018年第28期51卷 368-373页

作者： Murray, Alexander Engelmann, Alexander Hagenmeyer, Veit Faulwasser, Timm Institute for Automation and Applied Informatics Karlsruhe Institute of Technology Karlsruhe Germany

One key aspect of power system operation is the minimization of line losses while maintaining voltages within certain limits. Doing so can be achieved through the use of voltage regulators, tap changing transformers, and shunt capacitors. However, both tap changing transformers and/or shunt capacitors are operated in a discrete manner, i.e. the inputs can only take finitely many discrete values. Thus, the problem of minimizing line losses while maintaining voltage stability can be cast as a mixed-integer optimization problem. For large grids or cases where independent entities have concurrent control of the system, distributed optimization provides a solution. The present paper discusses a hierarchically distributed approach; i.e. the problem is partitioned into local subproblems and solved using a mixed-integer extension of the Augmented Lagrangian based Alternating Direction Inexact Newton (ALADIN) algorithm. We present results for the IEEE 14- and 30-bus systems and compare them with previous approaches, such as particle swarm optimization and genetic algorithms. © 2018

关键词： Electric load dispatching Concurrency control Constrained optimization Electric load flow Genetic algorithms integer programming Particle swarm optimization (PSO) Reactive power Voltage regulators Alternating directions Distributed approaches Distributed optimization mixed integer optimization mixed integer problems Optimal power flows Power system operations Reactive power dispatch

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Binary Search Algorithm for mixed integer optimization: Application to energy management in a microgrid.

Binary Search Algorithm for Mixed Integer Optimization: Appl...

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European Control Conference

作者： Paulo R. C. Mendes José M. Maestre Carlos Bordons Julio E. Normey-Rico Department of Automation and Systems Federal University of Santa Catarina Florianpolis Brazil Departamento de Ingeniería de Sistemas y Automática University of Seville Seville Spain

ISBN: (纸本)9781509025923

This paper presents a binary search algorithm to deal with binary variables in mixed integer optimization problems. One example of this kind of problem is the optimal operation of hydrogen storage and energy sale and purchase into a microgrids context. In this work was studied a system composed by a microgrid that has a connection with the external electrical network and a charging station for electric cars. The system modeling was carried out by the Energy Hubs methodology. The proposed algorithm transforms the MIQP (mixed integer Quadratic Program) problem into a QP (Quadratic Program) that is easier to solve. In this way the overall control task is carried out the electricity purchase and sale to the power grid, maximizes the use of renewable energy sources, manages the use of energy storages and supplies the charge of the parked vehicles.

关键词： MIQP Binary Search Algorithm mixed integer optimization

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A mixed-integer optimization Strategy for Oil Supply in Distribution Complexes

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optimization AND ENGINEERING 2003年第1-2期4卷 23-64页

作者： Mas, Rodrigo Pinto, Jose M. Univ Sao Paulo Dept Chem Engn BR-05508900 Sao Paulo Brazil

As a result of an increasingly competitive market, companies must find ways to organize their activities regarding their economic outcome. An important feature in this context involves transportation operations, usually considered one of the major bottlenecks in the production chain. While delays imply loss of time and lack of resources, deliveries ahead of the deadlines may cause excess of inventories. Therefore, every company must pursue efficient transportation schedules within their operational planning. This work addresses short-term crude oil scheduling problems in a distribution complex that contains ports, refineries and a pipeline infrastructure capable of transferring oil from the former to the latter. The ports comprise piers, which receive vessels for discharging, storage tanks and a network that connects each other. The refineries have their own storage infrastructure, modeled as a large storage unit, along with crude distillation units, considered as constant level consumers. The problem involves a number of other issues, including intermediate storage, settling tasks and allocation of crude oil by its qualitative characteristics. A decomposition strategy based on large-scale mixed-integer linear programming (MILP) continuous-time models is developed. First, an MILP model that considers an aggregate representation for the pipeline and intermediate storage infrastructure is proposed. Decision variables involve the assignment of oil tankers to piers as well as tanker unloading and pipeline loading operations. The solution of this model provides the initial conditions for MILP models that represent the pipeline and intermediate storage infrastructure at a detailed level. Algorithms based on the LP-based branch-and-bound method are employed. Results from a port scenario of 13 tankers, 4 piers, 14 crude types, 18 storage tanks and 2 pipelines were obtained in approximately 90 minutes from an MILP problem containing 1996 continuous variables, 1039 binary var

关键词： mixed integer optimization pipeline transportation scheduling crude oil

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A complete characterization of disjunctive conic cuts for mixed integer second order cone optimization

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DISCRETE optimization 2017年 24卷 3-31页

作者： Belotti, Pietro Goez, Julio C. Polik, Imre Ralphs, Ted K. Terlaky, Minas FICO Xpress Optimizer Team Birmingham W Midlands England NHH Norwegian Sch Econ Dept Business & Management Sci N-5045 Bergen Norway SAS Inst Cary NC 27513 USA Lehigh Univ Dept Ind & Syst Engn Bethlehem PA 18015 USA

We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization (MISOCO) problem. We extend our prior work on disjunctive conic cuts (DCCs), which has thus far been restricted to the case in which the intersection of the hyperplanes and the feasible set is bounded. Using a similar technique, we show that one can extend our previous results to the case in which that intersection is unbounded. We provide a complete characterization in closed form of the conic inequalities required to describe the convex hull when the hyperplanes defining the disjunction are parallel. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Second order cone optimization mixed integer optimization Disjunctive programming Disjunctive conic cuts

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MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys A DIRECT-inspired optimization algorithm for experimentally accessible computational material design

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COMPUTATIONAL optimization AND APPLICATIONS 2017年第3期68卷 671-687页

作者： Graf, Peter A. Billups, Stephen Natl Renewable Energy Lab Computat Sci Ctr Mail Stop ESIF 30115013 Denver West Pkwy Golden CO 80401 USA Univ Colorado Denver Dept Math & Stat Sci Denver CO USA

Computational materials design has suffered from a lack of algorithms formulated in terms of experimentally accessible variables. Here we formulate the problem of (ternary) alloy optimization at the level of choice of atoms and their composition that is normal for synthesists. Mathematically, this is a mixed integer problem where a candidate solution consists of a choice of three elements, and how much of each of them to use. This space has the natural structure of a set of equilateral triangles. We solve this problem by introducing a novel version of the DIRECT algorithm that (1) operates on equilateral triangles instead of rectangles and (2) works across multiple triangles. We demonstrate on a test case that the algorithm is both robust and efficient. Finally, we offer an explanation of the efficacy of DIRECT-specifically, its balance of global and local search-by showing that "potentially optimal rectangles" of the original algorithm are akin to the Pareto front of the "multi-component optimization" of global and local search.

关键词： mixed integer optimization DIRECT optimization Pareto front Sierpinski triangle Computational material design

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Topology optimization of tensegrity structures under compliance constraint: a mixed integer linear programming approach

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optimization AND ENGINEERING 2013年第1期14卷 61-96页

作者： Kanno, Yoshihiro Univ Tokyo Grad Sch Informat Sci & Technol Dept Math Informat Tokyo 1138656 Japan

A tensegrity structure is a prestressed pin-jointed structure consisting of discontinuous struts and continuous cables. For exploring new configurations of tensegrity structures, this paper addresses a topology optimization problem of tensegrity structures under the compliance constraint and the stress constraints. It is assumed that a cable loosens and loses the elongation stiffness when its tensile prestress vanishes due to the applied external load. It is shown that the topology optimization problem can be formulated as a mixed integer linear programming (MILP) problem. The proposed method does not require any connectivity information of cables and struts to be known in advance. Numerical experiments illustrate that various configurations of tensegrity structures can be found as the optimal solutions.

关键词： Tensegrity Topology optimization Tension structure mixed integer optimization Form-finding problem Nonsmooth mechanics

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Improved penalty algorithm for mixed integer PDE constrained optimization problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2022年 116卷 2-14页

作者： Garmatter, Dominik Porcelli, Margherita Rinaldi, Francesco Stoll, Martin Tech Univ Chemnitz Dept Math Reichenhainer Str 41 D-01926 Chemnitz Germany Univ Bologna Dept Math AM2 Piazza Porta San Donato 5 I-40126 Bologna Italy ISTI CNR Inst Informat Sci & Technol A Faedo Pisa Italy Univ Padua Dept Math Tullio Levi Civita Via Trieste 63 I-35121 Padua Italy

Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the branch-and-bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially in a large-scale context, this article investigates penalization techniques. Taking inspiration from a well-known family of existing exact penalty algorithms, a novel improved penalty algorithm is derived, whose key ingredients are a basin hopping strategy and an interior point method, both of which are specialized for the problem class. A thorough numerical investigation is carried out for a standard stationary test problem. Extensions to a convection-diffusion as well as a nonlinear test problem finally demonstrate the versatility of the approach.

关键词： mixed integer optimization Optimal control PDE-constrained optimization Exact penalty methods Interior point methods

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A branch-and-cut algorithm for mixed integer bilevel linear optimization problems and its implementation

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MATHEMATICAL PROGRAMMING COMPUTATION 2020年第4期12卷 529-568页

作者： Tahernejad, Sahar Ralphs, Ted K. DeNegre, Scott T. Lehigh Univ Dept Ind & Syst Engn Bethlehem PA 18015 USA Hosp Special Surg 535 E 70th St New York NY 10021 USA

In this paper, we describe a comprehensive algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) using a generalized branch-and-cut approach. The framework presented merges features from existing algorithms (for both traditional mixed integer linear optimization and MIBLPs) with new techniques to produce a flexible and robust framework capable of solving a wide range of bilevel optimization problems. The framework has been fully implemented in the open-source solver MibS. The paper describes the algorithmic options offered by MibS and presents computational results evaluating the effectiveness of the various options for the solution of a number of classes of bilevel optimization problems from the literature.

关键词： Bilevel optimization mixed integer optimization Branch-and-cut algorithm Open-source solver

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Two-stage mixed integer Stochastic Bilevel Linear optimization

Two-stage Mixed Integer Stochastic Bilevel Linear Optimizati...

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作者： Tahernejad, Sahar Lehigh University

学位级别：博士

This dissertation introduces a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer lin- ear optimization problems with recourse. This unified framework provides insights into the nature of these two well-known classes of optimization problem, which are traditionally studied by different research communities, including highlighting their common mathematical structure, and allowing results from the wider literature de- voted to both classes to be exploited for the development of a common algorithmic framework. We focus primarily on problems with two stages that we refer to as two- stage mixed integer stochastic bilevel linear optimization problems (2SMISBLPs). The general framework allows modeling of a vast number of applications in which the decisions are made by two possibly competing decision-makers, under additional uncertainty about the values of some input parameters. In short, we combine the game theoretic models, in which decisions are made in stages, with similar models from multistage stochastic optimization with recourse, where stochasticity is the main modeling challenge. In the first part of the dissertation, we focus on mixed integer bilevel linear opti- mization problems (MIBLPs), a special case of 2SMISBLPs. We lay the foundations for a theory of valid inequalities for MIBLPs, paralleling the one that already exists in the mixed integer linear optimization problems. Building on this foundation, we describe a comprehensive algorithmic framework for solving MIBLPs using a gen- eralized branch-and-cut approach. The framework presented merges features from existing algorithms (for both traditional mixed integer linear optimization and MI- BLPs) with new techniques to produce a flexible and robust framework capable of solving a wide range of bilevel optimization problems. The framework has been fully implemented in the open-source solver MibS. We describe the algorithmic options of

关键词： Bilevel optimization mixed integer optimization Stochastic optimization

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Long Trip Charging Planning of Battery Electric Vehicle Considering Vehicle Waiting Time Forecast at Fast Charging Stations: A mixed-integer Dynamic Programming Approach

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IEEE ACCESS 2025年 13卷 52100-52113页

作者： Bhat, Pradeep Krishna Wu, Zhouquan Chen, Bo Michigan Technol Univ Dept Mech & Aerosp Engn Houghton MI 49931 USA Michigan Technol Univ Dept Elect & Comp Engn Houghton MI 49931 USA

Battery electric vehicles have shared concerns such as range anxiety and long charging times compared to conventional vehicles. To consider an electric vehicle as a replacement for a conventional vehicle, it is essential to reduce the cost of ownership and encourage widespread adoption without range concerns. It is appropriate that charging planning should be utilized to tackle such problems. It can also be helpful to have information from charging planning services to apprise incoming vehicles for charging to prepare their trip itinerary. For long-distance road trips, choosing appropriate charging stations can be instrumental in achieving the optimization goal. Selecting the right charging station can affect the total trip time. To optimize charging planning, we utilize mixed-integer dynamic programming to achieve the global optimal solution. The information on vehicle waiting time is used and parameterized from open-source US household travel survey information. Probability distributions of daily trips, daily mileage, and probability distribution of arrival vehicle SOC can be derived. Monte Carlo simulation generates the waiting time at the charging station based on the probability distributions and station configuration. The presented optimal charging plan method is validated by multiple test cases. The test cases are designed based on US Alternate Fuel Corridors utilizing interstate highways. For the selected test scenarios up to 9.6% of time saving is observed when there is no waiting time at the charging stations. The validation tests with waiting time encountered at the charging station, time saving of up to 15.1% is achieved with energy level closer to the minimum limit at the end of the trip. This charging planning method significantly enhances the viability of EVs for long-distance travel by addressing core concerns like range anxiety and lengthy trip time.

关键词： Planning Batteries State of charge Electric vehicles Surveys optimization Fast charging Probability distribution Monte Carlo methods Anxiety disorders Long trip charging planning mixed integer optimization battery electric vehicles connected vehicles

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