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MIDAS: A mixed integer dynamic approximation scheme

MATHEMATICAL programming 2020年第1期181卷 19-50页

作者： Philpott, A. B. Wahid, F. Bonnans, J. F. Univ Auckland Elect Power Optimizat Ctr Auckland New Zealand Artelys Consulting Paris France Ecole Polytech INRIA Saclay France

mixed integer dynamic approximation scheme (MIDAS) is a new sampling-based algorithm for solving finite-horizon stochastic dynamic programs with monotonic Bellman functions. MIDAS approximates these value functions using step functions, leading to stage problems that are mixed integer programs. We provide a general description ofMIDAS, and prove its almost-sure convergence to a 2T e-optimal policy for problems with T stages when the Bellman functions are known to be monotonic, and the sampling process satisfies standard assumptions.

关键词： Stochastic programming Approximate dynamic programming Sampling mixed-integer programming

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Controlling transient gas flow in real-world pipeline intersection areas

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OPTIMIZATION AND ENGINEERING 2021年第2期22卷 687-734页

作者： Hennings, Felix Anderson, Lovis Hoppmann-Baum, Kai Turner, Mark Koch, Thorsten Zuse Inst Berlin Takustr 7 D-14195 Berlin Germany Tech Univ Berlin Chair Software & Algorithms Discrete Optimizat Inst Math Str 17 Juni 135 D-10623 Berlin Germany

Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network, they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner. As part of an ongoing project with one of Germany's largest transmission system operators to develop a decision support system for their dispatching center, we investigated how to automatize the control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area. Since the desired performance of the station changes over time, the configuration of the station has to adapt. Our goal is to minimize the necessary changes in the overall operation modes and related elements over time while fulfilling a preset performance envelope or demand scenario. This article describes the chosen model and the implemented mixed-integer programming based algorithms to tackle this challenge. By presenting extensive computational results on real-world data, we demonstrate the performance of our approach.

关键词： Transient gas network optimization mixed-integer programming Realistic modeling of compressor stations

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A solution framework for the integrated periodic supply vessel planning and port scheduling in oil and gas supply logistics

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OPTIMIZATION AND ENGINEERING 2023年第2期24卷 1115-1155页

作者： Seimetz Chagas, Rennan Danilo Carvalho de Oliveir Soares, Juliana Beatriz Longhi, Rafael Pedro Vieira, Bruno Ferreira de Arruda, Edilson Fernandes Bahiense da Silva Leite, Laura Silvia Martins Ferreira Filho, Virgilio Jose Univ Fed Rio de Janeiro COPPE Moniz Aragao 360Cidade Univ BR-21941594 Rio De Janeiro RJ Brazil CENPES Av Horacio Macedo 950 BR-21941915 Rio De Janeiro RJ Brazil Southampton Business Sch Dept Decis Analyt & Risk 12 Univ RdBldg 2 Southampton SO17 1BJ Hants England

In this study, we deal with a real-world problem on oil and gas upstream logistics, comprehending the transport of goods from ports to maritime units, through vessels called Platform Supply Vessels (PSVs). We present an integrated methodology to define the routes of these vessels and port schedules in a three-phase framework. In the first phase, we decompose the problem using a clustering heuristic and then solve periodic supply vessel routing problems for each cluster. The second phase employs a mixed-integer programming model for port scheduling and berth allocation. Finally, in the third phase, given port departure times, the routes are re-sequenced to respect opening time constraints at installations, aiming to reduce waiting times and to balance the intervals between successive services. The framework was validated and evaluated considering a real scenario from an industrial partner located in Rio de Janeiro, Brazil. The experiments' results revealed that the framework could consistently and significantly outperform the solution adopted by the company in terms of economic costs.

关键词： Offshore logistics Supply vessel planning Berth allocation problem mixed-integer programming Periodic vessel routing problem

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Scheduling deferrable electric appliances in smart homes: a bi-objective stochastic optimization approach

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2022年第1期19卷 34-65页

作者： Rossit, Diego G. Nesmachnow, Segio Toutouh, Jamal Luna, Francisco Univ Nacl Sur Dept Engn Bahia Blanca Buenos Aires Argentina INMABB UNS CONICET Bahia Blanca Buenos Aires Argentina Univ Republica Montevideo Uruguay Univ Malaga Dept Lenguajes & Ciencias Comp Malaga Spain

In the last decades, cities have increased the number of activities and services that depends on an efficient and reliable electricity service. In particular, households have had a sustained increase of electricity consumption to perform many residential activities. Thus, providing efficient methods to enhance the decision making processes in demand-side management is crucial for achieving a more sustainable usage of the available resources. In this line of work, this article presents an optimization model to schedule deferrable appliances in households, which simultaneously optimize two conflicting objectives: the minimization of the cost of electricity bill and the maximization of users satisfaction with the consumed energy. Since users satisfaction is based on human preferences, it is subjected to a great variability and, thus, stochastic resolution methods have to be applied to solve the proposed model. In turn, a maximum allowable power consumption value is included as constraint, to account for the maximum power contracted for each household or building. Two different algorithms are proposed: a simulation-optimization approach and a greedy heuristic. Both methods are evaluated over problem instances based on real-world data, accounting for different household types. The obtained results show the competitiveness of the proposed approach, which are able to compute different compromising solutions accounting for the trade-off between these two conflicting optimization criteria in reasonable computing times. The simulation-optimization obtains better solutions, outperforming and dominating the greedy heuristic in all considered scenarios.

关键词： smart cities smart homes urban data analysis household energy planning stochastic optimization mixed-integer programming Monte Carlo simulation bi-objective optimization greedy heuristic

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Enhancing Active Distribution Systems Resilience by Fully Distributed Self-Healing Strategy

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IEEE TRANSACTIONS ON SMART GRID 2022年第2期13卷 1023-1034页

作者： Nejad, Reza Roofegari Sun, Wei OSI Digital Grid Solut Dept Power Syst Dev Medina MN 55340 USA Univ Cent Florida Dept Elect & Comp Engn Orlando FL 32816 USA

Distributed restoration can exploit smart grid technologies to enhance the resilience of active distribution networks toward a self-healing smart grid. However, the large number of decision variables, especially the binary ones for reconfiguration, bring challenges to developing scalable distributed distribution service restoration (DDSR) strategies. This paper proposes a fully distributed solution procedure based on the alternating direction method of multipliers (ADMM) for mixed-integer programming problems and applies to develop the DDSR framework. The method consists of relax-drive-polish phases, 1) relaxing binary variables, and applying the convex ADMM as a warm start;2) driving the solutions toward Boolean values through a proximal operator;3) fixing the obtained binding binary variables and solving the rest of the problem to polish results and achieve a high-quality suboptimal solution. Then, an autonomous clustering strategy and consensus ADMM are integrated with the proposed method to realize the fully distributed cluster-based framework of DDSR. This framework can first determine DER scheduling and switch status for reconfiguration to energize the out-of-service areas from local faults, and then provide the load restoration solution in a distributed manner for total blackouts in large-scale distribution networks. The effectiveness and scalability of the proposed DDSR framework are demonstrated through testing on the IEEE 123-node, IEEE 8500-node, and synthetic 100k-node test feeders.

关键词： Switches Convex functions Smart grids programming Convergence Security Scalability Alternating direction method of multipliers (ADMM) distributed energy resources fully distributed service restoration mixed-integer programming reconfiguration

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On mixing sets arising in chance-constrained programming

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MATHEMATICAL programming 2012年第1-2期132卷 31-56页

作者： Kuecuekyavuz, Simge Ohio State Univ Dept Integrated Syst Engn Columbus OH 43210 USA

The mixing set with a knapsack constraint arises in deterministic equivalent of chance-constrained programming problems with finite discrete distributions. We first consider the case that the chance-constrained program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit inequalities for this set. We extend these inequalities to obtain valid inequalities for the mixing set with a knapsack constraint. In addition, we propose a compact extended reformulation (with polynomial number of variables and constraints) that characterizes a linear programming equivalent of a single chance constraint with equal scenario probabilities. We introduce a blending procedure to find valid inequalities for intersection of multiple mixing sets. We propose a polynomial-size extended formulation for the intersection of multiple mixing sets with a knapsack constraint that is stronger than the original mixing formulation. We also give a compact extended linear program for the intersection of multiple mixing sets and a cardinality constraint for a special case. We illustrate the effectiveness of the proposed inequalities in our computational experiments with probabilistic lot-sizing problems.

关键词： mixed-integer programming Facets Compact extended formulations Chance constraints Lot-sizing Computation

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Privacy-Preserving Operation Management of Battery Swapping and Charging System With Dual-Based Benders Decomposition

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IEEE TRANSACTIONS ON SMART GRID 2023年第5期14卷 3899-3912页

作者： Wan, Yanni Qin, Jiahu Shi, Yang Fu, Weiming Zhang, Dunfeng Ningxia Univ Sch Phys & Elect Elect Engn Yinchuan 750021 Ningxia Peoples R China Univ Sci & Technol China Dept Automat Hefei 230027 Peoples R China Hefei Comprehens Natl Sci Ctr Inst Artificial Intelligence Hefei 230088 Peoples R China Univ Victoria Dept Mech Engn Victoria BC V8W 3P6 Canada

The battery swapping and charging system (BSCS) is an emerging and promising infrastructure to provide the energy refueling service for EVs. However, each operator (i.e., battery swapping module (BSM) operator and battery charging module (BCM) operator) in BSCS has privacy-preserving requirement and individual interest, which brings challenge to the operation management of BSCS. To this end, this paper investigates the privacy-preserving operation management problem (OMP) of BSCS from a social perspective, in which a comprehensive battery-swapping-charging process is modeled. Specifically, we first model the OMP as a constrained mixed-integer programming (MIP), where the evolutionary of the dynamic battery inventory and the SoC of charging batteries are considered simultaneously. Due to the privacy-preserving requirements of different operators and the strong coupling between continuous and binary decision variables, a novel dual-based Benders decomposition (DBD) algorithm is then developed, which has the following two merits: 1) Each BCM and BSM operator can independently solve its own charging and swapping scheduling problem, thus preserving the privacy of individual operator;2) The combination of dual decomposition and Benders decomposition techniques facilitates a parallel implementation, thus improving the scheduling efficiency and saving the computational time. Finally, simulation results are provided to validate the effectiveness and scalability of the proposed algorithm.

关键词： Batteries Degradation Logistics Servers Costs Terminology Statistics Battery swapping and charging operation management mixed-integer programming Benders decomposition

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A novel MIQCP method for FACTS allocation in complex real-world grids

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2014年 62卷 735-743页

作者： Chang, Robert W. Saha, Tapan K. Univ Queensland Sch Informat Technol & Elect Engn Brisbane Qld 4072 Australia

This paper presents a novel Flexible AC Transmission Systems (FACTS) placement method based on mixed integer quadratically constrained programming (MIQCP). The method is capable of allocating both Static VAR Compensator (SVC) and Thyristor-Controlled Series Capacitor (TCSC) either separately or simultaneously, to determine concurrently their numbers, locations as well as sizes. The optimization objective is to maximize loadability and minimize compensation. The proposed MIQCP formulation partially incorporates key quadratic constraints, which were absent in mixed integer linear programming (MILP) placement methods reported in the past. The authors demonstrate significant improvements in accuracy over past MILP methods, with case studies presented on the simplified Southeast Australian network, and on a large scale real-world power system, Powerlink Queensland's HV transmission network, with 886 buses and 1087 branches. In addition, results and observations for simultaneous allocation of multiple TCSCs and SVCs in these networks are demonstrated in this paper. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： FACTS devices Optimal allocation mixed-integer programming SVC TCSC

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Modeling and Solution of the Large-Scale Security-Constrained Unit Commitment

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IEEE TRANSACTIONS ON POWER SYSTEMS 2013年第4期28卷 3524-3533页

作者： Fu, Yong Li, Zuyi Wu, Lei Mississippi State Univ Dept Elect & Comp Engn Mississippi State MS 39759 USA IIT Dept Elect & Comp Engn Chicago IL 60616 USA Clarkson Univ Dept Elect & Comp Engn Potsdam NY 13699 USA

Security-constrained unit commitment (SCUC), as one of key components in power system operation, is being widely applied in vertically integrated utilities and restructured power systems. The efficient solution framework is to implement iterations between a master problem (unit commitment) and subproblems (network security evaluations). In industrial applications, both Lagrangian relaxation and mixed-integer programming are commonly applied for the unit commitment problem, and both linear sensitivity factor and Benders cut methods are used to generate additional constraints in the phase of network security evaluations. This paper evaluates capabilities and performances of each algorithm through technical discussion and numerical testing. Special topics on the large-scale SCUC engine development are also discussed in this paper, such as input data screening, inactive constrains elimination, contingency management, infeasibility handling, parallel computing, and model simplification. This paper will benefit academic researchers, software developers, and system operators when they design, develop and assess effective models and algorithms for solving large-scale SCUC problems.

关键词： Benders decomposition Lagrangian relaxation linear sensitivity factors mixed-integer programming security-constrained unit commitment (SCUC)

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Polyhedral results and valid inequalities for the continuous energy-constrained scheduling problem

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DISCRETE APPLIED MATHEMATICS 2019年 258卷 188-203页

作者： Nattaf, Margaux Horvath, Marko Kis, Tamas Artigues, Christian Lopez, Pierre Univ Toulouse LAAS CNRS CNRS Toulouse France Hungarian Acad Sci Inst Comp Sci & Control Budapest Hungary

This paper addresses a scheduling problem involving a continuously-divisible cumulative resource with limited capacity. During its processing, each task requests a part of this resource, which lies between a minimum and a maximum requirement. A task is finished when a certain amount of energy is received by it within its time window. This energy is received via the resource and an amount of resource is converted into an amount of energy with an increasing and pseudo-linear efficiency function. The goal is to minimize the resource consumption. The paper focuses on an event-based mixed integer linear program, providing several valid inequalities, which are used to improve the performance of the model. Furthermore, we give a minimal description of the polytope of all feasible assignments to the on/off binary variable for a single activity along with a dedicated separation algorithm. Computational experiments are reported in order to show the effectiveness of the results. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Continuous scheduling Continuous resources Linear efficiency functions mixed-integer programming Valid inequalities Polyhedral combinatorics

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