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An Enhanced Optimal PV and Battery Sizing Model for Zero Energy Buildings Considering Environmental Impacts

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS 2020年第6期56卷 6846-6856页

作者： Mehrtash, Mahdi Capitanescu, Florin Heiselberg, Per Kvols Gibon, Thomas Bertrand, Alexandre LIST ERIN L-4422 Belvaux Luxembourg Univ British Columbia Fac Sci Appl Vancouver BC V6T 1Z2 Canada Aalborg Univ Dept Civil Engn DK-9220 Aalborg Denmark

The important focus of the energy strategy of the European Union relies on the concept of zero energy building (ZEB), which is, by definition, a building that roughly produces yearly as much renewable energy as it consumes. This article proposes an enhanced mixed-integer nonlinear programming model for optimal sizing of photovoltaic (PV) and battery energy storage systems to comply with the definition of a ZEB. A salient novel feature of the proposed model is that it factors in the environmental impacts, computed through rigorous life cycle assessment methodology, of buying electricity from the grid and manufacturing battery and PV systems. Furthermore, an adjustable parameter is introduced to make the model adaptive from the perspective of the building owners willingness-to-pay for environmental impacts. The proposed model is then rigorously reformulated, managing to accumulate its nonlinearity in only one constraint per time interval. Eventually, the reformulated model is linearized to a mixed-integer linear programming model using the McCormick relaxation technique. The case study conducted on archetypal buildings in Luxembourg reveals that the proposed McCormick-based linear model is able to provide high accuracy results with reasonable computational effort.

关键词： Batteries Buildings Computational modeling Investment Maintenance engineering Mathematical model Adaptation models Battery storage system environmental impacts McCormick envelops mixed-integer nonlinear programming optimal photovoltaic (PV) and battery sizing zero energy building (ZEB)

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Novel MINLP formulations for flexibility analysis for measured and unmeasured uncertain parameters

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COMPUTERS & CHEMICAL ENGINEERING 2020年第0期135卷 106727-000页

作者： Ochoa, M. Paz Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Ctr Adv Proc Decis Making Pittsburgh PA 15213 USA

In this work, we formulate the extended flexibility analysis, which takes into account two different types of uncertain parameters, measured (theta(m)) and unmeasured (theta(u)), as a rigorous multilevel optimization problem. We recursively reformulate the inner optimization problems by the KKT conditions and with a mixed-integer representation of the complementarity conditions to solve the resulting optimization problem. Special cases are identified, where models are comprised of convex constraints or constraints with monotonic variation of the uncertain parameters. In these cases, a vertex enumeration can be performed to solve the flexibility test. We propose two MINLP reformulations for the more general case yielding to similar results but different model sizes. The formulations are tested and compared in several examples. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Flexibility analysis Optimization under uncertainty mixed-integer nonlinear programming

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Improving the performance of DICOPT in convex MINLP problems using a feasibility pump

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OPTIMIZATION METHODS & SOFTWARE 2020年第1期35卷 171-190页

作者： Bernal, David E. Vigerske, Stefan Trespalacios, Francisco Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA GAMS Software GmbH Zuse Inst Berlin Berlin Germany ExxonMobil Corp Strateg Res Clinton NJ USA

The solver DICOPT is based on the outer-approximation algorithm used for solving mixed-integer nonlinear programming (MINLP) problems. This algorithm is very effective for solving some types of convex MINLPs. However, it has been observed that DICOPT has difficulties solving instances in which some of the nonlinear constraints are so restrictive that nonlinear subproblems generated by the algorithm are infeasible. This problem is addressed in this paper with a feasibility pump algorithm, which modifies the objective function in order to efficiently find feasible solutions. It has been implemented as a preprocessing algorithm, which is used to initialize both the incumbent and the mixed-integer linear relaxation of the outer-approximation algorithm. Computational comparisons with previous versions of DICOPT on a set of convex MINLPs demonstrate the effectiveness of the proposed algorithm in terms of solution quality and solution time.

关键词： Feasibility pump mixed-integer nonlinear programming primal heuristics

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Optimal scheduling of copper concentrate operations under uncertainty

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COMPUTERS & CHEMICAL ENGINEERING 2020年 140卷 106919-106919页

作者： Cheng, Pengfei Garcia-Herreros, Pablo Lalpuria, Mangalam Grossmann, Ignacio E. Georgia Inst Technol Sch Chem & Biomol Engn Atlanta GA 30332 USA Carnegie Mellon Univ Ctr Adv Proc Decis Making Dept Chem Engn Pittsburgh PA 15213 USA Aurubis AG Res Dev & Innovat Dept D-20539 Hamburg Germany

We propose a continuous-time scheduling model for the logistic and blending operations of copper concentrates with uncertain composition. The formulation, based on the Multi-Operation Sequencing (MOS) model, gives rise to a large-scale nonconvex mixed-integer nonlinear programming (MINLP) model. We adopt a two-step MILP-NLP decomposition strategy and enhance the MILP relaxation to propose schedules that significantly reduce the optimality gaps. The bounded uncertainty in element composition of the concentrates is addressed by an extended robust MOS model, which combines robust optimization and flexibility analysis techniques. The effectiveness of the models and the solution strategy is validated with an illustrative example and an industrial case study. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Scheduling Copper operations mixed-integer nonlinear programming Robust optimization

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LORM: Learning to Optimize for Resource Management in Wireless Networks With Few Training Samples

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2020年第1期19卷 665-679页

作者： Shen, Yifei Shi, Yuanming Zhang, Jun Letaief, Khaled B. Hong Kong Univ Sci & Technol Dept Elect & Comp Engn Hong Kong Peoples R China ShanghaiTech Univ Sch Informat Sci & Technol Shanghai 201210 Peoples R China Hong Kong Polytech Univ Dept Elect & Informat Engn Hong Kong Peoples R China

Effective resource management plays a pivotal role in wireless networks, which, unfortunately, typically results in challenging mixed-integer nonlinear programming (MINLP) problems. Machine learning-based methods have recently emerged as a disruptive way to obtain near-optimal performance for MINLPs with affordable computational complexity. There have been some attempts in applying such methods to resource management in wireless networks, but these attempts require huge amounts of training samples and lack the capability to handle constrained problems. Furthermore, they suffer from severe performance deterioration when the network parameters change, which commonly happens and is referred to as the task mismatch problem. In this paper, to reduce the sample complexity and address the feasibility issue, we propose a framework of Learning to Optimize for Resource Management (LORM). In contrast to the end-to-end learning approach adopted in previous studies, LORM learns the optimal pruning policy in the branch-and-bound algorithm for MINLPs via a sample-efficient method, namely, imitation learning. To further address the task mismatch problem, we develop a transfer learning method via self-imitation in LORM, named LORM-TL, which can quickly adapt a pre-trained machine learning model to the new task with only a few additional unlabeled training samples. Numerical simulations demonstrate that LORM outperforms specialized state-of-the-art algorithms and achieves near-optimal performance, while providing significant speedup compared with the branch-and-bound algorithm. Moreover, LORM-TL, by relying on a few unlabeled samples, achieves comparable performance with the model trained from scratch with sufficient labeled samples.

关键词： Resource management Optimization Machine learning algorithms Wireless networks Training Machine learning Heuristic algorithms Resource allocation mixed-integer nonlinear programming wireless communications few-shot learning transfer learning

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An adjoint optimization approach for the topological design of large-scale district heating networks based on nonlinear models

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APPLIED ENERGY 2020年 280卷 116025-116025页

作者： Blommaert, Maarten Wack, Y. Baelmans, M. Katholieke Univ Leuven Dept Mech Engn Celestijnenlaan 300 Box 2421 B-3001 Leuven Belgium EnergyVille Thor PkPoort Genk 8310 B-3600 Genk Belgium Flemish Inst Technol Res VITO Boeretang 200 B-2400 Mol Belgium

This article deals with the problem of finding the best topology, pipe diameter choices, and operation parameters for realistic district heating networks. Present design tools that employ non-linear flow and heat transport models for topological design are limited to small heating networks with up to 20 potential consumers. We introduce an alternative adjoint-based numerical optimization strategy to enable large-scale nonlinear thermal network optimization. In order to avoid a strong computational cost scaling with the network size, we aggregate consumer constraints with a constraint aggregation strategy. Moreover, to align this continuous optimization strategy with the discrete nature of topology optimization and pipe size choices, we present a numerical continuation strategy that gradually forces the design variables towards discrete design choices. As such, optimal network topology and pipe sizes are determined simultaneously. Finally, we demonstrate the scalability of the algorithm by designing a fictitious district heating network with 160 consumers. As a proof-of-concept, the network is optimized for minimal investment cost and pumping power, while keeping the heat supplied to the consumers within a thermal comfort range of 5%. Starting from a uniform distribution of 15 cm wide piping throughout the network, the novel algorithm finds a network layout that reduces piping investment by 23% and pump-related costs by a factor of 14 in less than an hour on a standard laptop. Moreover, the importance of embedding the non-linear transport model is clear from a temperature-induced variation in the consumer flow rates of 72%.

关键词： Optimal network design District heating networks Topology optimization Adjoint method mixed-integer nonlinear programming Constraint aggregation

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Solving mixed-integer nonlinear programmes using adaptively refined mixed-integer linear programmes

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OPTIMIZATION METHODS & SOFTWARE 2020年第1期35卷 37-64页

作者： Burlacu, Robert Geissler, Bjoern Schewe, Lars Friedrich Alexander Univ Erlangen Nurnberg FAU Erlangen Germany

We propose a method for solving mixed-integer nonlinear programmes (MINLPs) to global optimality by discretization of occurring nonlinearities. The main idea is based on using piecewise linear functions to construct mixed-integer linear programme (MIP) relaxations of the underlying MINLP. In order to find a global optimum of the given MINLP, we develop an iterative algorithm which solves MIP relaxations that are adaptively refined. We are able to give convergence results for a wide range of MINLPs requiring only continuous nonlinearities with bounded domains and an oracle computing maxima of the nonlinearities on their domain. Moreover, the practicalness of our approach is shown numerically by an application from the field of gas network optimization.

关键词： mixed-integer nonlinear programming piecewise linear approximation gas transport optimization global optimization adaptivity

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Price optimization with reference price effects: A generalized Benders' decomposition method and a myopic heuristic approach

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期280卷 555-567页

作者： Shams-Shoaaee, Seyed Shervin Hassini, Elkafi McMaster Univ Sch Computat Sci & Engn Hamilton ON Canada McMaster Univ DeGroote Sch Business Hamilton ON Canada

We consider a multi-period revenue maximization and pricing optimization problem in the presence of reference prices. We formulate the problem as a mixed integer nonlinear program and develop a generalized Benders' decomposition algorithm to solve it. In addition, we propose a myopic heuristic and discuss the conditions under which it produces efficient solutions. We provide analytical results as well as numerical computations to illustrate the efficiency of the solution approaches as well as some managerial pricing insights. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Pricing Reference pricing mixed-integer nonlinear programming Generalized Benders' decomposition

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Optimal crop allocation including market trends and water availability

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期285卷 728-739页

作者： Cervantes-Gaxiola, Maritza E. Sosa-Niebla, Erik F. Hernandez-Calderon, Oscar M. Ponce-Ortega, Jose M. Ortiz-del-Castillo, Jesus R. Rubio-Castro, Eusiel Univ Autonoma Sinaloa Chem & Biol Sci Dept Ext 177 Culiacan 80000 Sinaloa Mexico Univ Michoacana Chem Engn Dept Morelia 58060 Michoacan Mexico

This paper describes a multi-period mixed integer nonlinear programming model for determining the optimal crop allocation for several planting cycles based on future crop prices and fresh water availability. An autoregressive moving average model is implemented to predict prices, and a new superstructure that includes all configurations of interest for the reuse, recycling, storage, and regeneration of water is employed. Two characteristic examples considering maize, wheat, alfalfa, and beans and their optimal scheduling for the years 2020, 2021, and 2022 are solved with the objective of maximizing the total annual profit. In determining the profit, the operating costs include fresh water, fresh fertilizer, and pumping and the capital costs include storage tanks, treatment units, pipelines, and pumps. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Combinatorial optimization Assignment Water integration Price prediction mixed-integer nonlinear programming

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A new box selection criterion in interval Bernstein global optimization algorithm for MINLPs

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GRANULAR COMPUTING 2020年第2期5卷 155-168页

作者： Patil, Bhagyesh V. Zidna, Ahmed Cambridge Ctr Adv Res & Educ Singapore Ltd 1 Create Way CREATE Campus Singapore 138602 Singapore Univ Lorraine Lab Gnie Informat Prod & Maintenance LGIPM Lorraine France

mixed-integer nonlinear programming (MINLP) problems are known to be challenging due to the involvement of nonlinear mathematical relations and combinatorial complexities. In this paper, an interval form-based Bernstein global optimization algorithm is presented to solve polynomial MINLP problems. The major contribution of this paper is a new box selection criterion for this interval form-based Bernstein global optimization algorithm. This new box selection criterion promotes fast convergence of the Bernstein algorithm. Moreover, the new box selection criterion allows the construction of a hybrid branch-and-bound framework for the Bernstein algorithm, wherein a local search method is used to obtain a good upper bound on the global minimum, and the Bernstein form is employed to obtain a valid lower bound on the global minimum. We show with numerical results that it is possible to obtain a significant reduction in the number of subdivisions required with this new box selection criterion. Furthermore, the Bernstein algorithm with this new box selection criterion is evaluated numerically on a variety of small- to medium-size MINLP problem instances and its performance is compared with the previously reported Bernstein global optimization algorithm as well as with a few state-of-the-art MINLP solvers. The results of the numerical studies demonstrate satisfactory performance in terms of the chosen performance metrics. Finally, the trim-loss minimization problem from the paper industry is solved to demonstrate the practical applicability of the Bernstein algorithm.

关键词： Bernstein polynomial form Global optimization Local search mixed-integer nonlinear programming Trim-loss minimization problem

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