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 tran...
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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%.
We propose a method for solving mixed-integernonlinear programmes (MINLPs) to global optimality by discretization of occurring nonlinearities. The main idea is based on using piecewise linear functions to construct m...
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We propose a method for solving mixed-integernonlinear 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.
We consider a multi-period revenue maximization and pricing optimization problem in the presence of reference prices. We formulate the problem as a mixedintegernonlinear program and develop a generalized Benders'...
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We consider a multi-period revenue maximization and pricing optimization problem in the presence of reference prices. We formulate the problem as a mixedintegernonlinear 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.
This paper describes a multi-period mixedintegernonlinearprogramming model for determining the optimal crop allocation for several planting cycles based on future crop prices and fresh water availability. An autore...
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This paper describes a multi-period mixedintegernonlinearprogramming 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.
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 Bernste...
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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.
Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of r...
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Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and the recursive packing of rings into other rings. This problem is known as the Recursive Circle Packing Problem (RCPP). We present the first dedicated method for solving RCPP that provides strong dual bounds based on an exact Dantzig-Wolfe reformulation of a nonconvex mixed-integer nonlinear programming formulation. The key idea of this reformulation is to break symmetry on each recursion level by enumerating one-level packings, i.e., packings of circles into other circles, and by dynamically generating packings of circles into rectangles. We use column generation techniques to design a "price-and-verify" algorithm that solves this reformulation to global optimality. Extensive computational experiments on a large test set show that our method not only computes tight dual bounds, but often produces primal solutions better than those computed by heuristics from the literature.
Power distribution systems in the US are commonly supported by wood utility poles. These assets require regular maintenance to enhance the reliability of power delivery to support many dependent functions of the socie...
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Power distribution systems in the US are commonly supported by wood utility poles. These assets require regular maintenance to enhance the reliability of power delivery to support many dependent functions of the society. Limitations in budget, however, warrant efficient allocation of limited resources based on optimal preventive maintenance plans. A few studies have developed risk-based metrics to support risk-informed decision making in preventive maintenance planning for power distribution systems. However, integration of risk-based metrics and optimization for enhancing the life-cycle resilience of distribution systems has not been explored. To address this gap, this paper proposes a mixed-integer nonlinear programming (MINLP) model to maximize the life-cycle resilience of aging power distribution systems subject to multi-occurrences of hurricane events using an optimal risk-based maintenance planning. For this purpose, a risk-based index called the Expected Outages is proposed and integrated into the optimization problem to minimize the total expected number of power outages in the entire planning horizon. Various uncertainties in the performance of poles under stochastic occurrences of hazards are taken into account through advanced fragility models and an efficient recursive formulation that models the uncertainty of precedent pole failures. The proposed approach is applied to a large, realistic power distribution system for long-term maintenance planning given a total budget limit and different levels of periodic budget constraints. The resulting optimization problems are solved through the branch and bound algorithm. Results indicate that applying the presented methodology leads to a significant enhancement of the life-cycle resilience of distribution systems compared to the commonly implemented strength-based maintenance strategy set by National Electric Safety Code.
This work presents a whole-year simulation study on nonlinearmixed-integer Model Predictive Control (MPC) for a complex thermal energy supply system which consists of a heat pump, stratified water storages, free cool...
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This work presents a whole-year simulation study on nonlinearmixed-integer Model Predictive Control (MPC) for a complex thermal energy supply system which consists of a heat pump, stratified water storages, free cooling facilities, and a large underground thermal storage. For solution of the arising mixed-integer Non-Linear Programs (MINLPs) we apply an existing general and optimal-control-suitable decomposition approach. To compensate deviation of forecast inputs from measured disturbances, we introduce a moving horizon estimation step within the MPC strategy. The MPC performance for this study, which consists of more than 50,000 real-time suitable MINLP solutions, is compared to an elaborate conventional control strategy for the system. It is shown that MPC can significantly reduce the yearly energy consumption while providing a similar degree of constraint satisfaction, and autonomously identify previously unknown, beneficial operation modes.
The need to consider multiple objectives in molecular design, whether based on techno-economic, environmental or health and safety metrics is increasingly recognized. There is, however, limited understanding of the su...
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The need to consider multiple objectives in molecular design, whether based on techno-economic, environmental or health and safety metrics is increasingly recognized. There is, however, limited understanding of the suitability of different multi-objective optimization (MOO) algorithm for the solution of such design problems. In this work, we present a systematic comparison of the performance of five mixed-integer non-linear programming (MINLP) MOO algorithms on the selection of computer-aided molecular design (CAMD) and computer-aided molecular and process design (CAMPD) problems. The five methods are designed to address the discrete and nonlinear nature of the problem, with the aim of generating an accurate approximation of the Pareto front. They include: a weighted sum approach without global search phases (SWS), a weighted sum approach with simulated annealing (WSSA), a weighted sum approach with multi level single linkage (WSML), the sandwich algorithm with MLSL (SDML) and the non dominated sorting genetic algorithm-II (NSGA-II). The algorithms are compared systematically in two steps. The effectiveness of the global search methods is evaluated with SWS, WSSA and WSML. WSML is found to be most effective and a comparative analysis of WSML, SDML and NSGA-II is then undertaken. As a test set of these optimization techniques, two CAMD and one CAMPD problems of varying dimensionality are formulated as case studies. The results show that the SDML provides the most efficient generation of a diverse set of Pareto points, leading to the construction of an approximate Pareto front close to exact Pareto front. (C) 2020 Elsevier Ltd. All rights reserved.
This paper addresses the classical problem of optimal location and sizing of distributed generators (DGs) in radial distribution networks by presenting a mixed-integer nonlinear programming (MINLP) model. To solve suc...
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This paper addresses the classical problem of optimal location and sizing of distributed generators (DGs) in radial distribution networks by presenting a mixed-integer nonlinear programming (MINLP) model. To solve such model, we employ the General Algebraic Modeling System (GAMS) in conjunction with the BONMIN solver, presenting its characteristics in a tutorial style. To operate all the DGs, we assume they are dispatched with a unity power factor. Test systems with 33 and 69 buses are employed to validate the proposed solution methodology by comparing its results with multiple approaches previously reported in the specialized literature. A 27-node test system is also used for locating photovoltaic (PV) sources considering the power capacity of the Caribbean region in Colombia during a typical sunny day. Numerical results confirm the efficiency and accuracy of the MINLP model and its solution is validated through the GAMS package. (C) 2019 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Ain Shams University.
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