A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown-by several authors using different techniques-t...
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A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown-by several authors using different techniques-that the convex hull of the intersection of an ellipsoid, , and a split disjunction, with , equals the intersection of with an additional second-order-cone representable (SOCr) set. In this paper, we study more general intersections of the form and , where is a SOCr cone, is a nonconvex cone defined by a single homogeneous quadratic, and H is an affine hyperplane. Under several easy-to-verify conditions, we derive simple, computable convex relaxations and , where is a SOCr cone. Under further conditions, we prove that these two sets capture precisely the corresponding conic/convex hulls. Our approach unifies and extends previous results, and we illustrate its applicability and generality with many examples.
In this work we propose a mixed-integer nonlinear programming model to address the line pressure optimization problem for shale gas gathering systems. This model is designed to determine: a) the optimal timing for tur...
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In this work we propose a mixed-integer nonlinear programming model to address the line pressure optimization problem for shale gas gathering systems. This model is designed to determine: a) the optimal timing for turning prospective wells in-line, b) the optimal pressure profile within a gathering network, and c) the necessary compression power for delivering produced gas to long-distance transmission lines. We rely on a pressure-normalized decline curve model to quantify how line pressure variations impact the gas production of individual wells. The reservoir model itself is incorporated in a transmission optimization framework which rigorously evaluates pressure drops along pipeline segments. Moreover, we explicitly consider compression requirements to lift line pressure from gas gathering levels to setpoints dictated by transmission pipeline companies. Since the resulting optimization models are large-scale, nonlinear and nonconvex, we propose a solution procedure based on an efficient initialization strategy. Finally, we present a detailed case study, and show that the proposed optimization framework can be used effectively to manage line pressures in shale gas gathering systems by properly scheduling when, and how many, new wells are brought online.
We consider a challenging resource allocation problem arising in mobile wireless communications. The goal is to allocate the available channels and power in a so-called OFDMA system, in order to maximise the transmiss...
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We consider a challenging resource allocation problem arising in mobile wireless communications. The goal is to allocate the available channels and power in a so-called OFDMA system, in order to maximise the transmission rate, subject to quality of service constraints. Standard MINLP software struggled to solve even small instances of this problem. Using outer approximation, perspective cuts and several implementation "tricks", we are able to solve realistic instances in about one minute. A novel ingredient of our algorithm is what we call pre-emptive cut generation: the generation of cutting planes that are not violated in the current iteration, but are likely to be violated in subsequent iterations.
Mathematical programming has been widely applied for the planning of natural gas production infrastructure development. As the production infrastructure involves large investments and is expected to remain in operatio...
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Mathematical programming has been widely applied for the planning of natural gas production infrastructure development. As the production infrastructure involves large investments and is expected to remain in operation over several decades, the factors that will impact the gas production but cannot be foreseen before the development of the infrastructure need to be taken into account in the planning. Therefore, two scenario-based two-stage stochastic programming models are developed to facilitate natural gas production infrastructure development under uncertainty. One is called the stochastic pooling model, which tracks the qualities of gas streams throughout the production network via a generalized pooling model. The other is an enhancement of the stochastic pooling model with the consideration of pressure. Either model results in a large-scale nonconvex mixed-integer nonlinear programming (MINLP) problem, for which a global optimal solution, although very important for a problem that involves large investments, is very difficult to obtain. A novel optimization method, called nonconvex generalized Benders decomposition (NGBD), is developed for efficient global optimization of the large-scale nonconvex MINLP. Case studies of a real industrial natural gas production system show the advantages of the proposed stochastic programming models over deterministic optimization models, as well as the dramatic computational advantages of NGBD over a state-of-the-art global optimization solver.
This paper considers a novel formulation of the multi-period network interdiction problem. In this model, delivery of the maximum flow as well as the act of interdiction happens over several periods, while the budget ...
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This paper considers a novel formulation of the multi-period network interdiction problem. In this model, delivery of the maximum flow as well as the act of interdiction happens over several periods, while the budget of resource for interdiction is limit. It is assumed that when an edge is interdicted in a period, the evader considers a rate of risk of detection at consequent periods. Application of the generalized Benders decomposition algorithm considers solving the resulting mixed-integer nonlinear programming problem. Computational experiences denote reasonable consistency with expectations.
We propose a mixed-integer nonlinear programming (MINLP) model for the simultaneous chemical process synthesis and heat integration with unclassified process streams. The model accounts for (1) streams that cannot be ...
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We propose a mixed-integer nonlinear programming (MINLP) model for the simultaneous chemical process synthesis and heat integration with unclassified process streams. The model accounts for (1) streams that cannot be classified as hot or cold, and (2) variable stream temperatures and flow rates, thereby facilitating integration with a process synthesis model. The hot/cold stream "identities" are represented by classification binary variables which are (de)activated based on the relative stream inlet and outlet temperatures. Variables including stream temperatures and heat loads are disaggregated into hot and cold variables, and each variable is (de)activated by the corresponding classification binary variable. Stream inlet/outlet temperatures are positioned onto "dynamic" temperature intervals so that heat loads at each interval can be properly calculated. The proposed model is applied to two illustrative examples with variable stream flow rates and temperatures, and is integrated with a superstructure-based process synthesis model to illustrate its applicability. (C) 2017 Elsevier Ltd. All rights reserved.
作者:
Castro, Pedro M.Univ Lisbon
Ctr Matemat Aplicacoes Fundamentais & Invest Oper Fac Ciencias P-1749016 Lisbon Portugal
Spatial branch-and-bound (B&B) is widely used for the global optimization of non-convex problems. It basically works by iteratively reducing the domain of the variables so that tighter relaxations can be achieved ...
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Spatial branch-and-bound (B&B) is widely used for the global optimization of non-convex problems. It basically works by iteratively reducing the domain of the variables so that tighter relaxations can be achieved that ultimately converge to the global optimal solution. Recent developments for bilinear problems have brought us piecewise relaxation techniques that can prove optimality for a sufficiently large number of partitions and hence avoid spatial B&B altogether. Of these, normalized multiparametric disaggregation (NMDT) exhibits a good performance due to the logarithmic increase in the number of binary variables with the number of partitions. We now propose to integrate NMDT with spatial B&B for solving mixed-integer quadratically constrained minimization problems. Optimality-based bound tightening is also part of the algorithm so as to compute tight lower bounds in every step of the search and reduce the number of nodes to explore. Through the solution of a set of benchmark problems from the literature, it is shown that the new global optimization algorithm can potentially lead to orders of magnitude reduction in optimality gap when compared to commercial solvers BARON and GloMIQO.
The demand for natural gas is increasing in the energy market because of its lower emissions and sustainable development. This increasing demand for natural gas promotes the capacity expansion of raw natural gas refin...
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The demand for natural gas is increasing in the energy market because of its lower emissions and sustainable development. This increasing demand for natural gas promotes the capacity expansion of raw natural gas refining systems (RNGRSs), resulting in parallel refining processes in a RNGRS. Optimizing the material stream network between these refining processes is very challenging because of the complex thermodynamics, unit operations and utility configurations. An optimization framework is presented for the retrofit of the material stream network between these refining processes to improve the economic performance. The retrofit framework integrates raw natural gas supply, refining processes, utility subsystems and product delivery and is formulated as a mixed-integer nonlinear programming (MINLP) optimization model to obtain an optimal material stream network to increase profit. The model presented here is applied to a Chinese industrial RNGRS and results in an optimal retrofit. A comparison before and after the retrofit demonstrates a significant increase in profit. Crown Copyright (C) 2016 Published by Elsevier Ltd on behalf of The Royal College of Radiologists. All rights reserved.
Process intensification provides a whole toolbox of innovative solutions for improved energy efficiency of chemical processes. However, evaluation of this potential is hampered by the unavailability of suitable models...
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Process intensification provides a whole toolbox of innovative solutions for improved energy efficiency of chemical processes. However, evaluation of this potential is hampered by the unavailability of suitable models and design tools. Integrated processes like dividing wall columns either have to be mapped by available unit operation models or tailored equation-based models have to be developed. The current article reviews available methods for conceptual design and optimization of dividing wall columns and provides a detailed comparison of two representative optimization approaches.
Dimethyl ether (DME) is a clean and efficient synthetic fuel with the potential to substitute liquefied petroleum gas (LPG) and diesel. From both the environmental and economic viewpoints, there is a strong preference...
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Dimethyl ether (DME) is a clean and efficient synthetic fuel with the potential to substitute liquefied petroleum gas (LPG) and diesel. From both the environmental and economic viewpoints, there is a strong preference to use biomass as the feedstock of synthetic fuels. In this study, state-of-the-art technologies were surveyed and a superstructure representation for the DME production process involving the use of biomass as a feedstock was investigated. Moreover, a mixed-integer nonlinear programming (MINLP) model was proposed for developing a DME production process based on biomass gasification. A combination of optimal technologies was adopted;detailed studies are presented to demonstrate the key features of the proposed superstructure.
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