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Monomial-wise optimal separable underestimators for mixed-integer polynomial optimization

JOURNAL OF GLOBAL OPTIMIZATION 2017年第4期67卷 759-786页

作者： Buchheim, Christoph D'Ambrosio, Claudia TU Dortmund Fak Math Vogelpothsweg 87 D-44227 Dortmund Germany Ecole Polytech LIX CNRS UMR7161 F-91128 Palaiseau France

We introduce a new method for solving box-constrained mixed-integer polynomial problems to global optimality. The approach, a specialized branch-and-bound algorithm, is based on the computation of lower bounds provided by the minimization of separable underestimators of the polynomial objective function. The underestimators are the novelty of the approach because the standard approaches in global optimization are based on convex relaxations. Thanks to the fact that only simple bound constraints are present, minimizing the separable underestimator can be done very quickly. The underestimators are computed monomial-wise after the original polynomial has been shifted. We show that such valid underestimators exist and their degree can be bounded when the degree of the polynomial objective function is bounded, too. For the quartic case, all optimal monomial underestimators are determined analytically. We implemented and tested the branch-and-bound algorithm where these underestimators are hardcoded. The comparison against standard global optimization and polynomial optimization solvers clearly shows that our method outperforms the others, the only exception being the binary case where, though, it is still competitive. Moreover, our branch-and-bound approach suffers less in case of dense polynomial objective function, i.e., in case of polynomials having a large number of monomials. This paper is an extended and revised version of the preliminary paper [4].

关键词： Polynomial optimization mixed-integer nonlinear programming Separable underestimators

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Operational strategy and planning for raw natural gas refining complexes: Process modeling and global optimization

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AICHE JOURNAL 2017年第2期63卷 652-668页

作者： Zhang, Bing J. Chen, Qing L. Li, Jie Floudas, Christodoulos A. Sun Yat Sen Univ Sch Chem Engn & Technol Guangdong Engn Technol Res Ctr Petrochem Energy C Key Lab Low Carbon Chem & Energy Conservat Guangd 135 Xingang West Rd Guangzhou 510275 Guangdong Peoples R China Texas A&M Univ Artie McFerrin Dept Chem Engn 3122 TAMU College Stn TX 77843 USA Texas A&M Univ Texas A&M Energy Inst 3372 TAMU College Stn TX 77843 USA Univ Manchester Sch Chem Engn & Analyt Sci Manchester M13 9PL Lancs England

Optimal operational strategy and planning of a raw natural gas refining complex (RNGRC) is very challenging since it involves highly nonlinear processes, complex thermodynamics, blending, and utility systems. In this article, we first propose a superstructure integrating a utility system for the RNGRC, involving multiple gas feedstocks, and different product specifications. Then, we develop a large-scale nonconvex mixed-integer nonlinear programming (MINLP) optimization model. The model incorporates rigorous process models for input and output relations based on fundamentals of thermodynamics and unit operations and accurate models for utility systems. To reduce the noncovex items in the proposed MINLP model, equivalent reformulation techniques are introduced. Finally, the reformulated nonconvex MINLP model is solved to global optimality using state of the art deterministic global optimization approaches. The computational results demonstrate that a significant profit increase is achieved using the proposed approach compared to that from the real operation. (c) 2016 American Institute of Chemical Engineers AIChE J, 63: 652-668, 2017

关键词： natural gas operational planning mixed-integer nonlinear programming enterprise-wide optimization global optimization

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How to convexify the intersection of a second order cone and a nonconvex quadratic

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MATHEMATICAL programming 2017年第1-2期162卷 393-429页

作者： Burer, Samuel Kilinc-Karzan, Fatma Univ Iowa Dept Management Sci Iowa City IA 52242 USA Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA

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.

关键词： Convex hull Disjunctive programming mixed-integer linear programming mixed-integer nonlinear programming mixed-integer quadratic programming Nonconvex quadratic programming Second-order-cone programming Trust-region subproblem

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An exact algorithm for a resource allocation problem in mobile wireless communications

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2017年第2期68卷 193-208页

作者： Letchford, Adam N. Ni, Qiang Zhong, Zhaoyu Univ Lancaster Dept Management Sci Lancaster LA1 4YX England Univ Lancaster Sch Comp & Commun Lancaster LA1 4WA England

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.

关键词： mixed-integer nonlinear programming Mobile wireless communications OFDMA systems

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Natural gas production network infrastructure development under uncertainty

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OPTIMIZATION AND ENGINEERING 2017年第1期18卷 35-62页

作者： Li, Xiang Tomasgard, Asgeir Barton, Paul I. MIT Proc Syst Engn Lab Dept Chem Engn 77 Massachusetts Ave Cambridge MA 02139 USA Queens Univ Dept Chem Engn 19 Div St Kingston ON K7L 3N6 Canada Norwegian Univ Sci & Technol Dept Ind Econ & Technol Management N-7491 Trondheim Norway

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.

关键词： Natural gas production network mixed-integer nonlinear programming Stochastic programming Benders decomposition Global optimization

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Solving Multi-period Interdiction via Generalized Bender's Decomposition

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Acta Mathematicae Applicatae Sinica 2017年第3期33卷 633-644页

作者： Maryam SOLEIMANI-ALYAR Alireza GHAFFARI-HADIGHEH Department of Applied Mathematics Azarbaijan Shahid Madani UniversityTabrizIran

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.

关键词： Bi-level programming network interdiction mixed-integer nonlinear programming generalized benders decomposition

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Simultaneous chemical process synthesis and heat integration with unclassified hot/cold process streams

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COMPUTERS & CHEMICAL ENGINEERING 2017年 101卷 210-225页

作者： Kong, Lingxun Avadiappan, Venkatachalam Huang, Kefeng Maravelias, Christos T. Univ Wisconsin Dept Chem & Biol Engn 1415 Engn Dr Madison WI 53706 USA

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.

关键词： mixed-integer nonlinear programming Superstructure optimization

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Spatial branch-and-bound algorithm for MIQCPs featuring multiparametric disaggregation

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OPTIMIZATION METHODS & SOFTWARE 2017年第4期32卷 719-737页

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 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.

关键词： mixed-integer nonlinear programming nonlinear programming quadratic optimization discretization bilinear terms

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Material stream network modeling, retrofit and optimization for raw natural gas refining systems

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JOURNAL OF CLEANER PRODUCTION 2017年第Part4期142卷 3419-3436页

作者： Zhang, Bing J. Xu, Tao He, Chang Chen, Qing L. Luo, Xiang L. Sun Yat Sen Univ Sch Chem Engn & Technol Guangdong Engn Technol Res Ctr Petrochem Energy C 135 Xingang West Rd Guangzhou 510275 Guangdong Peoples R China Guangdong Univ Technol Sch Mat & Energy Guangzhou Higher Educ Mega Ctr 100 Waihuan West Rd Guangzhou 510006 Guangdong Peoples R China

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.

关键词： Raw natural gas Retrofit Optimization mixed-integer nonlinear programming Process modeling Utility system

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Conceptual Design of Highly Integrated Processes - Optimization of Dividing Wall Columns

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CHEMIE INGENIEUR TECHNIK 2017年第5期89卷 562-581页

作者： Waltermann, Thomas Skiborowski, Mirko TU Dortmund Univ Dept Biochem Lab Fluid Separat Chem Engn Emil Figge Str 70 D-44227 Dortmund Germany

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.

关键词： Computer aided process engineering Conceptual design Dividing wall columns mixed-integer nonlinear programming Optimization

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