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Time-optimal control of automobile test drives with gear shifts

OPTIMAL CONTROL APPLICATIONS & METHODS 2010年第2期31卷 137-153页

作者： Kirches, Christian Sager, Sebastian Bock, Hans Georg Schloeder, Johannes P. Heidelberg Univ Interdisciplinary Ctr Sci Comp IWR D-69120 Heidelberg Germany Univ Autonoma Madrid IMDEA Math E-28049 Madrid Spain

We present a numerical method and results for a recently published benchmark problem (Optim. Contr Appl. Met. 2005;26:1-18;Optim. Contr Appl. Met. 2006;27(3):169-182) in mixed-integer optimal control. The problem has its origin in automobile test-driving and involves discrete controls for the choice of gears. Our approach is based on a convexification and relaxation of the integer controls constraint. Using the direct multiple shooting method we solve the reformulated benchmark problem for two cases: (a) As proposed in (Optim. Contr Appl. Met. 2005;26:1-18), for a fixed, equidistant control discretization grid and (b) As formulated in (Optim. Contr Appl. Met. 2006;27(3):169-182), taking into account free switching times. For the first case, we reproduce the results obtained in (Optim. Contr Appl. Met. 2005;26:1-18) with a speed-up of several orders of magnitude compared with the Branch&Bound approach applied there (taking into account precision and the different computing environments). For the second case we optimize the switching times and propose to use an initialization based on the solution of (a). Compared with (Optim. Contr Appl. Met. 2006;27(3):169-182) we were able to reduce the overall computing time considerably, applying our algorithm. We give theoretical evidence on why our convex reformulation is highly beneficial in the case of time-optimal mixed-integer control problems as the chosen benchmark problem basically is (neglecting a small regularization term). Copyright (C) 2009 John Wiley & Sons, Ltd.

关键词： optimal control direct multiple shooting mixed-integer nonlinear optimization mixed-integer optimal control double-lane change manoeuvre gear choice

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Process synthesis of hybrid coal, biomass, and natural gas to liquids via Fischer-Tropsch synthesis, ZSM-5 catalytic conversion, methanol synthesis, methanol-to-gasoline, and methanol-to-olefins/distillate technologies

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COMPUTERS & CHEMICAL ENGINEERING 2012年 47卷 29-56页

作者： Baliban, Richard C. Elia, Josephine A. Weekman, Vern Floudas, Christodoulos A. Princeton Univ Dept Chem & Biol Engn Princeton NJ 08544 USA

Several technologies for synthesis gas (syngas) refining are introduced into a thermochemical based superstructure that will convert biomass, coal, and natural gas to liquid transportation fuels using Fischer-Tropsch (FT) synthesis or methanol synthesis. The FT effluent can be (i) refined into gasoline, diesel, and kerosene or (ii) catalytically converted to gasoline and distillate over a ZSM-5 zeolite. Methanol can be converted using ZSM-5 (i) directly to gasoline or to (ii) distillate via olefin intermediates. A mixed-integer nonlinear optimization model that includes simultaneous heat, power, and water integration is solved to global optimality to determine the process topologies that will produce the liquid fuels at the lowest cost. Twenty-four case studies consisting of different (a) liquid fuel combinations, (b) refinery capacities, and (c) superstructure possibilities are analyzed to identify important process topological differences and their effect on the overall system cost, the process material/energy balances, and the well-to-wheel greenhouse gas emissions. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Process synthesis with heat, power, and water integration Hybrid energy systems mixed-integer nonlinear optimization Fischer-Tropsch Methanol to gasoline Methanol to olefins and distillate

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Optimal price zones of electricity markets: a mixed-integer multilevel model and global solution approaches

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optimization METHODS & SOFTWARE 2019年第2期34卷 406-436页

作者： Grimm, Veronika Kleinert, Thomas Liers, Frauke Schmidt, Martin Zoettl, Gregor Friedrich Alexander Univ Erlangen Nurnberg Chair Econ Theory Lange Gasse 20 D-90403 Nurnberg Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany Friedrich Alexander Univ Erlangen Nurnberg Discrete Optimizat Cauerstr 11 D-91058 Erlangen Germany Friedrich Alexander Univ Erlangen Nurnberg Ind Org & Energy Markets Lange Gasse 20 D-90403 Nurnberg Germany

Mathematical modelling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design yields welfare-optimal outcomes. This problem leads to a challenging multilevel model that contains a graph-partitioning problem with multi-commodity flow connectivity constraints and nonlinearities due to proper economic modelling. Furthermore, it has highly symmetric solutions. We develop different problem-tailored solution approaches. In particular, we present an extended Karush-Kuhn-Tucker (KKT) transformation approach as well as a generalized Benders approach that both yield globally optimal solutions. These methods, enhanced with techniques such as symmetry breaking and primal heuristics, are evaluated in detail on academic as well as on realistic instances. It turns out that our approaches lead to effective solution methods for the difficult optimization tasks presented here, where the problem-specific generalized Benders approach performs considerably better than the methods based on KKT transformation.

关键词： multilevel optimization mixed-integer nonlinear optimization graph partitioning generalized Benders decomposition electricity market design

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Membrane system design for multicomponent gas mixtures via mixed-integer nonlinear programming

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COMPUTERS & CHEMICAL ENGINEERING 2000年第12期24卷 2719-2737页

作者： Qi, RH Henson, MA Louisiana State Univ Dept Chem Engn Baton Rouge LA 70803 USA

An optimal design strategy for membrane networks separating multicomponent gas mixtures based on an approximate permeator model and mixed-integer nonlinear programming (MINLP) is proposed. A permeator system superstructure is used to embed a very large number of possible network configurations and allows the permeator feed-side pressure to be fixed or a design variable. A MINLP design model is developed to minimize the total annual process cost by simultaneous optimization of the permeator configuration and operating conditions. Case studies for the separation of acid gases (CO2 and H2S) from crude natural gas mixtures with spiral-wound permeators are presented. Permeator configurations are derived for different number of separation stages for both continuous and discrete membrane areas. The method is sufficiently robust to handle product compositions that vary five orders of magnitude. The proposed approach provides an efficient methodology for preliminary screening of multi-stage membrane separation systems for multicomponent gas mixtures. (C) 2000 Elsevier Science Ltd. All rights reserved.

关键词： gas separations permeators process design mixed-integer nonlinear optimization

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Computing feasible points for binary MINLPs with MPECs

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MATHEMATICAL PROGRAMMING COMPUTATION 2019年第1期11卷 95-118页

作者： Schewe, Lars Schmidt, Martin Friedrich Alexander Univ Erlangen Nurnberg FAU Discrete Optimizat Cauerstr 11 D-91058 Erlangen Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany

Nonconvex mixed-binary nonlinear optimization problems frequently appear in practice and are typically extremely hard to solve. In this paper we discuss a class of primal heuristics that are based on a reformulation of the problem as a mathematical program with equilibrium constraints. We then use different regularization schemes for this class of problems and use an iterative solution procedure for solving series of regularized problems. In the case of success, these procedures result in a feasible solution of the original mixed-binary nonlinear problem. Since we rely on local nonlinear programming solvers the resulting method is fast and we further improve its reliability by additional algorithmic techniques. We show the strength of our method by an extensive computational study on 662 MINLPLib2 instances, where our methods are able to produce feasible solutions for 60% of all instances in at most 10 s.

关键词： mixed-integer nonlinear optimization MINLP MPEC Complementarity constraints Primal heuristic

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On a nonconvex MINLP formulation of the Euclidean Steiner tree problem in n-space: missing proofs

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optimization LETTERS 2020年第2期14卷 409-415页

作者： D'Ambrosio, Claudia Fampa, Marcia Lee, Jon Vigerske, Stefan Ecole Polytech LIX CNRS UMR7161 F-91128 Palaiseau France Univ Fed Rio de Janeiro Inst Matemat Rio De Janeiro RJ Brazil Univ Fed Rio de Janeiro COPPE Rio De Janeiro RJ Brazil Univ Michigan IOE Dept Ann Arbor MI 48109 USA ZIB Konrad Zuse Zentrum Informat Tech Berlin Berlin Germany

We supply proofs for a few key results concerning smoothing square roots and model strengthening for a mixed-integer nonlinear-optimization formulation of the the Euclidean Steiner tree problem.

关键词： Euclidean Steiner tree problem Smoothing Relaxation mixed-integer nonlinear optimization

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GLOBAL optimization OF mixed-integer ODE CONSTRAINED NETWORK PROBLEMS USING THE EXAMPLE OF STATIONARY GAS TRANSPORT

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SIAM JOURNAL ON optimization 2019年第4期29卷 2949-2985页

作者： Habeck, Oliver Pfetsch, Marc E. Ulbrich, Stefan Tech Univ Darmstadt Res Grp Optimizat Dept Math Darmstadt Germany

In this paper we propose a new approach for finding global solutions for a class of mixed-integer nonlinear optimization problems with ordinary differential equation (ODE) constraints on networks. Instead of using a discretize-then-optimize approach, we combine spatial and variable branching with appropriate discretizations of the differential equations to derive relaxations of the original problem. To construct the relaxations we derive sufficient conditions under which appropriate numerical discretization schemes yield lower and upper bounds on the ODE solutions. Moreover, we derive conditions that ensure the convexity or concavity of the obtained under- and overestimators. Thereby, we make use of the underlying network structure, where the solutions of the ODEs only need to be known at a finite number of points, that is, at the junctions of the network. This property enables us to adaptively refine the discretization and relaxation without introducing new variables in the mixed-integer optimization problem. The incorporation into a spatial branch-and-bound process allows us to compute global epsilon-optimal solutions or to decide infeasibility. We prove that this algorithm terminates finitely under some natural assumptions. We then show how this approach works for the example of stationary gas transport and provide some illustrative computational examples.

关键词： mixed-integer nonlinear optimization global optimization gas networks ODEs on graphs

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Optimal design of batch mass exchange networks with multipurpose exchange units

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COMPUTERS & CHEMICAL ENGINEERING 2016年 84卷 536-545页

作者： Zhou, Rui-Jie Li, Li-Juan Dong, Hong-Guang Stanford Univ Dept Elect Engn Stanford CA 94305 USA Rensselaer Polytech Inst Dept Chem & Biol Engn Troy NY 12180 USA Dalian Univ Technol Sch Chem Engn Dalian 116012 Peoples R China

A novel mathematical model for simultaneous optimization of batch mass exchange networks with multipurpose mass exchange units that can be shared by more than one match in different periods is presented in this work. It can be shown that both utility cost and capital investment can be reduced simultaneously with the use of multipurpose mass exchangers and mass storage tanks. Specifically, state-space superstructure that does not contain any structural simplification is proposed to capture the entire characteristics of the network configuration and a mixed-integer nonlinear optimization model is then formulated accordingly to generate the optimal batch operating policies and the corresponding flowsheet. Two examples are presented in this paper to demonstrate the validity and advantages of the proposed approach. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Batch process Mass exchange network Simultaneous optimization Multipurpose mass exchanger mixed-integer nonlinear optimization

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On the impact of running intersection inequalities for globally solving polynomial optimization problems

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MATHEMATICAL PROGRAMMING COMPUTATION 2020年第2期12卷 165-191页

作者： Del Pia, Alberto Khajavirad, Aida Sahinidis, Nikolaos, V Univ Wisconsin Dept Ind & Syst Engn Madison WI USA Univ Wisconsin Wisconsin Inst Discovery Madison WI USA Rutgers State Univ Rutgers Sch Business Dept Management Sci & Informat Syst New Brunswick NJ USA Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

We consider global optimization of nonconvex problems whose factorable reformulations contain a collection of multilinear equations of the form ze=f;e = \prod _{v \in e} {z_v}$$\end{document}, e is an element of E, where E denotes a set of subsets of cardinality at least two of a ground set. Important special cases include multilinear and polynomial optimization problems. The multilinear polytope is the convex hull of the set of binary points z satisfying the system of multilinear equations given above. Recently Del Pia and Khajavirad introduced running intersection inequalities, a family of facet-defining inequalities for the multilinear polytope. In this paper we address the separation problem for this class of inequalities. We first prove that separating flower inequalities, a subclass of running intersection inequalities, is NP-hard. Subsequently, for multilinear polytopes of fixed degree, we devise an efficient polynomial-time algorithm for separating running intersection inequalities and embed the proposed cutting-plane generation scheme at every node of the branch-and-reduce global solver BARON. To evaluate the effectiveness of the proposed method we consider two test sets: randomly generated multilinear and polynomial optimization problems of degree three and four, and computer vision instances from an image restoration problem Results show that running intersection cuts significantly improve the performance of BARON and lead to an average CPU time reduction of 50% for the random test set and of 63% for the image restoration test set.

关键词： Branch-and-cut Polynomial optimization Running-intersection inequalities Multilinear polytope Separation algorithm mixed-integer nonlinear optimization

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Transmission and generation investment in electricity markets: The effects of market splitting and network fee regimes

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2016年第2期254卷 493-509页

作者： Grimm, Veronika Martin, Alexander Schrnidt, Martin Weibelzahl, Martin Zoettl, Gregor Univ Erlangen Nurnberg Chair Econ Theory Lange Gasse 20 D-90403 Nurnberg Germany Univ Erlangen Nurnberg Discrete Optimizat Cauerstr 11 D-91058 Erlangen Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany Univ Erlangen Nurnberg Ind Econ & Energy Markets Lange Gasse 20 D-90403 Nurnberg Germany

We propose an equilibrium model that allows to analyze the long-run impact of the electricity market design on transmission line expansion by the regulator and investment in generation capacity by private firms in liberalized electricity markets. The model incorporates investment decisions of the transmission system operator and private firms in expectation of an energy-only market and cost-based redispatch. In different specifications we consider the cases of one vs. multiple price zones (market splitting) and analyze different approaches to recover network cost in particular lump sum, generation capacity based, and energy based fees. In order to compare the outcomes of our multilevel market model with a first best benchmark, we also solve the corresponding integrated planner problem. Using two test networks we illustrate that energy-only markets can lead to suboptimal locational decisions for generation capacity and thus imply excessive network expansion. Market splitting heals these problems only partially. These results are valid for all considered types of network tariffs, although investment slightly differs across those regimes. (C) 2016 The Authors. Published by Elsevier B.V.

关键词： Electricity market modeling mixed-integer nonlinear optimization Multilevel programming Network expansion Transmission management

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