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Global optimization of a MINLP process synthesis model for thermochemical based conversion of hybrid coal, biomass, and natural gas to liquid fuels

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COMPUTERS & CHEMICAL ENGINEERING 2012年 42卷 64-86页

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

A global optimization framework is proposed for a thermochemical based process superstructure to produce a novel hybrid energy refinery which will convert carbon-based feedstocks (i.e., coal, biomass, and natural gas) to liquid transportation fuels. The mathematical model for process synthesis includes simultaneous heat, power, and water integration and is formulated as a mixed-integer nonlinear optimization (MINLP) problem with nonconvex functions. The MINLP model is large-scale and includes 15,439 continuous variables, 30 binary variables, 15,406 equality constraints, 230 inequality constraints, and 335 nonconvex terms. The nonconvex terms arise from 274 bilinear terms, 1 quadrilinear term, and 60 concave cost functions. The proposed framework utilizes piecewise linear underestimators for the nonconvex terms to provide tight relaxations when calculating the lower bound. The bilinear terms are relaxed using a partitioning scheme that depends logarithmically on the number of binary variables, while the concave functions are relaxed using a linear partitioning scheme. The framework was tested on twelve case studies featuring three different plant capacities and four different feedstock-carbon conversion percentages and is able to solve each study to within a 3.22-8.56% optimality gap after 100 CPU hours. For 50% feedstock carbon conversion, the proposed global optimization framework shows that the break-even oil prices for liquid fuels production are $61.36/bbl for the small case study, $60.45/bbl for the medium case study, and $55.43/bbl for the large case study, while the corresponding efficiencies are 73.9%, 70.5%, and 70.1%, respectively. (c) 2012 Elsevier Ltd. All rights reserved.

关键词： Global optimization Piecewise linear underestimators Heat, power and water integration Hybrid energy systems mixed-integer nonlinear optimization Fischer-Tropsch

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Global optimization for the multilevel European gas market system with nonlinear flow models on trees

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JOURNAL OF GLOBAL optimization 2022年第3期82卷 627-653页

作者： Schewe, Lars Schmidt, Martin Thuerauf, Johannes Univ Edinburgh Sch Math James Clerk Maxwell BldgPeter Guthrie Tait Rd Edinburgh EH9 3FD Midlothian Scotland Trier Univ Dept Math Univ Ring 15 D-54296 Trier Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany

The European gas market is implemented as an entry-exit system, which aims to decouple transport and trading of gas. It has been modeled in the literature as a multilevel problem, which contains a nonlinear flow model of gas physics. Besides the multilevel structure and the nonlinear flow model, the computation of so-called technical capacities is another major challenge. These lead to nonlinear adjustable robust constraints that are computationally intractable in general. We provide techniques to equivalently reformulate these nonlinear adjustable constraints as finitely many convex constraints including integer variables in the case that the underlying network is tree-shaped. We further derive additional combinatorial constraints that significantly speed up the solution process. Using our results, we can recast the multilevel model as a single-level nonconvex mixed-integer nonlinear problem, which we then solve on a real-world network, namely the Greek gas network, to global optimality. Overall, this is the first time that the considered multilevel entry-exit system can be solved for a real-world sized network and a nonlinear flow model.

关键词： European entry-exit gas market Multilevel optimization Robust optimization mixed-integer nonlinear optimization nonlinear flows

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Process planning in a fuzzy environment

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1997年第1期100卷 142-169页

作者： Liu, ML Sahinidis, NV UNIV ILLINOIS DEPT MECH & IND ENGN URBANA IL 61801 USA

mixed-integer optimization models for chemical process planning typically assume that model parameters can be accurately predicted. As precise forecasts are difficult to obtain, process planning usually involves uncertainty and ambiguity in the data. This paper presents an application of fuzzy programming to process planning, The forecast parameters are assumed to be fuzzy with a linear or triangular membership function. The process planning problem is then formulated in terms of decision making in a fuzzy environment with fuzzy constraints and fuzzy net present value goals. The model is transformed to a deterministic mixed-integer linear program or mixed-integer nonlinear program depending on the type of uncertainty involved in the problem. For the nonlinear case, a global optimization algorithm is developed for its solution. This algorithm is applicable to general possibilistic programs and can be used as an alternative to the commonly used bisection method. Illustrative examples and computational results for a petrochemical complex with 38 processes and 24 products illustrate the applicability of the developed models and algorithms. (C) 1997 Elsevier Science B.V.

关键词： capacity expansion chemical processes fuzzy sets mixed-integer nonlinear optimization

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Global exact optimization for covering a rectangle with 6 circles

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JOURNAL OF GLOBAL optimization 2022年第1期83卷 163-185页

作者： Cafieri, Sonia Hansen, Pierre Messine, Frederic Univ Toulouse ENAC Toulouse France HEC Montreal GERAD Montreal PQ Canada Univ Toulouse ENSEEIHT INPT LAPLACE Toulouse France

We address the problem of covering a rectangle with six identical circles, whose radius is to be minimized. We focus on open cases from Melissen and Schuur (Discrete Appl Math 99:149-156, 2000). Depending on the rectangle side lengths, different configurations of the circles, corresponding to the different ways they are placed, yield the optimal covering. We prove the optimality of the two configurations corresponding to open cases. For the first one, we propose a mathematical mixed-integer nonlinear optimization formulation, that allows one to compute global optimal solutions. For the second one, we provide an analytical expression of the optimal radius as a function of one of the rectangle side lengths. All open cases are thus closed for the optimal covering of a rectangle with six circles.

关键词： Covering Global optimization mixed-integer nonlinear optimization Circle configuration Discrete geometry

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An Intelligent Scheduling System and Hybrid optimization Algorithm for Ship Locks of the Three Gorges Hub on the Yangtze River

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2024年 208卷

作者： Zhang, Hao Ke, Jiangcen Wuhan Univ Technol Sch Management Wuhan Peoples R China Wuhan Univ Technol Sch Transportat & Logist Engn Wuhan Peoples R China

The ship lock system of the Three Gorges Hub(TGH) stands out as the most intricate navigation system for ships passing through dams, which is composed of the the world's largest ship lock and ship lift. It operates with features like multi-dam configurations, multi-chambers, multi-operation modes and batch processing. This paper addresses the complex challenge of optimizing the lock schedule, ship entry timings, and ship placements within the lock chamber. By analyzing navigational rules, operational characteristics, and existing problems of TGH, this research introduces an intelligent scheduling system framework. With the incorporation of multiple objectives and constraints, a mixed-integer nonlinear programming(MINLP) model is formulated. Subsequently, a hybrid intelligent algorithm based on simulated annealing and heuristic search is constructed to achieve the optimization of the lock schedule. The algorithm efficacy is validated using the real-world data from TGH.

关键词： Three gorges hub Locks scheduling system mixed-integer nonlinear optimization Hybrid intelligent approach

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A Successive Linear Relaxation Method for MINLPs with Multivariate Lipschitz Continuous nonlinearities

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JOURNAL OF optimization THEORY AND APPLICATIONS 2023年第3期198卷 1077-1117页

作者： Gruebel, Julia Krug, Richard Schmidt, Martin Wollner, Winnifried Friedrich Alexander Univ Erlangen Nurnberg FAU Lange Gasse 20 D-90403 Nurnberg Germany Energie Campus Nurnberg Further Str 250 D-90429 Nurnberg Germany Friedrich Alexander Univ Erlangen Nurnberg FAU Dept Data Sci Cauerstr 11 D-91058 Erlangen Germany Trier Univ Dept Math Univ Ring 15 D-54296 Trier Germany Univ Hamburg Fachbereich Math MIN Fakulat Bundesstr 55 D-20146 Hamburg Germany

We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate them and that we know their global Lipschitz constants. The algorithm is a successive linear relaxation method in which we alternate between solving a master problem, which is a mixed-integer linear relaxation of the original problem, and a subproblem, which is designed to tighten the linear relaxation of the next master problem by using the Lipschitz information about the respective functions. By doing so, we follow the ideas of Schmidt, Sirvent, and Wollner (Math Program 178(1):449-483 (2019) and Optim Lett 16(5):1355-1372 (2022)) and improve the tackling of multivariate constraints. Although multivariate nonlinearities obviously increase modeling capabilities, their incorporation also significantly increases the computational burden of the proposed algorithm. We prove the correctness of our method and also derive a worst-case iteration bound. Finally, we show the generality of the addressed problem class and the proposed method by illustrating that both bilevel optimization problems with nonconvex and quadratic lower levels as well as nonlinear and mixed-integer models of gas transport can be tackled by our method. We provide the necessary theory for both applications and briefly illustrate the outcomes of the new method when applied to these two problems.

关键词： mixed-integer nonlinear optimization Global optimization Lipschitz optimization Bilevel optimization Gas networks

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Algorithmic and modeling insights via volumetric comparison of polyhedral relaxations

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MATHEMATICAL PROGRAMMING 2018年第1期170卷 121-140页

作者： Lee, Jon Skipper, Daphne Speakman, Emily Univ Michigan Dept IOE Ann Arbor MI 48109 USA US Naval Acad Dept Math Annapolis MD 21402 USA Otto von Guericke Univ Inst Math Optimizat Magdeburg Germany

This is mostly a survey on some mathematical results concerning volumes of polytopes of interest in non-convex optimization. Our motivation is in geometrically comparing relaxations in the context of mixed-integer linear and nonlinear optimization, with the goal of gaining algorithmic and modeling insights. We consider relaxations of: fixed-charge formulations, vertex packing polytopes, boolean-quadric polytopes, and relaxations of graphs of monomials on box domains. Besides surveying the area, we do give a few new results, and we provide many directions for further work.

关键词： Polytope Volume Global optimization mixed-integer nonlinear optimization Fixed charge Facility location Vertex packing Boolean quadric Monomial Spatial branch-and-bound

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Simultaneous process synthesis, heat, power, and water integration of thermochemical hybrid biomass, coal, and natural gas facilities

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COMPUTERS & CHEMICAL ENGINEERING 2012年 37卷 297-327页

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

A comprehensive wastewater network is introduced into a thermochemical based process superstructure that will convert biomass, coal, and natural gas to liquid (CBGTL) transportation fuels. The mixed-integer nonlinear optimization (MINLP) model includes simultaneous heat, power, and water integration that utilizes heat engines to recover electricity from waste heat and several treatment units to process and recycle wastewater. A total of 108 case studies are analyzed which consist of combinations of six coal feedstocks, three biomass feedstocks, three plant capacities, and two process superstructures. This study discusses important process topological differences between the case studies and illustrates each component of the process synthesis framework using the two medium-sized capacity case studies that have low-volatile bituminous coal and biomass feedstocks. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Process synthesis, heat, power and water integration Hybrid energy systems mixed-integer nonlinear optimization Fischer-Tropsch Biofuels

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Identifying Fixations in Gaze Data via Inner Density and optimization

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INFORMS JOURNAL ON COMPUTING 2019年第3期31卷 459-476页

作者： Trapp, Andrew C. Liu, Wen Djamasbi, Soussan Worcester Polytech Inst Robert A Foisie Business Sch Worcester MA 01609 USA Worcester Polytech Inst Data Sci Program Worcester MA 01609 USA

Eye tracking is an increasingly common technology with a variety of practical uses. Eye-tracking data, or gaze data, can be categorized into two main events: fixations represent focused eye movement, indicative of awareness and attention, whereas saccades are higher-velocity movements that occur between fixation events. Common methods to identify fixations in gaze data can lack sensitivity to peripheral points and may misrepresent positional and durational properties of fixations. To address these shortcomings, we introduce the notion of inner density for fixation identification, which concerns both the duration of the fixation and the proximity of its constituent gaze points. Moreover, we demonstrate how to identify fixations in a sequence of gaze data by optimizing for inner density. After decomposing the clustering of a temporal gaze data sequence into successive regions (chunks), we use nonlinear and linear 0-1 optimization formulations to identify the densest fixations within a given data chunk. Our approach is parametrized by a unique constant that adjusts the degree of desired density, allowing decision makers to have fine-tuned control over density during the process. Computational experiments on real data sets demonstrate the efficiency of our approach and its effectiveness in identifying fixations with greater density than existing methods, thereby enabling the refinement of key gaze metrics such as fixation duration and fixation center.

关键词： eye-tracking gaze data fixation identification fixation inner density mixed-integer nonlinear optimization

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Complexity of branch-and-bound and cutting planes in mixed-integer optimization

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MATHEMATICAL PROGRAMMING 2023年第1期198卷 787-810页

作者： Basu, Amitabh Conforti, Michele Di Summa, Marco Jiang, Hongyi Johns Hopkins Univ Dept Appl Math & Stat Baltimore MD 21218 USA Univ Padua Dipartimento Matemat Tullio Levi Civita Padua Italy

We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of disjunctions. We extend a result of Dash (International Conference on integer Programming and Combinatorial optimization (IPCO), pp. 145-160, 2002) to the nonlinear setting which shows that for convex 0/1 problems, CP does at least as well as BB, with variable disjunctions. We sharpen this by giving instances of the stable set problem where we can provably establish that CP does exponentially better than BB. We further show that if one moves away from 0/1 sets, this advantage of CP over BB disappears;there are examples where BB finishes in O(1) time, but CP takes infinitely long to prove optimality, and exponentially long to get to arbitrarily close to the optimal value (for variable disjunctions). We next show that if the dimension is considered a fixed constant, then the situation reverses and BB does at least as well as CP (up to a polynomial blow up factor), for quite general families of disjunctions. This is also complemented by examples where this gap is exponential (in the size of the input data).

关键词： Complexity bounds Branch-and-bound Cutting planes mixed-integer nonlinear optimization

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