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A generalized disjunctive programming model for the static bike sharing rebalancing problem with demand intervals

OPTIMIZATION AND ENGINEERING 2025年 1-33页

作者： Ikonen, Teemu J. Heljanko, Keijo Harjunkoski, Iiro Aalto Univ Dept Chem & Met Engn Kemistintie 1 Espoo 02150 Finland Univ Helsinki Dept Comp Sci Pietari Kalmin Katu 5 Helsinki 00560 Finland Univ Helsinki Helsinki Inst Informat Technol HIIT Pietari Kalmin Katu 5 Helsinki 00560 Finland Hitachi Energy Res Havellandstr 10-14 D-68309 Mannheim Germany

Solving a static bike sharing rebalancing problem requires finding the minimum-cost route for rebalancing vehicles, subject to meeting the demand at the bike sharing stations of the system. In this work, we study the variant of the problem where the demand is specified by intervals, which adds flexibility to the routing of the rebalancing vehicles. We propose a generalized disjunctive programming (GDP) model to represent the problem and its reformulation into a mixed-integer linear programming (MILP) model. We use demand splitting to duplicate stations that require multiple visits. The model is designed for single-vehicle routing but can be used jointly with a clustering approach proposed in the literature for multi-vehicle routing. The model can solve to optimality 86.8% of benchmark instances with 70 stations within two hours of computing time. On test cases derived from real process data, the model is more than two orders of magnitude faster than the reference model in the literature.

关键词： Routing Bike sharing Combinatorial optimization Inventory generalized disjunctive programming

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Extensions to generalized disjunctive programming: hierarchical structures and first-order logic

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OPTIMIZATION AND ENGINEERING 2024年第2期25卷 605-+页

作者： Perez, Hector D. Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

Optimization problems with discrete-continuous decisions are traditionally modeled in algebraic form via (non)linear mixed-integer programming. A more systematic approach to modeling such systems is to use generalized disjunctive programming (GDP), which extends the disjunctive programming paradigm proposed by Egon Balas to allow modeling systems from a logic-based level of abstraction that captures the fundamental rules governing such systems via algebraic constraints and logic. Although GDP provides a more general way of modeling systems, it warrants further generalization to encompass systems presenting a hierarchical structure. This work extends the GDP literature to address two major alternatives for modeling and solving systems with nested (hierarchical) disjunctions: explicit nested disjunctions and equivalent single-level disjunctions. We also provide theoretical proofs on the relaxation tightness of such alternatives, showing that explicitly modeling nested disjunctions is superior to the traditional approach discussed in literature for dealing with nested disjunctions.

关键词： generalized disjunctive programming Hierarchical systems Discrete-continuous optimization

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Convex mixed-integer nonlinear programs derived from generalized disjunctive programming using cones

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2024年第1期88卷 251-312页

作者： Neira, David E. Bernal Grossmann, Ignacio E. Purdue Univ Davidson Sch Chem Engn 480 Stadium Mall Dr W Lafayette IN 47907 USA Univ Space Res Assoc Res Inst Adv Comp Sci 425 3rd St SWSuite 950 Washington DC 20024 USA NASA Ames Res Ctr Quantum Artificial Intelligence Lab 5000 Forbes Ave Moffett Field CA 94035 USA Carnegie Mellon Univ Chem Engn Dept 5000 Forbes Ave Pittsburgh PA 15213 USA

We propose the formulation of convex generalized disjunctive programming (GDP) problems using conic inequalities leading to conic GDP problems. We then show the reformulation of conic GDPs into Mixed-Integer Conic programming (MICP) problems through both the big-M and hull reformulations. These reformulations have the advantage that they are representable using the same cones as the original conic GDP. In the case of the hull reformulation, they require no approximation of the perspective function. Moreover, the MICP problems derived can be solved by specialized conic solvers and offer a natural extended formulation amenable to both conic and gradient-based solvers. We present the closed form of several convex functions and their respective perspectives in conic sets, allowing users to formulate their conic GDP problems easily. We finally implement a large set of conic GDP examples and solve them via the scalar nonlinear and conic mixed-integer reformulations. These examples include applications from Process Systems Engineering, Machine learning, and randomly generated instances. Our results show that the conic structure can be exploited to solve these challenging MICP problems more efficiently. Our main contribution is providing the reformulations, examples, and computational results that support the claim that taking advantage of conic formulations of convex GDP instead of their nonlinear algebraic descriptions can lead to a more efficient solution to these problems.

关键词： Mixed-integer nonlinear programming Conic programming generalized disjunctive programming Perspective function

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Analysis and Optimization of Multistage Mixed Refrigerant Systems Using generalized disjunctive programming

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PROCESS INTEGRATION AND OPTIMIZATION FOR SUSTAINABILITY 2024年第2期8卷 439-454页

作者： Matovu, Fahad Mahadzir, Shuhaimi Rozali, Nor Erniza Mohammad Yoke Yi, Chiah Univ Teknol PETRONAS Dept Chem Engn Persiaran UTP Seri Iskandar 32610 Perak Malaysia Univ Teknol PETRONAS Inst Autonomous Syst Ctr Syst Engn Seri Iskandar Perak Malaysia

The synthesis and optimization of multistage mixed refrigerant systems is a highly challenging and complex problem. It is computationally expensive, highly non-linear, and highly sensitive to changes in composition of refrigerant mixture. Attempts to build a superstructure optimization model using mixed-integer non-linear programming (MINLP) may lead to computational difficulty arising from non-linear and non-convex functions. In this paper, a novel generalized disjunctive programming model formulation is proposed based on a multistage mixed refrigerant system. The model is developed based on mass, energy, phase equilibria, and thermodynamic relations. The main aim is to minimize the required shaft work of the system. The created model formulation is quite systematic and maintains the problem's logical structure. As a result, advanced solution methods such as the logic-based branch and bound may be used to solve the models. This ensures that the solution is sought in reduced space contrary to the full scale for the case of MINLP models. The proposed model is applied on the single mixed refrigerant (SMR) process, and shaft work results obtained are better than those in two referenced literature cases by atmost 25.6% and 13.6%. In addition, it is also applied on a two-stage mixed refrigerant (MR) system, and all results validated by simulation in Aspen Hysys. Model and Hysys results compare with differences of not more than 5.9% ad 1.81% for the SMR and two stage cases respectively. A shaft work consumption comparison of the SMR and two stage yields 24.92 MW versus 23.71 MW, a reduction of 4.9% with introduction of an additional stage. For Aspen Hysys results, a similar comparison yields 26.15 MW versus 24.138 MW, a reduction of 7.7%. The results demonstrates the effectiveness and efficiency of the formulation.

关键词： Multistage mixed refrigerant Optimization generalized disjunctive programming Logic-based algorithms

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Optimization of triple-pressure combined-cycle power plants by generalized disjunctive programming and extrinsic functions

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COMPUTERS & CHEMICAL ENGINEERING 2021年 146卷 107190-107190页

作者： Manassaldi, Juan I. Mussati, Miguel C. Scenna, Nicolas J. Mussati, Sergio F. Univ Tecnol Nacl Fac Reg Rosario CAIMI Ctr Aplicac Informat & Modelado Ingn Zeballos 1346S2000BQA Rosario Argentina INGAR Inst Desarrollo & Diseno CONICET UTN Avellaneda 3657S3002GJC Santa Fe Argentina

A new mathematical framework for optimal synthesis, design, and operation of triple-pressure steam reheat combined-cycle power plants (CCPP) is presented. A superstructure-based representation of the process, which embeds a large number of candidate configurations, is first proposed. Then, a generalized disjunctive programming (GDP) mathematical model is derived from it. Series, parallel, and combined series-parallel arrangements of heat exchangers are simultaneously embedded. Extrinsic functions executed outside GAMS from dynamic-link libraries (DLL) are used to estimate the thermodynamic properties of the working fluids. As a main result, improved process configurations with respect to two reported reference cases were found. The total heat transfer areas calculated in this work are by around 15% and 26% lower than those corresponding to the reference cases. This paper contributes to the literature in two ways: (i) with a disjunctive optimization model of natural gas CCPP and the corresponding solution strategy, and (ii) with improved HRSG configurations. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： generalized disjunctive programming Extrinsic functions Three-pressure reheat combined-cycle power plant Heat recovery steam generator HRSG GAMS

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Optimal design of ethylene and propylene coproduction plants with generalized disjunctive programming and state equipment network models

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COMPUTERS & CHEMICAL ENGINEERING 2021年 149卷 107295-107295页

作者： Pedrozo, H. A. Rodriguez Reartes, S. B. Vecchietti, A. R. Diaz, M. S. Grossmann, I. E. Planta Piloto Ingn Quim PLAPIQUI CONICET UNS Camino Carrindanga Km 7 Bahia Blanca Buenos Aires Argentina Univ Nacl UNS Dept Ingn Quim Bahia Blanca Buenos Aires Argentina Inst Design & Dev INGAR CONICET UTN Avellaneda 3657 Santa Fe Argentina Carnegie Mellon Univ Dept Chem Engn 5000 Forbes Ave Pittsburgh PA 15213 USA

In this work, we propose a superstructure optimization approach for the optimal design of an ethylene and propylene coproduction plant. We formulate a superstructure that embeds ethane and propane steam cracking technologies, propane dehydrogenation and olefin metathesis processes. We represent the superstructure with a generalized disjunctive programming model, and solve the problem through a custom implementation of the Logic-based Outer Approximation algorithm in GAMS. We propose a state-equipment-network representation to model potential distillation trains, as well as alternative acetylene reactor configurations. Rigorous models are formulated for distillation columns, compressors, turboexpanders, vessels and several process equipment units. The objective function is to maximize the net present value. We analyze four international price scenarios for raw material and utility costs, while considering global ethylene and propylene prices. We obtain the optimal scheme for each case. Numerical results show that the combination of ethane steam cracking, olefin metathesis and ethylene dimerization is the most profitable configuration under low ethane price scenarios, whereas the combination of ethane and propane steam cracking together with propane dehydrogenation is the optimal solution when the propane price is on the order of ethane price. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Olefin production Superstructure optimization Propane dehydrogenation Metathesis Steam cracking State equipment network representation Logic-based outer approximation algorithm generalized disjunctive programming

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The design of optimal mixtures from atom groups using generalized disjunctive programming

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COMPUTERS & CHEMICAL ENGINEERING 2018年 116卷 401-421页

作者： Jonuzaj, Suela Gupta, Aparana Adjiman, Claire S. Imperial Coll London Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England Indian Inst Technol Delhi Dept Chem Engn Delhi India

A comprehensive computer-aided mixture/blend design methodology for formulating a general mixture design problem where the number, identity and composition of mixture constituents are optimized simultaneously is presented in this work. Within this approach, generalized disjunctive programming (GDP) is employed to model the discrete decisions (number and identities of mixture ingredients) in the problems. The identities of the components are determined by designing molecules from UNIFAC groups. The sequential design of pure compounds and blends, and the arbitrary pre-selection of possible mixture ingredients can thus be avoided, making it possible to consider large design spaces with a broad variety of molecules and mixtures. The proposed methodology is first applied to the design of solvents and solvent mixtures for maximising the solubility of ibuprofen, often sought in crystallization processes;next, antisolvents and antisolvent mixtures are generated for minimising the solubility of the drug in drowning out crystallization;and finally, solvent and solvent mixtures are designed for liquid-liquid extraction. The GDP problems are converted into mixed-integer form using the big-M approach. Integer cuts are included in the general models leading to lists of optimal solutions which often contain a combination of pure and mixed solvents. (C) 2018 The Authors. Published by Elsevier Ltd.

关键词： Mixture design generalized disjunctive programming UNIFAC groups Crystallization Antisolvent Liquid-liquid extraction

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generalized disjunctive programming model for the multi-period production planning optimization: An application in a polyurethane foam manufacturing plant

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COMPUTERS & CHEMICAL ENGINEERING 2017年 103卷 69-80页

作者： Analia Rodriguez, Maria Marcelo Montagna, Jorge Vecchietti, Aldo Corsano, Gabriela Consejo Nacl Invest Cient & Tecn UNC PLAPIQUI IDTQ Av Velez Sarsfield 1611Ciudad UnivX5016GCA Cordoba Argentina Consejo Nacl Invest Cient & Tecn UTN INGAR Avellaneda 3657 RA-3000 Santa Fe Argentina

A generalized disjunctive programming (GDP) model for the optimal multi-period production planning and stock management is proposed in this work. The formulation is applied to a polyurethane foam manufacturing plant that comprises three stages: a first step that produces pieces with certain characteristics, a second process that involves the location of these pieces in a limited area and a third stage where pieces are stored in dedicated spaces. This article shows the GDP capabilities to provide a qualitative framework for representing the problem issues and their connections in a natural way, especially in a context where decisions integration is required. Due to the multi-period nature of the planning problem, a rolling horizon approach is suitable for solving it in reasonable computing time. It serves as a tool for analyzing the trade-offs among the different costs. Through the examples, the capabilities of the formulation and the proposed resolution method are highlighted. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： generalized disjunctive programming Production planning Stock Optimization Rolling horizon Mattress industry

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Designing optimal mixtures using generalized disjunctive programming: Hull relaxations

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CHEMICAL ENGINEERING SCIENCE 2017年 159卷 106-130页

作者： Jonuzaj, Suela Adjiman, Claire S. Imperial Coll London Ctr Proc Syst Engn Dept Chem Engn London SW7 2AZ England

A general modeling framework for mixture design problems, which integrates generalized disjunctive programming (GDP) into the Computer-Aided Mixture/blend Design (CAM(b)D) framework, was recently proposed (S. Jonuzaj, P.T. Akula, P.-M. Kleniati, C.S. Adjiman, 2016. The formulation of optimal mixtures with generalized disjunctive programming: A solvent design case study. AIChE Journal 62, 1616-1633). In this paper we derive Hull Relaxations (HRs) of GDP mixture design problems as an alternative to the big-M (BM) approach presented in this earlier work. We show that in restricted mixture design problems, where the number of components is fixed and their identities and compositions are optimised, BM and HR formulations are identical. For general mixture design problems, where the optimal number of mixture components is also determined, a generic approach is employed to enable the derivation and solution of the HR formulation for problems involving functions that are not defined at zero (e.g., logarithms). The design methodology is applied successfully to two solvent design case studies: the maximization of the solubility of a drug and the separation of acetic acid from water in a liquid-liquid extraction process. Promising solvent mixtures are identified in both case studies. The HR and BM approaches are found to be effective for the formulation and solution of mixture design problems, especially via the general design problem.

关键词： Mixture design generalized disjunctive programming Hull Reformulation Solubility Liquid-liquid extraction

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Process simulator-based optimization of biorefinery downstream processes under the generalized disjunctive programming framework

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COMPUTERS & CHEMICAL ENGINEERING 2016年 88卷 73-85页

作者： Corbetta, Michele Grossmann, Ignacio E. Manenti, Flavio Politecn Milan Dipartimento Chim Mat & Ingn Chim Giulio Natta Piazza Leonardo da Vinci 32 I-20133 Milan Italy Carnegie Mellon Univ Dept Chem Engn 5000 Forbes Ave Pittsburgh PA 15213 USA

Downstream processing of biofuels and bio-based chemicals represents a challenging problem for process synthesis and optimization, due to the intrinsic nonideal thermodynamics of the liquid mixtures derived from the (bio) chemical conversion of biomass. In this work, we propose a new interface between the process simulator PRO/II (SimSci, Schneider-Electric) and the optimization environment of GAMS for the structural and parameter optimization of this type of flowsheets with rigorous and detailed models. The optimization problem is formulated within the generalized disjunctive programming (GDP) framework and the solution of the reformulated MINLP problem is approached with a decomposition strategy based on the Outer-Approximation algorithm, where NLP subproblems are solved with the derivative free optimizer belonging to the BzzMath library, and MILP master problems are solved with CPLEX/GAMS. Several validation examples are proposed spanning from the economic optimization of two different distillation columns, the dewatering task of diluted bio-mixtures, up to the distillation sequencing with simultaneous mixed-integer design of each distillation column for a quaternary mixture in the presence of azeotropes. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： generalized disjunctive programming MINLP Downstream Process simulator Azeotropes Derivative free optimization

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