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Review of Mixed-Integer Nonlinear and generalized disjunctive programming Methods

CHEMIE INGENIEUR TECHNIK 2014年第7期86卷 991-1012页

作者： Trespalacios, Francisco Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

This work presents a review of the main deterministic mixed-integer nonlinear programming (MINLP) solution methods for problems with convex and nonconvex functions. An overview for deriving MINLP formulations through generalized disjunctive programming (GDP), which is an alternative higher-level representation of MINLP problems, is also presented. A review of solution methods for GDP problems is provided. Some relevant applications of MINLP and GDP in process systems engineering are described in this work.

关键词： generalized disjunctive programming Mixed-integer nonlinear programming Nonlinear programming Optimization

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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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ε-OA for the solution of bi-objective generalized disjunctive programming problems in the synthesis of nonlinear process networks

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COMPUTERS & CHEMICAL ENGINEERING 2015年 72卷 199-209页

作者： Fattahi, Ali Turkay, Metin Koc Univ Dept Ind Engn TR-34450 Istanbul Turkey

There has been an increasing interest in multicriteria optimization (MCO) of nonlinear process network problems in recent years. Several mathematical models have been developed and solved using MCO methodologies including e-constraint, weighted sum, and minimum distance. In this paper, we investigate the bi-objective nonlinear network synthesis problem and propose an effective algorithm, epsilon-OA, based on augmented epsilon-constraint and logic-based outer approximation (OA). We provide theoretical characterization of the proposed algorithm and show that the solutions generated are efficient. We illustrate the effectiveness of our novel algorithm on two benchmark problems. The epsilon-OA is compared to the straightforward use of OA with augmented epsilon-constraint algorithm (epsilon-con + OA), the augmented epsilon-constraint without OA (E-MINLP), and the traditional epsilon-constraint (T-epsilon-con). Based on the results, our novel algorithm is very effective in solving the bi-objective generalized disjunctive programming problems in the synthesis of process networks. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： generalized disjunctive programming Multiple criteria optimization Outer approximation Mixed integer nonlinear programming epsilon-Constraint method

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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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Retrofit of multiproduct batch plants through generalized disjunctive programming

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MATHEMATICAL AND COMPUTER MODELLING 2003年第5-6期38卷 465-479页

作者： Montagna, JM Vecchietti, AR UTN Fac Reg Santa Fe Inst Desarrollo & Diseno INGAR RA-3000 Santa Fe Argentina

The retrofit problem for multiproduct batch plants deals with the modification of the original structure of the plant to meet new production conditions such as the introduction of Dew products, a new supply pattern, etc. For this problem, a disjunctive model is presented, which takes into consideration every usual alternative about the configuration of units and storage tanks. A disjunction is generated for that purpose. The selection of one of those alternatives sets up all the corresponding constraints, which are: operation time, unit size and cost, etc. Finally, the performance of this approach is analyzed through the resolution of a set of examples. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： generalized disjunctive programming MINLP retrofit multiproduct batch plants

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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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Logic-Based Discrete-Steepest Descent: A solution method for process synthesis generalized disjunctive Programs

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COMPUTERS & CHEMICAL ENGINEERING 2025年 195卷

作者： Ovalle, Daniel Linan, David A. Lee, Albert Gomez, Jorge M. Ricardez-Sandoval, Luis Grossmann, Ignacio E. Neira, David E. Bernal Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA Univ Andes Dept Chem & Food Engn Bogota 1100123 Colombia Univ Waterloo Dept Chem Engn Waterloo ON N2L 3G1 Canada Purdue Univ Davidson Sch Chem Engn W Lafayette IN 47907 USA NASA Ames Res Ctr Quantum Artificial Intelligence Lab Mountain View CA 94035 USA Univ Space Res Assoc Res Inst Adv Comp Sci Mountain View CA 94043 USA

Optimization of chemical processes is challenging due to nonlinearities arising from chemical principles and discrete design decisions. The optimal synthesis and design of chemical processes can be posed as a generalized disjunctive programming (GDP) problem. While reformulating GDP problems as Mixed-Integer Nonlinear programming (MINLP) problems is common, specialized algorithms for GDP remain scarce. This study introduces the Logic-Based Discrete-Steepest Descent Algorithm (LD-SDA) as a solution method for GDP problems involving ordered Boolean variables. LD-SDA transforms these variables into external integer decisions and uses a two-level decomposition: the upper-level sets external configurations, and the lower- level solves the remaining variables, efficiently exploiting the GDP structure. In the case studies presented in this work, including batch processing, reactor superstructures, and distillation columns, LD-SDA consistently outperforms conventional GDP and MINLP solvers, especially as the problem size grows. LD-SDA also proves superior when solving challenging problems where other solvers encounter difficulties finding optimal solutions.

关键词： Superstructure optimization Optimal process design generalized disjunctive programming MINLP Process intensification

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Maritime inventory routing with speed optimization: A MIQCP formulation for a tanker fleet servicing FPSO units

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COMPUTERS & CHEMICAL ENGINEERING 2025年 192卷

作者： Castro, Pedro M. Univ Lisbon Dept Engn Quim CERENA Inst Super Tecn P-1049001 Lisbon Portugal

This paper presents a continuous-time formulation for the management of deep-sea floating production storage and offloading (FPSO) units, which process and store crude oil from nearby oil platforms while waiting for a shuttle tanker to arrive and collect it. A heterogeneous fleet of tanker vessels travelling between the FPSO units and a port refinery is available, with the optimization deciding on the number and type of vessels to use, their route and travelling speed. The goal is to achieve an environmentally friendly solution featuring vessels travelling at lower speeds to minimize fuel consumption (a quadratic function of speed), which may require renting additional shuttle tankers to maintain production. The resulting mixed-integer quadratically constrained problems (MIQCP) can be solved by GUROBI, but not to global optimality, whereas a mixed-integer linear programming (MILP) relaxation that underestimates the total operating cost can tackle moderate problem sizes (5 FPSOs and 4 shuttle tankers).

关键词： Crude oil logistics Green scheduling generalized disjunctive programming Multiple time grids

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