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Advances to modeling and solving infinite-dimensional optimization problems in ***

DIGITAL CHEMICAL ENGINEERING 2025年 15卷

作者： Gondosiswanto, Evelyn Pulsipher, Joshua L. Univ Waterloo Dept Chem Engn 200 Univ Ave W Waterloo ON N2L 3G1 Canada

This paper details two extensions for the unifying abstraction behind ***: infinite-dimensional generalized disjunctive programming (InfiniteGDP) and GPU-compatible direct transcription solution techniques with an abstraction called InfiniteSIMD-NLP. *** is a Julia package that provides an efficient framework for formulating and solving a wide range of infinite-dimensional optimization (InfiniteOpt) problems. The InfiniteGDP abstraction builds upon traditional GDP techniques to enable intuitive modeling of discrete events and complex logic over continuous domains (e.g., position, time, and/or uncertainty);this abstraction is implemented in ***. Moreover, the InfiniteSIMDNLP abstraction, implemented in ***, exploits the recurrent structure of transcribed InfiniteOpt problems to efficiently discretize, differentiate, and solve such problems on high performance CPU and GPU architectures. We use a diverse set of case studies in dynamic, PDE-constrained, and stochastic optimization to demonstrate the relative merits of these abstraction extensions. The results demonstrate the utility of the InfiniteGDP abstraction to model continuous space-time switching constraints and how the InfiniteSIMD-NLP abstraction is able to accelerate the solution of InfiniteOpt problems by one to two orders-of-magnitude relative to existing state-of-the-art approaches.

关键词： Infinite-dimensional optimization generalized disjunctive programming Dynamic optimization PDE-constrained optimization Stochastic optimization

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A Benders decomposition framework for the optimization of disjunctive superstructures with ordered discrete decisions

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AICHE JOURNAL 2023年第5期69卷 e18008-e18008页

作者： Linan, David A. Ricardez-Sandoval, Luis A. Univ Waterloo Dept Chem Engn Waterloo ON N2L 3G1 Canada

This study introduces the logic-based discrete-Benders decomposition (LD-BD) for generalized disjunctive programming (GDP) superstructure problems with ordered Boolean variables. The key idea is to obtain Benders cuts that use neighborhood information of a reformulated version of Boolean variables. These Benders cuts are iteratively refined, which guarantees convergence to a local optimum. A mathematical case study, the optimization of a network with Continuous Stirred-Tank Reactors (CSTRs) in series, and a large-scale problem involving the design of a distillation column are considered to demonstrate the features of LD-BD. The results from these case studies have shown that the LD-BD method exhibited good performance by finding attractive locally optimal solutions relative to existing logic-based solvers for GDP problems. Based on these tests, the LD-BD method is a promising strategy to solve optimal synthesis problems with ordered discrete decisions emerging in chemical engineering applications.

关键词： external variables generalized disjunctive programming logic-based Benders decomposition optimization superstructure

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Integration of different models in the design of chemical processes: Application to the design of a power plant

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APPLIED ENERGY 2014年 124卷 256-273页

作者： Caballero, Jose A. Navarro, Miguel A. Ruiz-Femenia, Ruben Grossmann, Ignacio E. Univ Alicante Dept Chem Engn E-03080 Alicante Spain Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the 'best available model'. However, in practice, these models are usually little more than a black box with a rigid input output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Process synthesis generalized disjunctive programming Utility systems Modular optimization Kriging

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Algorithmic Approach for Improved Mixed-Integer Reformulations of Convex generalized disjunctive Programs

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INFORMS JOURNAL ON COMPUTING 2015年第1期27卷 59-74页

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

In this work, we propose an algorithmic approach to improve mixed-integer models that are originally formulated as convex generalized disjunctive programs (GDPs). The algorithm seeks to obtain an improved continuous relaxation of the mixed-integer linear and mixed-integer nonlinear programming (MILP/MINLP) model reformulation of the GDP while limiting the growth in the problem size. There are three main stages that form the basis of the algorithm. The first one is a presolve, consequence of the logic nature of GDP, which allows us to reduce the problem size, find good relaxation bounds, and identify properties that help us determine where to apply a basic step. The second stage is the iterative application of basic steps, selecting where to apply them and monitoring the improvement of the formulation. Finally, we use a hybrid reformulation of GDP that seeks to exploit both of the advantages attributed to the two common GDP-to-MILP/MINLP transformations, the Big-M, and the Hull reformulation. We illustrate the application of this algorithm with several examples. The results show the improvement in the problem formulations by generating models with improved relaxed solutions and relatively small growth of continuous variables and constraints. The algorithm generally leads to reduction in the solution times.

关键词： generalized disjunctive programming mixed-integer nonlinear programming

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Rigorous design of reaction-separation processes using disjunctive programming models

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COMPUTERS & CHEMICAL ENGINEERING 2018年 111卷 16-26页

作者： Zhang, Xiang Song, Zhen Zhou, Teng Max Planck Inst Dynam Complex Tech Syst Proc Syst Engn Sandtorstr 1 D-39106 Magdeburg Germany Hong Kong Univ Sci & Technol Dept Chem & Biol Engn Hong Kong Peoples R China

A systematic and efficient method for the rigorous design of complex chemical processes is significant in the chemical industry. In this paper, a superstructure-based optimization approach for the rigorous and simultaneous design of reaction and separation processes using generalized disjunctive programming (GDP) models is presented. In the reactor network, disjunctions for conditional reactors are introduced where the balance and reaction kinetic equations are applied only if the reactor is selected. Based on the proposed reactor disjunctions, two different reactor superstructures are developed and employed. In addition, the GDP representation of distillation columns is used to model the separation network. The reliability and efficiency of the proposed optimization method are demonstrated on two case studies, i.e., one cyclohexane oxidation process and one benzene chlorination process. The flowsheet structure and process-unit operating conditions are simultaneously optimized to minimize the total annual cost of the processes. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Reaction-separation process design Process optimization generalized disjunctive programming Cyclohexane oxidation Benzene chlorination

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Optimization of water distribution networks using a deterministic approach

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ENGINEERING OPTIMIZATION 2021年第1期53卷 107-124页

作者： Cassiolato, Gustavo Carvalho, Esdras P. Caballero, Jose A. Ravagnani, Mauro A. S. S. Univ Estadual Maringa Chem Engn Grad Program Maringa Parana Brazil Univ Alicante Inst Chem Proc Engn Alicante Spain

Water distribution networks (WDNs) are the main component of industrial and urban water distribution systems and are currently formed by pipes, nodes and loops. In this article, a deterministic mathematical programming approach is proposed, aiming to minimize the cost of looped WDNs, considering known pipe lengths and a discrete set of commercially available diameters. The optimization model constraints are mass balances in nodes, energy balances in loops and hydraulic equations, in such a way that no additional software is needed to find the appropriate pressure drops and water velocities. generalized disjunctive programming is used to reformulate the discrete optimization problem to a mixed-integer nonlinear programming (MINLP) problem. The GAMS (General Algebraic Modeling System) environment is used to solve the problem. Four cases are studied to test the applicability of the model and the results show compatibility with the literature.

关键词： Water distribution networks optimization generalized disjunctive programming MINLP GAMS

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Short-term scheduling of multiple source pipelines with simultaneous injections and deliveries

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COMPUTERS & OPERATIONS RESEARCH 2016年 73卷 27-42页

作者： Mostafaei, Hossein Castro, Pedro M. Ghaffari-Hadigheh, Alireza Azarbaijan Shahid Madani Univ Dept Appl Math Tabriz Iran Univ Lisbon Ctr Matemat Aplicacooes Fundamentais & Invest Ope Fac Ciencias P-1749016 Lisbon Portugal

This paper addresses the optimal scheduling of straight pipelines featuring multiple intermediate nodes acting as dual-purpose stations, with a continuous-time Mixed-Integer Linear programming formulation partly derived from generalized disjunctive programming. The new model allows for an intermediate station to act as an output and input terminal at the same time so as to reduce the number of segment switches between active and idle, and consequently decrease operating costs. Contrary to previous approaches, decisions related to batch sizing, batch sequencing and timing are determined in a single step. Several examples of growing complexity are solved to illustrate the effectiveness and computational advantage of the proposed model in both solution quality and CPU time. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Mathematical modeling Mixed-integer linear programming generalized disjunctive programming Multiproduct pipelines

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A disjunctive programming model for superstructure optimization of power and desalting plants

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DESALINATION 2008年第1-3期222卷 457-465页

作者： Mussati, S. F. Barttfeld, M. Aguirre, P. A. Scenna, N. J. Consejo Nacl Invest Cient & Tecn Inst Desarrollo & Diseno INGAR RA-3000 Santa Fe Argentina Univ Erlangen Nurnberg Inst Chem Engn D-91023 Erlangen Germany

In this paper, a new formulation based on disjunctive programming to model the superstructure of alternative configurations for the synthesis, design and analysis of combined cycle power and desalination plant recently developed in Mussati et al. [Desalination, 182 (2005) 123-129] is presented. In this new formulation, boolean variables model discrete decisions while continuous variables represent the operation conditions of the process, e.g., flow rates, energy demand. Optimal unit configuration and operating conditions are computed by solving the proposed model in order to satisfy electricity generation and freshwater productions demands. Rigorous, non-convex and highly non-linear constraints are involved in the formulation, therefore, robust and efficient solution algorithms have to be used. The Logic-Based Outer Approximation (LOA) algorithm developed by Turkay and Grossmann [Comp. Chem. Eng., 20 (8) (1996) 959] with the modifications introduced by Yeomans and Grossmann [Ind. Eng. Chem. Res., 39 (6) (2000) 1637] are used as part of the solution procedure. The model is implemented and solved in the General Algebraic Modeling System (GAMS). Several study cases for different required power to water ratios are presented and analyzed in order to illustrate the robustness and computational performance of the proposed model.

关键词： superstructure optimization synthesis and design of chemical process optimization generalized disjunctive programming

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Expanding scope and computational challenges in process scheduling

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COMPUTERS & CHEMICAL ENGINEERING 2018年 114卷 14-42页

作者： Castro, Pedro M. Grossmann, Ignacio E. Zhang, Qi Univ Lisbon Fac Ciencias Ctr Matemat Aplicacoes Fundamentals Invest Operat P-1749016 Lisbon Portugal Carnegie Mellon Univ Ctr Adv Proc Decis Making Dept Chem Engn Pittsburgh PA 15213 USA BASF SE D-67063 Ludwigshafen Germany

In this paper, we present a brief overview of enterprise-wide optimization and challenges in multiscale temporal modeling and integration of different models for the levels of planning, scheduling and control. Next, we review generalized disjunctive programming (GDP), as a new modeling paradigm for scheduling problems that are illustrated with the STN and RTN models. We then address scheduling problems that expand the scope of the area: simultaneous scheduling and heat integration, pipeline scheduling, crude oil and refined products blending, and demand side management. We illustrate the advantage of the GDP modeling framework, describe effective strategies for global optimization, and describe multistage affinely adjustable robust optimization for uncertain interruptible load. We address integration of planning and scheduling, for which several approaches are reviewed, including use of traveling salesman constraints for multiperiod refinery planning, and multisite planning and scheduling of multiproduct batch plants. We report computational results to highlight the challenges. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Planning Scheduling Demand side management Mixed-integer programming generalized disjunctive programming

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A robust disjunctive formulation for the redesign of forest biomass-based fuels supply chain under multiple factors of uncertainty

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COMPUTERS & CHEMICAL ENGINEERING 2024年 181卷

作者： Piedra-Jimenez, Frank Torres, Ana I. Rodriguez, Maria Analia Univ Nacl Cordoba Fac Ciencias Exactas Fis & Nat Lab Anal Cuencas Cordoba Argentina CONICET Inst Invest n & Desarrollo Ingn Proc & Qui Cordoba Argentina Carnegie Mellon Univ 5000 Forbes AveDoherty Hall Pittsburgh PA 15213 USA

This article addresses redesigning the forest supply chain (FSC) to produce biomass-based fuels in synergy with existing fossil-based fuel production facilities under uncertainty. The decision-making problem simultaneously considers many aspects in which the forest supply chain must be adapted, including harvesting decisions, new processing facilities and technologies to efficiently produce alternative fuels from residual biomass obtained from multiple points of the supply chain, and changes in the demand for biofuels. The problem is formulated as a robust linear generalized disjunctive programming model that captures its logic and hierarchical nature while providing accurate and efficient results in terms of computational performance. A case study from the Argentinean Forest sector exemplifies the proposed approach.

关键词： Forest supply chain Residual biomass Robust model generalized disjunctive programming

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