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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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Energy Efficient Temperature and Humidity Control in Building Climate Systems 12

Energy Efficient Temperature and Humidity Control in Buildin...

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12th IFAC Symposium on Advanced Control of Chemical Processes (ADCHEM)

作者： Ghawash, Faiq Hovd, Morten Schofield, Brad Norwegian Univ Sci & Technol Trondheim Norway CERN Beams Dept Ind Controls & Safety Syst Grp Meyrin Switzerland

Energy efficient building climate control involves maintaining thermal comfort across a wide range of environmental conditions while minimizing energy usage. However, the design of energy efficient control poses a significant challenge owing to the strong coupling between temperature and humidity. In this work, we present a control oriented model for the heating, ventilation and air conditioning (HVAC) system and provide a polytopic approximation of thermal comfort in terms of temperature and humidity ratio. A novel energy optimal control formulation based on generalized disjunctive programming is proposed to systematically account for the strong coupling effects and latent heat consideration. An extensive simulation study is performed to validate the efficcacy of the proposed control strategy across a wide range of operational and weather conditions.

关键词： HVAC Control generalized disjunctive programming Hybrid MPC Energy Efficiency

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***: an ecosystem for logic based modeling and optimization development

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OPTIMIZATION AND ENGINEERING 2022年第1期23卷 607-642页

作者： Chen, Qi Johnson, Emma S. Bernal, David E. Valentin, Romeo Kale, Sunjeev Bates, Johnny Siirola, John D. Grossmann, Ignacio E. Carnegie Mellon Univ Ctr Adv Proc Decis Making Dept Chem Engn Pittsburgh PA 15213 USA Sandia Natl Labs Albuquerque NM 87123 USA

We present three core principles for engineering-oriented integrated modeling and optimization tool sets-intuitive modeling contexts, systematic computer-aided reformulations, and flexible solution strategies-and describe how new developments in *** for generalized disjunctive programming (GDP) advance this vision. We describe a new logical expression system implementation for *** allowing for a more intuitive description of logical propositions. The logical expression system supports automated reformulation of these logical constraints to linear constraints. We also describe two new logic-based global optimization solver implementations built on *** that exploit logical structure to avoid "zero-flow" numerical difficulties that arise in nonlinear network design problems when nodes or streams disappear. These new solvers also demonstrate the capability to link to external libraries for expanded functionality within an integrated implementation. We present these new solvers in the context of a flexible array of solution paths available to GDP models. Finally, we present results on a new library of GDP models demonstrating the value of multiple solution approaches.

关键词： Mathematical programming generalized disjunctive programming MINLP

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Cost-optimal design of reverse electrodialysis process for salinity gradient-based electricity generation in desalination plants

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ENERGY 2024年 313卷

作者： Tristan, C. Fallanza, M. Ortiz, I. Ibanez, R. Grossmann, I. E. Univ Cantabria Dept Chem & Biomol Engn Ave Castros 46 Santander 39005 Spain Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

Salinity gradient-based technologies offer a solution for desalination plants seeking clean, uninterrupted electricity to support their decarbonization and circularity. This work provides cost-optimal designs of a large-scale reverse electrodialysis (RED) system deployed in a desalination plant using mathematical programming. The optimization model determines the hydraulic topology and RED units' working conditions that maximize the net present value (NPV) of the RED process recovering salinity gradient energy between brine and treated wastewater effluents. We examine how electricity, carbon and membranes prices, desalination plant capacity, and membrane resistance may affect the NPV-optimal design's competitiveness and performance. We also compare the conventional series-parallel configuration and the NPV-optimal solution with recycling and added reuse alternatives. In the context of soaring electricity prices and strong green financing support, with the use of highperforming, affordable membranes (similar to 10 (sic)/m(2)), RED could save 8 % of desalination plant energy demand from the grid, earning 5 M(sic) profits and LCOE of 66-126 (sic)/MWh, comparable to other renewable and conventional power technologies. The optimization model finds profitable designs for the entire range of medium-capacity desalination plants. The findings underscore the optimization model effectiveness in streamlining decision making and exploiting the synergies of full-scale, RED-based electricity in the energy-intensive water sector.

关键词： Renewable energy generalized disjunctive programming Reverse osmosis Wastewater treatment Water-energy nexus

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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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Optimization-based cosmetic formulation: Integration of mechanistic model, surrogate model, and heuristics

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AICHE JOURNAL 2021年第1期67卷 e17064-e17064页

作者： Zhang, Xiang Zhou, Teng Ng, Ka Ming Hong Kong Univ Sci & Technol Dept Chem & Biol Engn Clear Water Bay Hong Kong Peoples R China Max Planck Inst Dynam Complex Tech Syst Proc Syst Engn Magdeburg Germany Otto von Guericke Univ Proc Syst Engn Magdeburg Germany

Multiple functional and hard-to-quantify sensorial product attributes that can be satisfied by a large number of cosmetic ingredients are required in the design of cosmetics. To overcome this problem, a new optimization-based approach for expediting cosmetic formulation is presented. It exploits the use of a hierarchy of models in an iterative manner to refine the search for creating the highest-quality cosmetic product. First, a systematic procedure is proposed for optimization problem formulation, where the cosmetic formulation problem is defined, design variables are specified, and a set of models for sensorial perception and desired product properties are identified. Then, a solution strategy that involves iterative model adoption and two numerical techniques (i.e., generalized disjunctive programming reformulation and model substitution) is applied to improve the efficiency of solving the optimization problem and to find better solutions. The applicability of the proposed procedure and solution strategy is illustrated with a perfume formulation example.

关键词： cosmetic formulation generalized disjunctive programming mechanistic model perfume surrogate model

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Energy Efficient Temperature and Humidity Control in Building Climate Systems

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IFAC-PapersOnLine 2024年第14期58卷 544-549页

作者： Faiq Ghawash Morten Hovd Brad Schofield Norwegian University of Science and Technology Trondheim Norway Beams Department Industrial Controls and Safety Systems Group CERN Meyrin Switzerland

Energy Efficient building climate control involves maintaining thermal comfort across a wide range of environmental conditions while minimizing energy usage. However, the design of energy Efficient control poses a significant challenge owing to the strong coupling between temperature and humidity. In this work, we present a control oriented model for the heating, ventilation and air conditioning (HVAC) system and provide a polytopic approximation of thermal comfort in terms of temperature and humidity ratio. A novel energy optimal control formulation based on generalized disjunctive programming is proposed to systematically account for the strong coupling effects and latent heat consideration. An extensive simulation study is performed to validate the efficcacy of the proposed control strategy across a wide range of operational and weather conditions.

关键词： HVAC Control generalized disjunctive programming Hybrid MPC Energy efficiency

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A hierarchy of relaxations for nonlinear convex generalized disjunctive programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第1期218卷 38-47页

作者： Ruiz, Juan P. Grossmann, Ignacio E. Carnegie Mellon Univ Dept Chem Engn Pittsburgh PA 15213 USA

We propose a framework to generate alternative mixed-integer nonlinear programming formulations for disjunctive convex programs that lead to stronger relaxations. We extend the concept of "basic steps" defined for disjunctive linear programs to the nonlinear case. A basic step is an operation that takes a disjunctive set to another with fewer number of conjuncts. We show that the strength of the relaxations increases as the number of conjuncts decreases, leading to a hierarchy of relaxations. We prove that the tightest of these relaxations, allows in theory the solution of the disjunctive convex program as a nonlinear programming problem. We present a methodology to guide the generation of strong relaxations without incurring an exponential increase of the size of the reformulated mixed-integer program. Finally, we apply the theory developed to improve the computational efficiency of solution methods for nonlinear convex generalized disjunctive programs (GDP). This methodology is validated through a set of numerical examples. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Combinatorial optimization Convex programming disjunctive programming generalized disjunctive programming Tight relaxations

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Event constrained programming

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COMPUTERS & CHEMICAL ENGINEERING 2025年 199卷

作者： Ovalle, Daniel Mazzadi, Stefan Laird, Carl D. Grossmann, Ignacio E. Pulsipher, Joshua L. Carnegie Mellon Univ Dept Chem Engn Doherty Hall5000 Forbes Ave Pittsburgh PA 15213 USA Univ Waterloo Dept Chem Engn 200 Univ Ave Waterloo ON N2L 3G1 Canada

In this paper, we present event constraints as a new modeling paradigm that generalizes joint chance constraints from stochastic optimization to: (1) enforce a constraint on the probability of satisfying a set of constraints aggregated via application-specific logic (constituting an event), and (2) to be applied to general infinite-dimensional optimization (InfiniteOpt) problems (i.e., time, space, and/or uncertainty domains). This new constraint class offers significant modeling flexibility in posing InfiniteOpt constraints that are enforced over a certain portion of their domain (e.g., to a certain probability level), but can be challenging to reformulate/solve due to difficulties in representing arbitrary logical conditions and specifying a probabilistic measure on a collection of constraints. To address these challenges, we derive a generalized disjunctive programming (GDP) representation of event constrained optimization problems, which readily enables posing logical event conditions in a standard form and allows to draw from a suite of GDP solution strategies that leverage the special structure of this problem class. We also extend several approximation techniques from the chance constraint literature to provide a means to reformulate certain event constraints without the use of binary variables. We illustrate these findings with case studies in stochastic optimal power flow, dynamic disease control, and optimal 2D diffusion.

关键词： Infinite-dimensional optimization Event constraints Chance constraints generalized disjunctive programming Stochastic programming Dynamic programming

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GDP-based approach for optimal design of forest biorefinery supply chain considering circularity and conversion facilities co-location

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COMPUTERS & CHEMICAL ENGINEERING 2022年 163卷

作者： Piedra-Jimenez, Frank Tassin, Natalia G. Novas, Juan M. Rodriguez, Maria Analia Quim Aplicada IPQA Univ Nacl Cordoba Inst Invest & Desarrollo Ingeniena Proc CONICET RA-5000 Cordoba Argentina Estudios Matemat CIEM Univ Nacl Cordoba Ctr Invest CONICET RA-5000 Cordoba Argentina Desarrollo & Transferencia Sistemas Informac CIDS Fac Cordoba Ctr Invest RA-5000 Cordoba Argentina

The Forest Biorefinery Supply Chain (FBSC) design problem is addressed. A general mathematical framework based on a generalized disjunctive programming (GDP) formulation is proposed as an efficient decision-making tool for the optimal FBSC. The approach simultaneously tackles the dynamic capacity allocation and the facilities' co-location, features that are explicitly modelled. The FBSC superstructure promotes the circularity of the network by including flexible processing recipes and the use of multiple biomass residues as biorefineries raw materials as well as paper recycling. The proposed case study copes with the production of paper and biofuels in Argentina, showing the advantage of the integration of biorefineries with the existing forest industries as well as the addition of value to biomass industrial waste and by-products. Additionally, a set of scenarios are considered and tested. By these examples, key features of the proposed approach are highlighted as essential to reach a profitable FBSC. (c) 2022 Elsevier Ltd. All rights reserved.

关键词： Supply Chain Design Optimization Forest Biorefinery generalized disjunctive programming

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