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Satisfiability modulo theories for process systems engineering

COMPUTERS & CHEMICAL ENGINEERING 2018年 113卷 98-114页

作者： Mistry, Miten D'Iddio, Andrea Callia Huth, Michael Misener, Ruth Imperial Coll London Dept Comp London SW7 2AZ South Kensingto England

Process systems engineers have long recognized the importance of both logic and optimization for automated decision-making. But modern challenges in process systems engineering could strongly benefit from methodological contributions in computer science. In particular, we propose satisfiability modulo theories (SMT) for process systems engineering applications. We motivate SMT using a series of test beds and show the applicability of SMT algorithms and implementations on (i) two-dimensional bin packing, (ii) model explainers, and (iii) mixed-integer nonlinear optimization solvers. (C) 2018 The Authors. Published by Elsevier Ltd.

关键词： Satisfiability modulo theories Mixed-integer optimization generalized disjunctive programming Mixed logical-linear programming

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Logic hybrid simulation-optimization algorithm for distillation design

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COMPUTERS & CHEMICAL ENGINEERING 2015年 72卷 284-299页

作者： Caballero, J. A. Univ Alicante Dept Chem Engn E-03080 Alicante Spain

In this paper, we propose a novel algorithm for the rigorous design of distillation columns that integrates a process simulator in a generalized disjunctive programming formulation. The optimal distillation column, or column sequence, is obtained by selecting, for each column section, among a set of column sections with different number of theoretical trays. The selection of thermodynamic models, properties estimation, etc. is all in the simulation environment. All the numerical issues related to the convergence of distillation columns (or column sections) are also maintained in the simulation environment. The model is formulated as a generalized disjunctive programming (GDP) problem and solved using the logic based outer approximation algorithm without MINLP reformulation. Some examples involving from a single column to thermally coupled sequence or extractive distillation shows the performance of the new algorithm. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Distillation generalized disjunctive programming Simulation Optimization

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Mid-term planning optimization model with sales contracts under demand uncertainty

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COMPUTERS & CHEMICAL ENGINEERING 2012年 47卷 227-236页

作者： Analia Rodriguez, Maria Vecchietti, Aldo INGAR CONICET UTN Santa Fe RA-3000 Santa Fe Argentina

Uncertainty modeling is a challenging topic in supply chain and operation management. When planning material purchase and stock levels, demand uncertainty could have an important impact on the plan results and its feasibility. Additionally, uncertainty could greatly affect customer satisfaction, inventory costs and company profits. From a modeling perspective, problems considering uncertainty are difficult to tackle and lead to complex optimization approaches. This work proposes a mid-term planning model dealing with sales contracts to diminish the effect of uncertainty. Another interesting feature is given by the selection of different price levels. Price elasticity functions are introduced for each customer in order to jointly decide demand targets and prices. A linear generalized disjunctive programming model is developed. Short execution time shows that this model can be applied to analyze several real scenarios to decide material purchase plan, inventory levels, sales strategies, prices and demand levels in a medium term horizon planning. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Demand uncertainty Planning Contracts generalized disjunctive programming

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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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Simultaneous environmental and economic process synthesis of isobutane alkylation

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JOURNAL OF CLEANER PRODUCTION 2014年第0期81卷 270-280页

作者： Garcia, Norberto Fernandez-Torres, Maria J. Caballero, Jose A. Univ Alicante Dept Chem Engn E-03080 Alicante Spain

This multidisciplinary study concerns the optimal design of processes with a view to both maximizing profit and minimizing environmental impacts. This can be achieved by a combination of traditional chemical process design methods, measurements of environmental impacts and advanced mathematical optimization techniques. More to the point, this paper presents a hybrid simulation-multiobjective optimization approach that at once optimizes the production cost and minimizes the associated environmental impacts of isobutane alkylation. This approach has also made it possible to obtain the flow-sheet configurations and process variables that are needed to manufacture isooctane in a way that satisfies the above-stated double aim. The problem is formulated as a generalized disjunctive programming problem and solved using state-of-the-art logic-based algorithms. It is shown, starting from existing alternatives for the process, that it is possible to systematically generate a superstructure that includes alternatives not previously considered. The optimal solution, in the form a Pareto curve, includes different structural alternatives from which the most suitable design can be selected. To evaluate the environmental impact, Life Cycle Assessment based on two different indicators is employed: Ecoindicator 99 and Global Warming Potential. (c) 2014 Elsevier Ltd. All rights reserved.

关键词： Life Cycle Assessment Multiobjective optimization generalized disjunctive programming Global Warming Potential Ecoindicator-99 Isobutane alkylation

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Optimal Design and Operation of a Steel Plant Integrated with a Polygeneration System

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AICHE JOURNAL 2013年第10期59卷 3659-3670页

作者： Ghanbari, Hamid Saxen, Henrik Grossmann, Ignacio E. Abo Akad Univ Dept Chem Engn Thermal & Flow Engn Lab SF-20500 Turku Finland Carnegie Mellon Univ Dept Chem Engn Ctr Adv Proc Decis Making Pittsburgh PA 15213 USA

A process integration approach has been applied to integrate a traditional steelmaking plant with a polygeneration system to increase energy efficiency and suppress carbon dioxide emissions from the system. Using short-cut models and empirical equations for different units and available technologies for gas separation, methane gasification, and methanol synthesis, a mixed integer nonlinear model is applied to find the optimal design of the polygeneration plant and operational conditions of the system. Due to the complexity of the blast furnace (BF) operation, a surrogate model technique is chosen based on an existing BF model. The results show that from an economic perspective, the pressure swing adsorption process with gas-phase methanol unit is preferred. The results demonstrate that integration of conventional steelmaking with a polygeneration system could decrease the specific emissions by more than 20 percent. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 3659-3670, 2013

关键词： process integration polygeneration system carbon dioxide emission steelmaking generalized disjunctive programming

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Cutting Plane Algorithm for Convex generalized disjunctive Programs

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INFORMS JOURNAL ON COMPUTING 2016年第2期28卷 209-222页

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

In this work, we propose a cutting plane algorithm to improve optimization models that are originally formulated as convex generalized disjunctive programs. generalized disjunctive programs are traditionally reformulated as mixed-integer nonlinear programming (MINLP) problems using either the big M (BM) or the hull reformulation (HR). The former yields a smaller MILP/MINLP problem, whereas the latter yields a tighter one. The HR can be further strengthened by using the concept of basic step from disjunctive programming. The proposed algorithm uses the strengthened formulation to derive cuts for the big-M formulation, generating a stronger formulation with small growth in problem size. We test the algorithm with several instances. The results show that the algorithm improves generalized disjunctive programming convex models, in the sense of providing formulations with stronger continuous relaxations than the BM formulation, with few additional constraints. In general, the algorithm also leads to a reduction in the solution time of the problems.

关键词： generalized disjunctive programming mixed-integer nonlinear programming

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disjunctive modeling for optimal control of hybrid systems

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COMPUTERS & CHEMICAL ENGINEERING 2008年第10期32卷 2346-2364页

作者： Oldenburg, Jan Marquardt, Wolfgang Univ Aachen Rhein Westfal TH Aachen Lehrstuhl Prozesstech D-52064 Aachen Germany

In this contribution. a novel approach for the modeling and numerical optimal control of hybrid (discrete-continuous dynamic) systems based on a disjunctive problem formulation is proposed. It is shown that a disjunctive model representation, which constitutes an alternative to mixed-integer model formulations, provides a very flexible, intuitive and effective way to formulate hybrid (discrete-continuous dynamic) optimization problems. The structure and properties of the disjunctive process models can be exploited for an efficient and robust numerical solution by applying generalized disjunctive programming techniques. The proposed modeling and optimization approach will be illustrated by means of optimal control of hybrid systems embedding linear discrete-continuous dynamic models. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： hybrid systems optimal control discrete-continuous dynamic systems generalized disjunctive programming convex hull method big-M method

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Numerical solution of optimal control problems with explicit and implicit switches

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OPTIMIZATION METHODS & SOFTWARE 2018年第3期33卷 450-474页

作者： Bock, Hans Georg Kirches, Christian Meyer, Andreas Potschka, Andreas Heidelberg Univ Interdisciplinary Ctr Sci Comp IWR Heidelberg Germany Tech Univ Braunschweig Inst Math Optimierung Braunschweig Germany

In this article, we present a unified framework for the numerical solution of optimal control problems (OCPs) constrained by ordinary differential equations with both implicit and explicit switches. We present the problem class and qualify different types of implicitly switched systems. This classification significantly affects opportunities for solving such problems numerically. By using techniques from generalized disjunctive programming, we transform the problem into a counterpart one wherein discontinuities no longer appear implicitly. Instead, the new problem contains discrete decision variables and vanishing constraints. Recent results from the field of mixed-integer optimal control theory enable us to omit integrality constraints on variables, and allow to solve a relaxed OCP. We use a first discretize, then optimize' approach to solve the problem numerically. A direct method based on adaptive collocation is used for the discretization. The resulting finite dimensional optimization problems are mathematical programs with vanishing constraints, and we discuss numerical techniques to solve sequences of this challenging problem class. To demonstrate the efficacy and merit of our proposed approach, we investigate three benchmark problems for hybrid dynamic systems.

关键词： switched systems generalized disjunctive programming optimal control mixed-integer optimal control direct transcription methods mathematical programs with vanishing constraints

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Optimal mitigation and control over power system dynamics for stochastic grid resilience

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

作者： Stewart, Nathan Arguello, Bryan Hoffman, Matthew Nicholson, Bethany Garrett, Richard Sandia Natl Labs Albuquerque NM 87123 USA

Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the western system coordinating council 9-bus test system using synthetic multi-device outage scenarios.

关键词： Power system dynamics Control optimization Stochastic optimization generalized disjunctive programming

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