Designing optimal mixtures using generalized disjunctive programming: Hull relaxations

A general modeling framework for mixture design problems, which integrates Generalized Disjunctive Programming (GDP) into the Computer-Aided Mixture/blend Design (CAMbD) framework, was recently proposed (S. Jonuzaj, P.T. Akula, P.-M. Kleniati, C.S. Adjiman, 2016. AIChE Journal 62, 1616–1633). In this paper we derive Hull Relaxations (HR) 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 optimized, 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

Computer-aided design of optimal environmentally benign solvent-based adhesive products

The manufacture of improved adhesive products that meet specified target properties has attracted increasing interest over the last decades. In this work, a general systematic methodology for the design of optimal adhesive products with low environmental impact is presented. The proposed approach integrates computer-aided design tools and Generalised Disjunctive Programming (GDP), a logic-based framework, to formulate and solve the product design problem. Key design decisions in product design (i.e., how many components should be included in the final product, which active ingredients and solvent compounds should be used and in what proportions) are optimised simultaneously. This methodology is applied to the design of solvent-based acrylic adhesives, which are commonly used in construction. First, optimal product formulations are determined with the aim to minimize toxicity. This reveals that number of components in the product formulation does not correlate with performance and that high performance can be achieved by investigating different number of components as well as by optimising all ingredients simultaneously rather than sequentially. The relation between two competing objectives (product toxicity and concentration of the active ingredient) is then explored by obtaining a set of Pareto optimal solutions. This leads to significant trade-offs and large areas of discontinuity driven by discrete changes in the list of optimal ingredients in the product

Essays on Stochastic Frontier Models

This thesis consists of three independent chapters. The first chapter “Bayesian Inference in Dynamic Panel Stochastic Frontier Models” proposes a new stochastic frontier model which accounts for the intertemporal production behaviour. The conceptualization is based on the notion that firms face production adjustment costs in the short run due to the presence of quasi-fixed inputs. Consequently, this sluggish adjustment of the entire production process will create a dependency between the current and past production state. To capture this dynamic process, this chapter utilizes the traditional partial adjustment mechanism. The mechanism delivers a dynamic specification and allows factor inputs and inefficiency shocks to have an intertemporal effect on the production process. Moreover, the model allows heterogeneous adjustment speeds and input elasticities across the production units. Model inference is based on Bayesian MCMC techniques with data-augmentation. We illustrate the new model in an empirical application where we estimate the productivity and efficiency growth of the Egyptian private manufacturing sector during the early 90’s. In a similar vein, the second chapter, “Dynamic Panel Stochastic Frontier Models with Inefficiency Effects”, deals with dynamic panel frontier models where inefficiency effects can be a function of exogenous environmental variables. This chapter builds upon advancements in the field and utilizes parametric cumulative distribution functions to specify technical efficiency. The proposed model allows the presence of fixed effects and time-varying inefficiencies. Model estimation is based on the Generalized Method of Moments (GMM) approach, where various forms of input endogeneity can be effectively addressed. Last, the third chapter “A simple method for modelling the energy efficiency rebound effects with an application to energy demand frontiers” proposes a new simple method for estimating the energy inefficiency rebound effects. Model estimation is based on a two-stage approach. In the first stage, we argue in estimating a reduced form stochastic frontier model with country-specific inefficiency heteroscedastic effects. In the second stage, the energy efficiency rebound effects can be obtained effectively using moment-matching methods such as the GMM approach. We apply the proposed model on aggregate energy frontiers where we estimate the energy efficiency and the corresponding rebound effects for a balanced panel of OECD economies. The empirical results suggest an overall upward trend of energy efficiency scores. The energy rebound effects range from 28% to 92%, indicating that energy efficiency actions could have a limited impact on achieving environmental objectives

Rational mixture design: optimisation-based approaches

The main focus of this thesis is on the development of new techniques for the rational design of mixtures, based on a computer-aided mixture/blend design (CAMbD) framework, with applications to the chemical industry. Systematic CAMbD approaches for the design of mixtures and blends have the potential to deliver better products and processes and they enhance innovation in a highly competitive environment. In many existing mixture design methodologies, a simplified reduced version of the CAMbD problem is posed and solved, where the number of mixture ingredients is fixed in advance (usually a binary mixture is designed) and the identity of at least one compound is chosen from a given set of candidate molecules. A key achievement of this work is the development of a novel comprehensive and systematic approach for the formulation and solution of the general mixture problem where the number, identity and composition of mixture constituents are optimized simultaneously. A logic-based method, generalized disjunctive programming (GDP), is integrated for the first time into the CAMbD framework to formulate the discrete choices of mixture problems. In working towards creating a general CAMbD model, the standard (restricted) CAMbD problem is first formulated for the design of multicomponent mixtures (without focusing only on the design of binary mixtures), where the number of mixture ingredients is fixed a priori. Next, the mixture formulation is generalized by making the number, N, of components in the mixture a variable and optimising at the same time the three main decision variables of the problem, i.e., the number, identity and composition of the compounds that participate in the mixture. In the restricted and general models, the components are selected from a given list of candidate molecules. The GDP formulations are converted into mixed-integer form using the big-M (BM) approach in order to exploit the existing MINLP algorithms. The design methodology is demonstrated through a case study involving solid-liquid equilibrium calculations, where optimal solvent mixtures are determined for maximising the solubility of a drug. Solving the mixed integer optimization problems derived using BM can be challenging due to nonconvexities in the space of the continuous variables and a large combinatorial solution space which may lead to several numerical difficulties. To address the difficulties arising from the complexity of the models and facilitate problem formulation, the use of different relaxation techniques, including the big-M approach and Hull reformulations (HR), is investigated to convert the disjunctive constraints into mixed-integer form. Both solution strategies (i.e., BM and HR) are applied successfully to two case studies where optimal solvent mixtures that dissolve ibuprofen and separate acetic acid from water in a single stage liquid extraction process, respectively, are defined. The concept of a truly general approach for mixture design, where the optimal components that participate in mixtures are not selected from restricted lists or databases, is considered. In this general formulation, the molecules are designed (built) from an extensive set of atom groups, leading to the design of countless new and/or existing molecules and mixtures. The general methodology is once again applied to the design of solvent mixtures for separation processes, including crystallization and liquid extraction. First, the design of optimal solvent and antisolvent mixtures for cooling and drowning out crystallization, respectively, is resented. Next, optimal solvent mixtures are designed to separate acetic acid from water in a single-stage liquid extraction process. Integer cuts are introduced to the general mixture formulations and a list of optimal solutions (i.e., list of mixtures with different number, identity and compositions of ingredients) is obtained for each problem. The overall proposed mixture design approach paves the way for identifying innovative solutions (e.g., new molecular structures, mixtures, property functions) which play an integral role in the development of process, chemical and biochemical technologies. Part of the work presented in this thesis has been published in Jonuzaj and Adjiman [2016, 2017] and Jonuzaj et al. [2016].Open Acces

Computer aided design of solvent blends for hybrid cooling and antisolvent crystallization of active pharmaceutical ingredients

Choosing a solvent and an antisolvent for a new crystallization process is challenging due to the sheer number of possible solvent mixtures and the impact of solvent composition and crystallization temperature on process performance. To facilitate this choice, we present a general computer aided mixture/blend design (CAMbD) formulation for the design of optimal solvent mixtures for the crystallization of pharmaceutical products. The proposed methodology enables the simultaneous identification of the optimal process temperature, solvent, antisolvent, and composition of solvent mixture. The SAFT-γ Mie group-contribution approach is used in the design of crystallization solvents; based on an equilibrium model, both the crystal yield and solvent consumption are considered. The design formulation is implemented in gPROMS and applied to the crystallization of lovastatin and ibuprofen, where a hybrid approach combining cooling and antisolvent crystallization is compared to each method alone. For lovastatin, the use of a hybrid approach leads to an increase in crystal yield compared to antisolvent crystallization or cooling crystallization. Furthermore, it is seen that using less volatile but powerful crystallization solvents at lower temperatures can lead to better performance. When considering ibuprofen, the hybrid and antisolvent crystallization techniques provide a similar performance, but the use of solvent mixtures throughout the crystallization is critical in maximizing crystal yields and minimizing solvent consumption. We show that our more general approach to rational design of solvent blends brings significant benefits for the design of crystallization processes in pharmaceutical and chemical manufacturing

The formulation of optimal mixtures with generalized disjunctive programming: a solvent design case study

Systematic approaches for the design of mixtures, based on a computer‐aided mixture/blend design (CAMbD) framework, have the potential to deliver better products and processes. In most existing methodologies the number of mixture ingredients is fixed (usually a binary mixture) and the identity of at least one compound is chosen from a given set of candidate molecules. A novel CAMbD methodology is presented for formulating the general mixture design problem where the number, identity and composition of mixture constituents are optimized simultaneously. To this end, generalized disjunctive programming is integrated into the CAMbD framework to formulate the discrete choices. This generic methodology is applied to a case study to find an optimal solvent mixture that maximizes the solubility of ibuprofen. The best performance in this case study is obtained with a solvent mixture, showing the benefit of using mixtures instead of pure solvents to attain enhanced behavior

A Convex Hull Formulation for the Design of Optimal Mixtures

The files contain some of the formulations implemented in GAMS for this publication. All problems are solved in GAMS version 24.2.3 and are run on a single core of a dual 6 core Intel Xeon X5675 machine at 3.07 GHz.The files contain some of the formulations implemented in GAMS for this publication. All problems are solved in GAMS version 24.2.3 and are run on a single core of a dual 6 core Intel Xeon X5675 machine at 3.07 GHz

Computer-aided solvent mixture design for the crystallisation and isolation of mefenamic acid

The files contain the MINLP formulations presented in this publication. The MINLP problems are implemented and solved in GAMS version 28.2.0, using SBB, a local branch-&-bound MINLP solver.The files contain the MINLP formulations presented in this publication. The MINLP problems are implemented and solved in GAMS version 28.2.0, using SBB, a local branch-&-bound MINLP solver.

The design of optimal mixtures from atom groups using Generalized Disjunctive Programming

A comprehensive computer-aided mixture/blend design methodology for formulating a gen- eral mixture design problem where the number, identity and composition of mixture constituents are optimized simultaneously is presented in this work. Within this approach, Generalized Dis- junctive 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 max- imising 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

Computer-aided design of optimal environmentally benign solvent-based adhesive products

In this work, a general systematic methodology for the design of optimal adhesive products with low environmental impact is presented. The proposed approach integrates computer-aided design tools and Generalised Disjunctive Programming to formulate and solve the product design problem. Key design decisions in product design (number of ingredients, identity of compounds and their proportions) are optimised simultaneously. This methodology is applied to the design of solvent-based acrylic adhesives, which are commonly used in construction. First, optimal product formulations are determined with the aim to minimize toxicity. This reveals that that high performance can be achieved by investigating different number of components as well as by optimising all ingredients simultaneously rather than sequentially. The relation between two competing objectives is then explored by obtaining a set of Pareto optimal solutions. This leads to significant trade-offs and large areas of discontinuity driven by discrete changes in the list of optimal product ingredients.In this work, a general systematic methodology for the design of optimal adhesive products with low environmental impact is presented. The proposed approach integrates computer-aided design tools and Generalised Disjunctive Programming to formulate and solve the product design problem. Key design decisions in product design (number of ingredients, identity of compounds and their proportions) are optimised simultaneously. This methodology is applied to the design of solvent-based acrylic adhesives, which are commonly used in construction. First, optimal product formulations are determined with the aim to minimize toxicity. This reveals that that high performance can be achieved by investigating different number of components as well as by optimising all ingredients simultaneously rather than sequentially. The relation between two competing objectives is then explored by obtaining a set of Pareto optimal solutions. This leads to significant trade-offs and large areas of discontinuity driven by discrete changes in the list of optimal product ingredients.