Industrial & Engineering Chemistry Research, Jun 9, 2007
... method was used to both obtain the model and classify the molecules according to ... We use a... more ... method was used to both obtain the model and classify the molecules according to ... We use a sequence of methods for characterizing the activity levels of drug candidates ... A novel classification method based on mixed-integer programming, the hyperbox method, is presented as ...
This paper presents a multi-objective mixed-integer programming problem for integrating specific ... more This paper presents a multi-objective mixed-integer programming problem for integrating specific characteristics of synchromodal transportation. The problem includes different objective functions including total transportation cost, travel time and CO 2 emissions while optimizing the proposed network structure. Traffic congestion, time-dependent vehicle speeds and vehicle filling ratios are considered and computational results for different illustrative cases are presented with real data from the Marmara Region of Turkey. The defined non-linear model is converted into linear form and solved by using a customized implementation of the ∊-constraint method. Then, the sensitivity analysis of proposed mathematical models with pre-processing constraints is summarized for decision makers.
Abstract Developing forecasting models that incorporate that external parameters in addition to p... more Abstract Developing forecasting models that incorporate that external parameters in addition to past data for crude oil and derivatives are a challenging task since it is highly dependent on economic, geographical, and political issues. However, forecasting the prices is very important for strategic planning and oil refineries’ operational decisions. This paper presents an automated tool to predict crude oil prices and their main products by applying Box-Jenkins methodology for the next two months at the beginning of each month in a rolling horizon manner. The resulting forecast is shared with related departments to develop their production plans accordingly. We show that improved accuracy with this forecasting approach is beneficial in any planning and decision-making process and increases profit.
ABSTRACT During the last decade, there has been a growing awareness of the importance of incorpor... more ABSTRACT During the last decade, there has been a growing awareness of the importance of incorporating environmental concerns along with traditional economic criteria in the optimization of industrial processes. This trend has been motivated by several issues, a major one being the tighter government's regulations. Additionally, the need to improve the perception of the firm by customers for being more environmentally conscious, which may eventually lead to higher product sales, has also contributed to this business trend. Particularly, nowadays a high percent of the total human-originated environmental impact is energy related [1]. For this reason, there has been extensive research on the area of design and planning of efficient energy systems considering both financial and environmental objectives [2,3]. A typical energy production system consists of (1) storage tanks to store raw materials, (2) boilers that convert fuel into steam at high pressure, (3) turbines that expand higher pressure steam into lower pressure steam in order to generate electricity and (4) mixing equipments for mixing compatible materials originated from different sources in the system. The goal of the environmentally conscious modeling tools that address the optimization of these systems is to reduce their environmental impact without having to sacrifice the economic performance of the process. Unfortunately, despite the effort made so far, the majority of the strategies devised so far focused on the manufacturing stage, and for this reason their scope is rather limited. Because of this, they can sometimes lead to solutions that decrease the impact locally at the expense of increasing certain negative effects in other stages of the life cycle of the process, in such a manner that the overall environmental damage is increased. This drawback can be overcome by expanding the boundaries of the study beyond the production stage in order to include a wider range of production and logistic activities. Thus, in the past decade it has become clear that the environmental issues must be considered throughout the entire production chain [4]. With the aim to expand the scope of the modeling strategies for energy systems, this work presents a novel approach that relies on the combined use of multi-objective optimization and life cycle assessment (LCA) [5]. In our framework, the design and planning of energy systems is formulated as a multi-objective mixed integer lineal problem (mo-MILP) that simultaneously accounts for the minimization of cost and environmental impact. The latter objective is explicitly captured within the model by making use of the Eco-indicator 99 [6], which incorporates the recent advances made in LCA. The solution of the proposed formulation, which can be obtained via standard techniques for multi-objective optimization, provides as output the set of Pareto points that represent the optimal trade-off between the criteria considered in the analysis. The capabilities of the proposed modeling framework and solution strategy are illustrated through a case study based on a real industrial scenario. In this context, our model is used to investigate a number of alternatives to produce and deliver electricity. The environmental data for the case study was retrieved from the Eco-invent database [7], which contains information regarding the main emissions associated with a wide range of industrial processes used in Europe. In this case study, it is clearly shown how the solely minimization of the environmental impact measured within the boundaries of the system leads to solutions where the environmental problem is just transferred to other stages of the energy supply chain (i.e., raw materials extraction, generation of utilities, etc.). The obtained results demonstrate the benefits of using a holistic environmental assessment method that covers the entire production chain (i.e., LCA), starting from the extraction of raw materials and ending with the delivery of energy to the final customers. The proposed method is intended to guide the decision-makers towards the adoption of more sustainable production patterns for energy generation, thus leading to a reduction of the overall impact caused to the environment. References: [1] EIA, Annual Energy Review 2005, Energy Information Administration, Report No. DOE/EIA-0384, 2005. [2] Trkay, M., Oru, C., Fujita, K., Asakura, T. 2004. Computers and Chemical Engineering, 28, 985-992. [3] Solyu, A., Oru, C., Trkay, M., Fujita, K., Asakura, T. 2006. European Journal of Operations Research, 174(1), 387-403. [4] Srivastava, S. K. 2007. International journal of management reviews, 9(1), 53-80. [5] Guine, J. B.; Gorre, M.; Heijungs, R.; Huppes, G.; Kleijn, R.; de Koning, A.; van Oers, L.; Sleeswijk, A. W.; S. Suh, S.; de Haes, H. A. U.; de Bruijn, H.; van Duin, R.;Huijbregts, M. A. J. Handbook on Life Cycle Assessment. Operational Guide to the ISO Standards; Kluwer Academic Publishers: Dordrecht,…
Metabolic networks are defined as the collection of biochemical reactions within a cell that defi... more Metabolic networks are defined as the collection of biochemical reactions within a cell that define the functions of that cell. Due to the growing need to understand the functions of biological organisms for industrial and medical purposes, modeling and simulation of metabolic networks has attracted a lot of attention recently. Traditionally, metabolic networks are modeled such as flux-balance analysis that considers the steady state nature of the cell. However, it is important to consider the dynamic behavior of a cell since the environmental conditions change continuously. Sometimes due to the critical changes in the environment some of the reactions exhibit completely different behavior leading to discrete changes in the metabolic network. Therefore, a cell exhibits discrete-continuous behavior in continuous time. Since hybrid systems exhibit the same characteristics modeling a cell as a hybrid system gives an accurate representation. The aim of this paper is to develop a simulation framework to model the evolving structure of the cell metabolism under changes in the environment. The metabolic responses that cell gives, against multiple changes in the environment are not fully understood. Therefore, in this study, a cell is modeled as a hybrid system that is composed of a system of differential and algebraic equations. The changes in the concentration of metabolites in the environment are represented by Ordinary Differential Equations and the intracellular cell metabolism is represented by a set of algebraic equations. To understand the feedback relationship between intracellular and extracellular changes, the system is solved considering the effects of extracellular stresses on the metabolic responses.
ABSTRACT Mathematical modelling and simulation of a styrene plant was made for the synthesis of a... more ABSTRACT Mathematical modelling and simulation of a styrene plant was made for the synthesis of a regulatory control structure for the purpose of replacing the existing one. The structural model was constructed considering the differential and algebraic relations describing the process. Utilizing the structural model, alternative feasible control structures were determined by integer linear programming (ILP) techniques developed in this study. The ILP formulations developed were proved to be very efficient in generating structurally controllable alternative feasible control configurations. The performances of the alternative structures were evaluated by utilizing the gain information obtained by steady-state modelling and using the interaction criteria RGA, NI, SVD, IMCIM and RDG. Thus, a systematic procedure for synthesizing regulatory control structures for a large-scale process is established by utilizing ILP1 and ILP2 formulations which are the modified versions of the MILP formulations proposed by Georgiou and Floudas (81st AIChE Annual Meeting 1989). The necessary improvements in MILP formulations were made in order to make them applicable for a large-scale system.
Most real-world problems involve multiple conflicting criteria. These problems are called multicr... more Most real-world problems involve multiple conflicting criteria. These problems are called multicriteria/multi-objective optimization problems (MOOP). The main task in solving MOOPs is to find the nondominated (ND) points in the objective space or efficient solutions in the decision space. A ND point is a point in the objective space with objective function values that cannot be improved without worsening another objective function. In this paper, we present a new method that generates the set of ND points for a multiobjective mixed-integer linear program (MOMILP). The Generator of ND and Efficient Frontier (GoNDEF) for MOMILPs finds that the ND points represented as points, line segments, and facets consist of every type of ND point. First, the GoNDEF sets integer variables to the values that result in ND points. Fixing integer variables to specific values results in a multi-objective linear program (MOLP). This MOLP has its own set of ND points. A subset of this set establishes a subset of the ND points set of the MOMILP. In this paper, we present an extensive theoretical analysis of the GoNDEF and illustrate its effectiveness on a set of instance problems.
Conserved residues in protein-protein interfaces correlate with residue hot-spots. To obtain insi... more Conserved residues in protein-protein interfaces correlate with residue hot-spots. To obtain insight into their roles, we have studied their mobility. We have performed 39 explicit solvent simulations of 15 complexes and their monomers, with the interfaces varying in size, shape, and function. The dynamic behavior of conserved residues in unbound monomers illustrates significantly lower flexibility as compared to their environment, suggesting that already before binding they are constrained in a boundlike configuration. To understand this behavior, we have analyzed the inter-and intrachain hydrogen-bond residence-time in the interfaces. We find that conserved residues are not involved significantly in hydrogen bonds across the interface as compared to nonconserved. However, the monomer simulations reveal that conserved residues contribute dominantly to hydrogen-bond formation before binding. Packing of conserved residues across the trajectories is significantly higher before and after the binding, rationalizing their lower mobility. Backbone torsional angle distributions show that conserved residues assume restricted regions of space and the most visited conformations in the bound and unbound trajectories are similar, suggesting that conserved residues are preorganized. Combined with previous studies, we conclude that conserved residues, hot spots, anchor, and interface-buried residues may be similar residues, fulfilling similar roles.
The demand for portable electronic devices grows everyday and the batteries that power them pose ... more The demand for portable electronic devices grows everyday and the batteries that power them pose important environmental problems. Batteries contain heavy metals such as; lead, mercury, cadmium that can contaminate the environment when batteries are disposed of improperly. The question is "How to manage this large amount of waste batteries?" In order to minimize the negative impacts of batteries on the environment, legislations have been published in the last two decades. In Turkey, the Regulation on Control of Waste Batteries and Accumulators APAK is published in 2004 and the project 'Development of Waste Battery Disposal and Recycling Technologies' is in progress. Within the scope of the project we do research on logistics of waste batteries. A multi period mixed-integer linear programming (MILP) model is developed to design the reverse logistics network for waste batteries. We solved the model with the objective of minimizing the total present value of waste battery management system under a variety of scenarios in order to provide an effective decision support tool and offer useful outputs to decision-makers.
This thesis deals with Generalized Disjunctive Programming (GDP) models and solution techniques f... more This thesis deals with Generalized Disjunctive Programming (GDP) models and solution techniques for the optimization of process flowsheets. GDP is a natural framework for modeling discrete optimization problems and models containing discontinuous functions. Conventional mathematical programming approaches for the synthesis and design of process systems often fail because of singularities and discontinuities. In order to deal with these difficulties, disjunctions are used to model units and discontinuities in the design and synthesis of flowsheets. Logic-based versions of outer-approximation (OA) and generalized Benders decomposition (GBD) methods are developed for the synthesis of process flowsheets. The convex hull formulation of disjunctions is used to convert the disjunctive LP master problem into an MILP problem for the logic-based version of the OA method. To derive the logic-based version of the GBD method a relation is exploited between the master problem of OA and the master problem of GBD. The modeling of discontinuous cost functions is investigated through the use of disjunctions. The convex hull formulation of a disjunction is shown to be an exact linearization of nonlinear terms in the equations for the disjunctions. It is also shown that the convex hull formulation of the disjunctions provides a tighter relaxation compared to big-M formulation. The synthesis of process flowsheets with complex investment cost functions is studied and a GDP method is proposed which has the novelty of having MINLP subproblems for fixed flowsheet configurations. Numerical results on a large number of problems including the synthesis of a vinyl chloride (VCM) process are presented. Finally, solution of algebraic systems of disjunctive equations are studied as a particular case of GDP. Solution methods and numerical results for linear and nonlinear systems are presented.
Abstract Management of energy is a critical factor in refinery operations, having a significant i... more Abstract Management of energy is a critical factor in refinery operations, having a significant impact on the production costs. The effective management of the energy system in the refinery can improve the economic performance significantly. The energy demand in refineries changes continuously in the presence of changing crude oil properties, operation conditions of process units, and cost of fuels. We present a decision support system to manage the complex energy network of the refinery by determining the optimum operational combinations of the equipment for minimizing the energy costs. In addition to operational optimization of the energy network, we also examine the impact of policy decisions through scenario analysis. We show that around 3.5 % cost reduction is possible without capital investment.
In this supplementary material, the details of the two-phase algorithm, an illustrative example a... more In this supplementary material, the details of the two-phase algorithm, an illustrative example and and extensive comparison with other methods on benchmark problems are presented.
The optimization of process systems with complex investment cost functions, defined over several ... more The optimization of process systems with complex investment cost functions, defined over several intervals of equipment sizes, operating pressures and temperatures, is addressed in this paper. The discontinuities with respect to these variables are modeled with disjunctions that are converted into tight mixed-integer constraints with the convex hull formulation for each disjunction. The efficiency of the resulting MINLP model for fixed structures is shown on a flowsheet optimization problem and compared with the big-M formulation. To address the structural optimization of process flowsheets, we propose a generalized disjunctive programming algorithm (GDP) in which the complex investment cost functions are formulated as embedded disjunctions. The GDP algorithm consists of MINLP subproblems for the optimization of fixed flowsheet structures and MILP master problems to predict new flowsheets to be optimized. The proposed algorithm is tested on the synthesis of a process network with nine units, and the synthesis of a vinyl chloride monomer production process consisting of 32 process units. It is shown that the proposed GDP algorithm is rigorous for handling discontinuities in complex cost functions, and is robust and efficient for structural flowsheet optimization problems.
Industrial & Engineering Chemistry Research, Jun 9, 2007
... method was used to both obtain the model and classify the molecules according to ... We use a... more ... method was used to both obtain the model and classify the molecules according to ... We use a sequence of methods for characterizing the activity levels of drug candidates ... A novel classification method based on mixed-integer programming, the hyperbox method, is presented as ...
This paper presents a multi-objective mixed-integer programming problem for integrating specific ... more This paper presents a multi-objective mixed-integer programming problem for integrating specific characteristics of synchromodal transportation. The problem includes different objective functions including total transportation cost, travel time and CO 2 emissions while optimizing the proposed network structure. Traffic congestion, time-dependent vehicle speeds and vehicle filling ratios are considered and computational results for different illustrative cases are presented with real data from the Marmara Region of Turkey. The defined non-linear model is converted into linear form and solved by using a customized implementation of the ∊-constraint method. Then, the sensitivity analysis of proposed mathematical models with pre-processing constraints is summarized for decision makers.
Abstract Developing forecasting models that incorporate that external parameters in addition to p... more Abstract Developing forecasting models that incorporate that external parameters in addition to past data for crude oil and derivatives are a challenging task since it is highly dependent on economic, geographical, and political issues. However, forecasting the prices is very important for strategic planning and oil refineries’ operational decisions. This paper presents an automated tool to predict crude oil prices and their main products by applying Box-Jenkins methodology for the next two months at the beginning of each month in a rolling horizon manner. The resulting forecast is shared with related departments to develop their production plans accordingly. We show that improved accuracy with this forecasting approach is beneficial in any planning and decision-making process and increases profit.
ABSTRACT During the last decade, there has been a growing awareness of the importance of incorpor... more ABSTRACT During the last decade, there has been a growing awareness of the importance of incorporating environmental concerns along with traditional economic criteria in the optimization of industrial processes. This trend has been motivated by several issues, a major one being the tighter government's regulations. Additionally, the need to improve the perception of the firm by customers for being more environmentally conscious, which may eventually lead to higher product sales, has also contributed to this business trend. Particularly, nowadays a high percent of the total human-originated environmental impact is energy related [1]. For this reason, there has been extensive research on the area of design and planning of efficient energy systems considering both financial and environmental objectives [2,3]. A typical energy production system consists of (1) storage tanks to store raw materials, (2) boilers that convert fuel into steam at high pressure, (3) turbines that expand higher pressure steam into lower pressure steam in order to generate electricity and (4) mixing equipments for mixing compatible materials originated from different sources in the system. The goal of the environmentally conscious modeling tools that address the optimization of these systems is to reduce their environmental impact without having to sacrifice the economic performance of the process. Unfortunately, despite the effort made so far, the majority of the strategies devised so far focused on the manufacturing stage, and for this reason their scope is rather limited. Because of this, they can sometimes lead to solutions that decrease the impact locally at the expense of increasing certain negative effects in other stages of the life cycle of the process, in such a manner that the overall environmental damage is increased. This drawback can be overcome by expanding the boundaries of the study beyond the production stage in order to include a wider range of production and logistic activities. Thus, in the past decade it has become clear that the environmental issues must be considered throughout the entire production chain [4]. With the aim to expand the scope of the modeling strategies for energy systems, this work presents a novel approach that relies on the combined use of multi-objective optimization and life cycle assessment (LCA) [5]. In our framework, the design and planning of energy systems is formulated as a multi-objective mixed integer lineal problem (mo-MILP) that simultaneously accounts for the minimization of cost and environmental impact. The latter objective is explicitly captured within the model by making use of the Eco-indicator 99 [6], which incorporates the recent advances made in LCA. The solution of the proposed formulation, which can be obtained via standard techniques for multi-objective optimization, provides as output the set of Pareto points that represent the optimal trade-off between the criteria considered in the analysis. The capabilities of the proposed modeling framework and solution strategy are illustrated through a case study based on a real industrial scenario. In this context, our model is used to investigate a number of alternatives to produce and deliver electricity. The environmental data for the case study was retrieved from the Eco-invent database [7], which contains information regarding the main emissions associated with a wide range of industrial processes used in Europe. In this case study, it is clearly shown how the solely minimization of the environmental impact measured within the boundaries of the system leads to solutions where the environmental problem is just transferred to other stages of the energy supply chain (i.e., raw materials extraction, generation of utilities, etc.). The obtained results demonstrate the benefits of using a holistic environmental assessment method that covers the entire production chain (i.e., LCA), starting from the extraction of raw materials and ending with the delivery of energy to the final customers. The proposed method is intended to guide the decision-makers towards the adoption of more sustainable production patterns for energy generation, thus leading to a reduction of the overall impact caused to the environment. References: [1] EIA, Annual Energy Review 2005, Energy Information Administration, Report No. DOE/EIA-0384, 2005. [2] Trkay, M., Oru, C., Fujita, K., Asakura, T. 2004. Computers and Chemical Engineering, 28, 985-992. [3] Solyu, A., Oru, C., Trkay, M., Fujita, K., Asakura, T. 2006. European Journal of Operations Research, 174(1), 387-403. [4] Srivastava, S. K. 2007. International journal of management reviews, 9(1), 53-80. [5] Guine, J. B.; Gorre, M.; Heijungs, R.; Huppes, G.; Kleijn, R.; de Koning, A.; van Oers, L.; Sleeswijk, A. W.; S. Suh, S.; de Haes, H. A. U.; de Bruijn, H.; van Duin, R.;Huijbregts, M. A. J. Handbook on Life Cycle Assessment. Operational Guide to the ISO Standards; Kluwer Academic Publishers: Dordrecht,…
Metabolic networks are defined as the collection of biochemical reactions within a cell that defi... more Metabolic networks are defined as the collection of biochemical reactions within a cell that define the functions of that cell. Due to the growing need to understand the functions of biological organisms for industrial and medical purposes, modeling and simulation of metabolic networks has attracted a lot of attention recently. Traditionally, metabolic networks are modeled such as flux-balance analysis that considers the steady state nature of the cell. However, it is important to consider the dynamic behavior of a cell since the environmental conditions change continuously. Sometimes due to the critical changes in the environment some of the reactions exhibit completely different behavior leading to discrete changes in the metabolic network. Therefore, a cell exhibits discrete-continuous behavior in continuous time. Since hybrid systems exhibit the same characteristics modeling a cell as a hybrid system gives an accurate representation. The aim of this paper is to develop a simulation framework to model the evolving structure of the cell metabolism under changes in the environment. The metabolic responses that cell gives, against multiple changes in the environment are not fully understood. Therefore, in this study, a cell is modeled as a hybrid system that is composed of a system of differential and algebraic equations. The changes in the concentration of metabolites in the environment are represented by Ordinary Differential Equations and the intracellular cell metabolism is represented by a set of algebraic equations. To understand the feedback relationship between intracellular and extracellular changes, the system is solved considering the effects of extracellular stresses on the metabolic responses.
ABSTRACT Mathematical modelling and simulation of a styrene plant was made for the synthesis of a... more ABSTRACT Mathematical modelling and simulation of a styrene plant was made for the synthesis of a regulatory control structure for the purpose of replacing the existing one. The structural model was constructed considering the differential and algebraic relations describing the process. Utilizing the structural model, alternative feasible control structures were determined by integer linear programming (ILP) techniques developed in this study. The ILP formulations developed were proved to be very efficient in generating structurally controllable alternative feasible control configurations. The performances of the alternative structures were evaluated by utilizing the gain information obtained by steady-state modelling and using the interaction criteria RGA, NI, SVD, IMCIM and RDG. Thus, a systematic procedure for synthesizing regulatory control structures for a large-scale process is established by utilizing ILP1 and ILP2 formulations which are the modified versions of the MILP formulations proposed by Georgiou and Floudas (81st AIChE Annual Meeting 1989). The necessary improvements in MILP formulations were made in order to make them applicable for a large-scale system.
Most real-world problems involve multiple conflicting criteria. These problems are called multicr... more Most real-world problems involve multiple conflicting criteria. These problems are called multicriteria/multi-objective optimization problems (MOOP). The main task in solving MOOPs is to find the nondominated (ND) points in the objective space or efficient solutions in the decision space. A ND point is a point in the objective space with objective function values that cannot be improved without worsening another objective function. In this paper, we present a new method that generates the set of ND points for a multiobjective mixed-integer linear program (MOMILP). The Generator of ND and Efficient Frontier (GoNDEF) for MOMILPs finds that the ND points represented as points, line segments, and facets consist of every type of ND point. First, the GoNDEF sets integer variables to the values that result in ND points. Fixing integer variables to specific values results in a multi-objective linear program (MOLP). This MOLP has its own set of ND points. A subset of this set establishes a subset of the ND points set of the MOMILP. In this paper, we present an extensive theoretical analysis of the GoNDEF and illustrate its effectiveness on a set of instance problems.
Conserved residues in protein-protein interfaces correlate with residue hot-spots. To obtain insi... more Conserved residues in protein-protein interfaces correlate with residue hot-spots. To obtain insight into their roles, we have studied their mobility. We have performed 39 explicit solvent simulations of 15 complexes and their monomers, with the interfaces varying in size, shape, and function. The dynamic behavior of conserved residues in unbound monomers illustrates significantly lower flexibility as compared to their environment, suggesting that already before binding they are constrained in a boundlike configuration. To understand this behavior, we have analyzed the inter-and intrachain hydrogen-bond residence-time in the interfaces. We find that conserved residues are not involved significantly in hydrogen bonds across the interface as compared to nonconserved. However, the monomer simulations reveal that conserved residues contribute dominantly to hydrogen-bond formation before binding. Packing of conserved residues across the trajectories is significantly higher before and after the binding, rationalizing their lower mobility. Backbone torsional angle distributions show that conserved residues assume restricted regions of space and the most visited conformations in the bound and unbound trajectories are similar, suggesting that conserved residues are preorganized. Combined with previous studies, we conclude that conserved residues, hot spots, anchor, and interface-buried residues may be similar residues, fulfilling similar roles.
The demand for portable electronic devices grows everyday and the batteries that power them pose ... more The demand for portable electronic devices grows everyday and the batteries that power them pose important environmental problems. Batteries contain heavy metals such as; lead, mercury, cadmium that can contaminate the environment when batteries are disposed of improperly. The question is "How to manage this large amount of waste batteries?" In order to minimize the negative impacts of batteries on the environment, legislations have been published in the last two decades. In Turkey, the Regulation on Control of Waste Batteries and Accumulators APAK is published in 2004 and the project 'Development of Waste Battery Disposal and Recycling Technologies' is in progress. Within the scope of the project we do research on logistics of waste batteries. A multi period mixed-integer linear programming (MILP) model is developed to design the reverse logistics network for waste batteries. We solved the model with the objective of minimizing the total present value of waste battery management system under a variety of scenarios in order to provide an effective decision support tool and offer useful outputs to decision-makers.
This thesis deals with Generalized Disjunctive Programming (GDP) models and solution techniques f... more This thesis deals with Generalized Disjunctive Programming (GDP) models and solution techniques for the optimization of process flowsheets. GDP is a natural framework for modeling discrete optimization problems and models containing discontinuous functions. Conventional mathematical programming approaches for the synthesis and design of process systems often fail because of singularities and discontinuities. In order to deal with these difficulties, disjunctions are used to model units and discontinuities in the design and synthesis of flowsheets. Logic-based versions of outer-approximation (OA) and generalized Benders decomposition (GBD) methods are developed for the synthesis of process flowsheets. The convex hull formulation of disjunctions is used to convert the disjunctive LP master problem into an MILP problem for the logic-based version of the OA method. To derive the logic-based version of the GBD method a relation is exploited between the master problem of OA and the master problem of GBD. The modeling of discontinuous cost functions is investigated through the use of disjunctions. The convex hull formulation of a disjunction is shown to be an exact linearization of nonlinear terms in the equations for the disjunctions. It is also shown that the convex hull formulation of the disjunctions provides a tighter relaxation compared to big-M formulation. The synthesis of process flowsheets with complex investment cost functions is studied and a GDP method is proposed which has the novelty of having MINLP subproblems for fixed flowsheet configurations. Numerical results on a large number of problems including the synthesis of a vinyl chloride (VCM) process are presented. Finally, solution of algebraic systems of disjunctive equations are studied as a particular case of GDP. Solution methods and numerical results for linear and nonlinear systems are presented.
Abstract Management of energy is a critical factor in refinery operations, having a significant i... more Abstract Management of energy is a critical factor in refinery operations, having a significant impact on the production costs. The effective management of the energy system in the refinery can improve the economic performance significantly. The energy demand in refineries changes continuously in the presence of changing crude oil properties, operation conditions of process units, and cost of fuels. We present a decision support system to manage the complex energy network of the refinery by determining the optimum operational combinations of the equipment for minimizing the energy costs. In addition to operational optimization of the energy network, we also examine the impact of policy decisions through scenario analysis. We show that around 3.5 % cost reduction is possible without capital investment.
In this supplementary material, the details of the two-phase algorithm, an illustrative example a... more In this supplementary material, the details of the two-phase algorithm, an illustrative example and and extensive comparison with other methods on benchmark problems are presented.
The optimization of process systems with complex investment cost functions, defined over several ... more The optimization of process systems with complex investment cost functions, defined over several intervals of equipment sizes, operating pressures and temperatures, is addressed in this paper. The discontinuities with respect to these variables are modeled with disjunctions that are converted into tight mixed-integer constraints with the convex hull formulation for each disjunction. The efficiency of the resulting MINLP model for fixed structures is shown on a flowsheet optimization problem and compared with the big-M formulation. To address the structural optimization of process flowsheets, we propose a generalized disjunctive programming algorithm (GDP) in which the complex investment cost functions are formulated as embedded disjunctions. The GDP algorithm consists of MINLP subproblems for the optimization of fixed flowsheet structures and MILP master problems to predict new flowsheets to be optimized. The proposed algorithm is tested on the synthesis of a process network with nine units, and the synthesis of a vinyl chloride monomer production process consisting of 32 process units. It is shown that the proposed GDP algorithm is rigorous for handling discontinuities in complex cost functions, and is robust and efficient for structural flowsheet optimization problems.
Uploads
Papers by Metin Türkay