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• This paper presents the optimal design of distillation columns using Set Trimming and Enumeration. • The Set Trimming algorithm reduces the number of design solution candidates to evaluate. • The smart enumeration algorithm guarantees global optimality and has a lower computational effort than complete enumeration. • The scheme Set Trimming followed by Enumeration is robust and does not fail. In this article, we present an alternative approach to the use of metaheuristic methods (GA, PSO, SA, etc.) or mathematical programming (MINLP solvers) for the optimal design of one-feed-two-products distillation columns. We propose the use of Set Trimming followed by candidate enumeration. For the evaluation of the performance of each candidate solution, the method relies on solving the associated system of equations. Three different enumeration procedures are tested: Exhaustive Enumeration, Smart Enumeration, and Segmental Smart Enumeration. Smart Enumeration is an optimization procedure that identifies the solution through a search in the set of candidates organized in ascending order of the objective function lower bound, while Segmental Smart Enumeration is introduced in this article. We compare the results of the proposed procedure with the results using an MINLP approach with different solvers. Numerical results indicate that the best alternative of the enumeration algorithms can identify the global optimum faster than a global solver of mathematical optimization. Numerical tests also showed local solvers which attained optimal solutions quickly but may be trapped in a local optimum. [ABSTRACT FROM AUTHOR]

The refined oil transportation problem investigated in this paper lies on the intersection of the scheduling and routing of tramp shipping and the petroleum supply chain, with unprecedented large-scale and complex rules. Two mixed-integer linear programming formulations are developed for the assignment between tasks, vessels, and timing issues. The first model uses a time-slot concept under a continuous-time representation, where the constraints that deal with vessel assignment, capacity, timing, demand, and slack stock control are considered. The second model uses a discrete-time representation with time assignment, portal counting, and strict stock control constraints. By virtue of the data collected from an oil company, this modeling approach is validated and used to generate feasible scheduling solutions with lower costs than are currently achieved in the real situation. Finally, the impact of the model parameters is analyzed under different optimization scenarios. [ABSTRACT FROM AUTHOR]

Optimization under uncertainty has been an active area of research for many years. However, its application in Process Systems Engineering has faced a number of important barriers that have prevented its effective application. Barriers include availability of information on the uncertainty of the data (ad-hoc or historical), determination of the nature of the uncertainties (exogenous vs. endogenous), selection of an appropriate strategy for hedging against uncertainty (robust/chance constrained optimization vs. stochastic programming), large computational expense (often orders of magnitude larger than deterministic models), and difficulty of interpretation of the results by non-expert users. In this paper, we describe recent advances that have addressed some of these barriers for mostly linear models. [ABSTRACT FROM AUTHOR]

In this paper, the problem of how to efficiently operate a natural gas transmission network under steady-state assumptions is considered. The problem is modeled as a nonlinear network optimization problem where the decision variables are mass flow rate in each arc and gas pressure in each node. The objective function to be minimized is the total amount of fuel consumed in the system by the compressor stations. In the past, several techniques ranging from classical gradient-based procedures to dynamic programming, for solving this difficult nonconvex problem have been applied with limited success, particularly when applied to cyclic network topologies. A cyclic system is defined as a network containing at least one cycle involving two or more compressor stations. In this paper we propose a hybrid metaheuristic procedure that efficiently exploits the problem structure. This hybrid procedure combines very effectively a nonsequential dynamic programming algorithm for finding an optimal set of pressure variables for a fixed set of mass flow rate varables, and short-term memory tabu search procedure for guiding the search in the flow variable space. The proposed procedure represents an improvement to the best existing approach to the best of our knowledge. In addition, empirical evidence over a number of instances supports the effectiviness of the proposed procedure outperforming a multi-start GRG method both in terms of solution quality and feasibility. Furthermore, to assess the quality of the solutions obtained by the algorithm, a lower bound is derived. It is found that the solution quality obtained by the proposed procedure is relatively good. [Copyright &y& Elsevier]

This work studies the supply allocation problem, using a Stackelberg game, for an established timberlands supply chain with an additional decision of new biorefinery investments. In a timberlands system, harvester and manufacturer decision makers have separate objectives to maximize their respective profits. This interaction is represented with a turn based Stackelberg game. The harvesters decide first on the quantity harvested, and the manufacturers decide on how much to utilize. This game is modeled with a bilevel mathematical program. The novel feature of this paper's bilevel formulation is the inclusion of parametric uncertainty in a two stage model. The first stage problem involves logistical decisions around biorefinery investments, such as location and capacity, while the second stage problem involves a bilevel timberlands model with parameter uncertainty. Studying this problem formulation revealed interesting insights for solving multiperiod problems with bilevel stages as well as the decision maker's behavior for the timberlands model. [ABSTRACT FROM AUTHOR]

Safety and performance are important factors in the design and operation of chemical plants. This paper describes the formulation of a mixed integer nonlinear programming model for the optimization of plant layout with safety considerations. The model considers a quantitative risk analysis to take safety into account, and a bowtie analysis is used to identify possible catastrophic outcomes. These effects are quantified through consequence analyses and probit models. The model allows the location of facilities at any available point, an advantage over grid-based models. Two case studies are solved to show the applicability of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: This article describes the key challenges and opportunities in modeling and optimization of biomass-to-bioenergy supply chains. It reviews the major energy pathways from terrestrial and aquatic biomass to bioenergy/biofuel products as well as power and heat with an emphasis on “drop-in” liquid hydrocarbon fuels. Key components of the bioenergy supply chains are then presented, along with a comprehensive overview and classification of the existing contributions on biofuel/bioenergy supply chain optimization. This paper identifies fertile avenues for future research that focuses on multi-scale modeling and optimization, which allows the integration across spatial scales from unit operations to biorefinery processes and to biofuel value chains, as well as across temporal scales from operational level to strategic level. Perspectives on future biofuel supply chains that integrate with petroleum refinery supply chains and/or carbon capture and sequestration systems are presented. Issues on modeling of sustainability and the treatment of uncertainties in bioenergy supply chain optimization are also discussed. [Copyright &y& Elsevier]

Abstract: An important and challenging problem is the determination of appropriate control structures that minimize the loss of process performance under the effect of uncertainties. This can be achieved by selecting subsets of controlled and manipulated variables and designing their interconnection. In this paper, a systematic optimization methodology for the Control Structure Selection Problem (CSSP) is presented. The proposed formulation (a) improves the accuracy of calculations and (b) reduces computational time and effort necessary. Specifically, the error involved in the approximation of the nonlinear constraint that defines the magnitude of the back-off vector is reduced by the introduction of a more accurate linear approximation. In addition, the methodology is able to handle simultaneously occurring disturbances and estimate their worst impact on process economics. The computational time is significantly reduced by eliminating the state variables from the final formulation. Two case studies are presented to demonstrate the benefits of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: LNG liquefaction is an energy-intensive process. Energy efficiency is the major concern in LNG liquefaction process design and operation. In this paper, a new methodology for LNG liquefaction synthesis targeting energy consumption minimization is presented. It is based on thermodynamic analysis, mathematical programming, and rigorous simulation. The procedure for MINLP (mixed-integer non-linear programming) model development and simplification is described in detail. LINDOGlobal solver in GAMS is employed to solve the MINLP problem and the optimization results are further validated through rigorous simulations. Based on the development, the optimal design and operational conditions for LNG liquefaction process can be simultaneously achieved. A C3MR LNG liquefaction process is employed to demonstrate the efficacy of the developed methodology. Comprehensive thermodynamic analysis is also conducted to give insights of the optimization results. [Copyright &y& Elsevier]

Abstract: This paper presents a new mathematical programming model for the optimal synthesis of recycle and reuse networks considering simultaneously the integration of the water network system and the surrounding watershed to satisfy process and environmental constraints. The model considers the optimal location of the new industrial facility to integrate its wastewater discharge to the environment with the surrounding watershed through a disjunctive formulation. The pollutants discharged for the new plant are tracked simultaneously with the other discharges to the watershed (i.e., residential, sanitary, industrial and extractions), and the natural phenomena that affect the composition of the watershed (i.e., evaporation, filtration, etc.), in addition to the chemical reactions that are carried out in the rivers. The objective function consists in minimizing the total annual cost that is constituted by the installation of the new plant cost (including the transportation for raw materials, products and services, as well as the land cost), the wastewater treatment costs (including the piping cost) and the fresh sources cost. Two example problems were used to show the applicability of the proposed methodology. [Copyright &y& Elsevier]

Abstract: Bioprocesses are of growing importance as an avenue to produce chemicals. Microorganisms containing only desired catalytic and replication capabilities in their metabolic pathways are expected to offer efficient processes for chemical production. Realizing such minimal cells is the holy grail of metabolic engineering. In this paper, we propose a new method that combines graph-theoretic approaches with mixed-integer liner programming (MILP) to design metabolic networks with minimal reactions. Existing MILP based computational approaches are computationally complex especially for large networks. The proposed graph-theoretic approach offers an efficient divide-and-conquer strategy using the MILP formulation on sub-networks rather than considering the whole network monolithically. In addition to the resulting improvement in computational complexity, the proposed method also aids in identifying the key reactions to be knocked-out in order to achieve the minimal cell. The efficacy of the proposed approach is demonstrated using three case studies from two organisms, Escherichia coli and Saccharomyces cerevisiae. [Copyright &y& Elsevier]

Abstract: Sustainability has recently emerged as a key issue in process systems engineering (PSE). Mathematical programming techniques offer a general modeling framework for including environmental concerns in the synthesis and planning of chemical processes. In this paper, we review major contributions in process synthesis and supply chain management, highlighting the main optimization approaches that are available, including the handling of uncertainty and the multi-objective optimization of economic and environmental objectives. Finally, we discuss challenges and opportunities identified in the area. [Copyright &y& Elsevier]

Abstract: The paper examines the applicability of mathematical programming methods to the simultaneous optimization of the structure and the operational parameters of a combined-cycle-based cogeneration plant. The optimization problem is formulated as a nonconvex mixed-integer nonlinear problem (MINLP) and solved by the MINLP solver LaGO. The algorithm generates a convex relaxation of the MINLP and applies a Branch and Cut algorithm to the relaxation. Numerical results for different demands for electric power and process steam are discussed and a sensitivity analysis is performed. [Copyright &y& Elsevier]

Abstract: In this paper, a novel systematic model-based methodology for performing integrated process design and controller design (IPDC) for chemical processes is presented. The methodology uses a decomposition method to solve the IPDC typically formulated as a mathematical programming (optimization with constraints) problem. Accordingly the optimization problem is decomposed into four sub-problems: (i) pre-analysis, (ii) design analysis, (iii) controller design analysis, and (iv) final selection and verification, which are relatively easier to solve. The methodology makes use of thermodynamic-process insights and the reverse design approach to arrive at the final process design–controller design decisions. The developed methodology is illustrated through the design of: (a) a single reactor, (b) a single separator, and (c) a reactor–separator-recycle system and shown to provide effective solutions that satisfy design, control and cost criteria. The advantage of the proposed methodology is that it is systematic, makes use of thermodynamic-process knowledge and provides valuable insights to the solution of IPDC problems in chemical engineering practice. [Copyright &y& Elsevier]

Abstract: Extended mathematical programs are collections of functions and variables joined together using specific optimization and complementarity primitives. This paper outlines a mechanism to describe such an extended mathematical program by means of annotating the existing relationships within a model to facilitate higher level structure identification. The structures, which often involve constraints on the solution sets of other models or complementarity relationships, can be exploited by modern large scale mathematical programming algorithms for efficient solution. A specific implementation of this framework is outlined that communicates structure from the GAMS modeling system to appropriate solvers in a computationally beneficial manner. Example applications are taken from chemical engineering. [Copyright &y& Elsevier]

Abstract: In this paper we present a multi-period mixed integer linear programming model for the simultaneous planning and scheduling of single-stage multi-product continuous plants with parallel units. While effective for short time horizons, the proposed scheduling model becomes computationally expensive to solve for long time horizons. In order to address this problem, we propose a bi-level decomposition algorithm in which the original problem is decomposed into an upper level planning and a lower level scheduling problem. For the representation of the upper level, we propose an MILP model which is based on a relaxation of the original model, but accounts for the effects of scheduling by incorporating sequencing constraints, which results in very tight upper bounds. In the lower level the simultaneous planning and scheduling model is solved for a subset of products predicted by the upper level. These sub-problems are solved iteratively until the upper and lower bounds converge. A number of examples are presented that show that the planning model can often obtain the optimal schedule in one single iteration. [Copyright &y& Elsevier]

Abstract: In this paper, mathematical programming coupled with superstructure is utilized to optimize regeneration recycling water networks at the stage of grass-roots design. The optimization is virtually a multi-objective problem with several important parameters on regeneration recycling involved. Considering the relative importance of these parameters, sequential optimization is adopted to solve this multi-objective problem. Freshwater consumption, regenerated water flowrate and contaminant regeneration load, are in turn minimized, which correspond to three mathematical models. By solving these models step by step, a regeneration recycling water network can be constructed, which is economically favorable in terms of qualitative analysis. The complexity of water network configuration is also taken into account by minimizing the number of interconnections among processes. Additionally several examples are used to demonstrate the application of the proposed methodology. In comparison with the available technologies, the proposed methodology excels in simplicity and adaptability for grass-roots design by exempting from complicated and variable economic parameters. [Copyright &y& Elsevier]

Abstract: This paper presents a systematic method for optimal lumping of a large number of components in order to minimize the loss of information. In principle, a rigorous composition-based model is preferable to describe a system accurately. However, computational intensity and numerical issues restrict such applications in process modeling, simulation and design. A pseudo-component approach that lumps a large number of components in a system into a much smaller number of hypothetical groups reduces the dimensionality at the cost of losing information. Moreover, empirical and heuristic approaches are commonly used to determine the lumping scheme. Given an objective function defined with a linear weighting rule, an optimal lumping problem is formulated as a mixed integer nonlinear programming (MINLP) problem both in discrete and in continuous settings. A reformulation of the original problem is also presented, which significantly reduces the number of independent variables. The application to a system with 144 components demonstrates that the optimal lumping problem can be efficiently solved with a stochastic optimization method, Tabu Search (TS) algorithm. The case study also reveals that the discrete formulation is preferable due to the reduced search space compared to a continuous model formulation. [Copyright &y& Elsevier]

This paper presents a technique for simultaneous targeting and design in cooling water systems comprising of at least two cooling towers and several cooling water using operations. The presented technique is based on a superstructure from which a mathematical formulation is derived using system specific variables and parameters. It is demonstrated that in a system like this, true optimality can only be realized by a holistic consideration of the entire cooling water system. Consideration of individual subsets of cooling towers with their dedicated cooling water operations yields suboptimal results. Four operational cases are considered and structural considerations of corresponding mathematical formulations presented. The first case results in a linear programming (LP) formulation, the second case yields a mixed integer linear programming (MILP) formulation whilst the other two cases yield mixed integer nonlinear programming (MINLP) formulations which cannot be exactly linearized. However, in all cases significant improvements in excess of 40% were realized in targeting, without compromising the heat duty of the cooling water using operations. The main objective of this investigation is to debottleneck the overall cooling water supply for the cooling water network. [Copyright &y& Elsevier]

Abstract: Mathematical programming has long been recognized as a promising direction to the efficient solution of design, synthesis and operation problems that can gain industry the competitive advantage required to survive in today''s difficult economic environment. Most of the engineering design problems can be modelled as MINLP problems with stochastic parameters. In this paper a decomposition algorithm is presented to solve convex stochastic MINLP problems. The proposed approach is an extension of the simplicial approximation approach proposed by Goyal and Ierapetritou [Goyal, V., & Ierapetritou, M. G. (2004a). MINLP optimization using simplicial approx imation method for classes of non-convex problems. In C. A. Floudas, & P. M. Pardalos (Eds.), Frontiers in Global Optimization (p. 165). Goyal, V., & Ierapetritou, M. G. (2004b). Computational studies using a novel simplicial-approximation based algorithm for MINLP optimisation. Computers and Chemical Engineering, 28, 1771], for solving deterministic MINLP problems and is based on the idea of representing the feasible region by a close approximation of its convex hull. Two case studies are presented illustrating the applicability and efficiency of the proposed approach. [Copyright &y& Elsevier]

This paper treats the solution of nonlinear optimization problems involving discrete decision variables, also known as generalized disjunctive programming (GDP) or mixed-integer nonlinear programming (MINLP) problems, that arise in process engineering. The key idea is to eliminate the discrete decision variables by adding a set of continuous variables and constraints that represent the discrete decision space of the optimization problem. With such a reformulation, we are able to apply solution algorithms for purely continuous nonlinear optimization problems to efficiently calculate local minima of GDP or MINLP problems. In this contribution, we propose different alternatives to reformulate GDP/MINLP problems as continuous optimization problems. We furthermore investigate theoretical properties of the different reformulations with regard to their numerical solution. The proposed formulations are illustrated and analyzed on the basis of optimization problems dealing with process engineering applications involving stationary as well as dynamic process models. [Copyright &y& Elsevier]

A new approach for the optimisation of steam levels of total site utility systems satisfying varying utility demands is presented, accounting for interactions between total site utility systems and chemical processes. The optimisation problem involves the selection of the steam levels with respect to their temperatures. In this paper, by exploiting total site analysis techniques, a new transhipment network is developed to represent the heat flows of a total site. Base on the transhipment network representation of the total site, a general multi-period mixed-integer linear programming (MILP) model is presented for identifying the optimal steam levels of the total site utility system. By using engineering and thermodynamic knowledge, a boiler hardware model (BHM) is developed to describe the performance of boilers, and the turbine hardware model (THM) is applied for the shaft-work targeting of steam turbines. Both models are capable of predicting the real efficiency trends of the units. The application of the proposed optimisation approach is illustrated through two case studies including single operation scenario and multiple operation scenarios. [Copyright &y& Elsevier]

This paper presents a general mathematical programming formulation for the multi-floor process plant layout problem, which considers a number of cost and management/engineering drivers within the same framework thus resolving various trade-offs at an optimal manner. The proposed model determines simultaneously the number of floors, land area, floor allocation of each equipment item and detailed layout for each floor. The overall problem is formulated as a mixed integer linear programming (MILP) model based on a continuous domain representation. The applicability of the model is demonstrated by three illustrative examples. [Copyright &y& Elsevier]