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• A mathematical model is proposed for tissue paper drying process. • The model realizes the accurate simulation of key parameters in the drying process. • The model provides global optimization scheme for key operating parameters. • The model improves the competitiveness by reducing 8.72% of the drying cost. The drying process accounts for the largest proportion of energy consumption in paper mills. Energy system optimization has a great significance for reducing the energy consumption of the paper drying process. The drying process is a complex system that consists of several subsystems, such as cylinder and air hood systems. Previous optimization models for energy systems usually focused on these subsystems. A global optimization methodology for the entire drying process is lacking, and no existing models can be applied in practice. In this work, an energy system optimization model for the tissue paper drying process is proposed based on a process simulation model. The modeling process integrates the various subsystems and fully considers the coupling of the paper drying process, which greatly enhances the industrial application value of the model. Industrial operating data are used to test the simulation model, and the results show that the simulation error of each key variable is within 5%, which meets the real-world production requirements and lays the foundation for an energy efficiency analysis of each subsystem. Applying the optimization model to a tissue paper mill, the results show that it can reduce drying costs by 8.71%. [ABSTRACT FROM AUTHOR]

• A new generic approach in global optimization using cutting plane decomposition. • Use of AI in outer approximation and equality relaxation problems. • Data-enabled lower space decomposition methods in non-convex optimization formulations. • Development of a new metric (affinity) to assess and screen cutting planes. • Significant improvements (40-80%) in closing duality gaps in non-convex quadratic problems. Data-driven technologies have demonstrated their potential on various scientific and industrial applications. Their use in the development of generic optimization algorithms is relatively unexplored. The paper presents such an application to design a global optimization algorithm that is generic and suitable to address quadratic box constraint problems. The new method reformulates cutting plane decomposition methods substituting the solution of the master problem by a data-driven selection of cutting planes. The paper presents the theoretical background, data technologies used and computational results that compare the new against state-of-the-art methods. Computational experiments include 100 quadratic programming (QP) problems featuring a wide range of density (25-75%), size (40-100 variables), and complexity. Results are particularly encouraging and demonstrate significant reductions in the duality gap, as high as 40-60% scope on average. Largest improvements are traced in larger formulations (over 100 variables, 75% density). The research is based solely on data produced at a particular iteration. Future work is intended to extend the analysis comparing and considering data patterns across different iterations, also to apply the methodology in other classes of optimization problems. [ABSTRACT FROM AUTHOR]

This paper addresses the design and planning of manufacturing networks considering the option of centralized and distributed facilities, taking into account the potential trade-offs between investments and transportation. The problem is formulated as an extension of the Capacitated Multi-facility Weber Problem, which involves the selection of which facilities to build in each time period, and their location in the continuous two-dimensional space, in order to meet demand and minimize costs. The model is a multi-period GDP, reformulated as a nonconvex MINLP. We propose an accelerated version of the Bilevel Decomposition by Lara et al. (2018) that finds stronger bounds in the decomposition scheme. We benchmark the performance of our algorithm against the original Bilevel Decomposition and commercial global solvers and show that our approach outperforms the others in all instances tested. Additionally, we illustrate the applicability of the proposed model and solution framework with a biomass supply chain case study. [ABSTRACT FROM AUTHOR]

Abstract: High performance processes should operate close to design boundaries and specification limits, while still guaranteeing robust performance without design constraint violations. Since design chemical process is operating close to tighter boundaries safely; much attention has been devoted to integrating design and control, in which the design decisions, dynamics, and control performance are considered simultaneously in some optimal fashion. However, rigorous methods for solving design and control simultaneously lead to challenging mathematical formulations which easily become computationally intractable. In an earlier paper of our group, a new mathematical methodology to reduce the combinatorial complexity of integrating design and control was introduced (). We showed that substantial problem size reduction can be achieved by embedding control for specific process designs. In this paper, we extend the embedded control methodologies to plantwide flowsheet. The case study for the reactor-column flowsheet will demonstrate the current capabilities of the methodology for integrating design and control under uncertainty. [Copyright &y& Elsevier]

Highlights • A self-adaptive differential evolution optimization method is proposed. • The proposed method enhances the convergence speed and the exploitation capabilities. • The performance of the proposed method outperforms the original differential evolution method. • The operational parameters in ES-SAGD process are optimized to achieve maximal NPV. Abstract Differential evolution (DE) algorithm has shown good performance in many optimization problems. However, its control parameters greatly affect its performance and require many trials to determine the optimum values of control parameters for each specific optimization problem. In this paper, we present a self-adaptive DE with a new adaptation technique to improve the solution quality as well as increase the speed of convergence with a reduction in the computational cost. The proposed approach, called modified self-adaptive differential evolution (MSaDE), employs a new success-rate indicator of the strategies used to generate the trial vectors in conventional self-adaptive differential evolution (SaDE) algorithm. The proposed method has been tested on 22 benchmark problems and on the expanded solvent steam-assisted gravity drainage (ES-SAGD) recovery process. The results show that a significant speed-up is achieved in the exploitation and exploration capabilities of the self-adaptive DE algorithm. [ABSTRACT FROM AUTHOR]

• 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]

In this paper, a new global optimization approach for the synthesis of heat exchanger networks is presented. The Synheat model by [Comp. Chem. Eng. 1 (1990) 1165] uses a promising superstructure that includes the most common heat exchanger structures, and optimizes utility costs, the number of units and heat exchanger areas simultaneously. With some minor modifications of the model, it is possible to apply a new global optimization strategy to the problem. The heart of the strategy is to convexify signomial terms, and create approximate convexified subproblems. If the Synheat model is extended in an appropriate way, the isothermal mixing assumption can be removed. Applying the new global optimization strategy to the model allowing non-isothermal mixing makes it possible to find truly optimal network configurations for the case of constant heat-capacity flow rates and heat transfer coefficients. Some examples to illustrate the global optimization strategy and to illustrate that the Synheat model can exclude optimal configurations due to the isothermal mixing assumption are also given in this paper. [Copyright &y& Elsevier]

In this paper, we present a brief overview of enterprise-wide optimization and challenges in multiscale temporal modeling and integration of different models for the levels of planning, scheduling and control. Next, we review Generalized Disjunctive Programming (GDP), as a new modeling paradigm for scheduling problems that are illustrated with the STN and RTN models. We then address scheduling problems that expand the scope of the area: simultaneous scheduling and heat integration, pipeline scheduling, crude oil and refined products blending, and demand side management. We illustrate the advantage of the GDP modeling framework, describe effective strategies for global optimization, and describe multistage affinely adjustable robust optimization for uncertain interruptible load. We address integration of planning and scheduling, for which several approaches are reviewed, including use of traveling salesman constraints for multiperiod refinery planning, and multisite planning and scheduling of multiproduct batch plants. We report computational results to highlight the challenges. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce a new generalized multiperiod scheduling version of the pooling problem to represent time varying blending systems. A general nonconvex MINLP formulation of the problem is presented. The primary difficulties in solving this optimization problem are the presence of bilinear terms, as well as binary decision variables required to impose operational constraints. An illustrative example is presented to provide unique insight into the difficulties faced by conventional MINLP approaches to this problem, specifically in finding feasible solutions. Based on recent work, a new radix-based discretization scheme is developed with which the problem can be reformulated approximately as an MILP, which is incorporated in a heuristic procedure and in two rigorous global optimization methods, and requires much less computational time than existing global optimization solvers. Detailed computational results of each approach are presented on a set of examples, including a comparison with other global optimization solvers. [Copyright &y& Elsevier]

Abstract: In this paper we present a strategy to improve the relaxation for the global optimization of non-convex MINLPs. The main idea consists in recognizing that each constraint or set of constraints has a meaning that comes from the physical interpretation of the problem. When these constraints are relaxed part of this meaning is lost. Adding redundant constraints that recover that physical meaning strengthens the relaxation. We propose a methodology to find such redundant constraints based on engineering knowledge and physical insight. [Copyright &y& Elsevier]

Abstract: This paper presents a discretize-then-relax method to construct convex/concave bounds for the solutions of a wide class of parametric nonlinear ODEs. The algorithm builds upon Taylor model methods recently developed for verified solution of parametric ODEs. To enable the propagation of convex/concave state bounds, a new type of Taylor model is introduced, in which convex/concave bounds for the remainder term are computed in addition to the usual interval bounds. At each time step, a two-phase procedure is applied: a priori convex/concave bounds that are valid over the entire time step are calculated in the first phase; then, pointwise-in-time convex/concave bounds at the end of the time step are obtained in the second phase. This algorithm is implemented in an object-oriented manner using templates and operator overloading. It is demonstrated and compared to other available approaches on a selection of problems from the literature. [Copyright &y& Elsevier]

Abstract: Environmental Protection Agency (EPA) Title 40 Code of Federal Regulations Part 80.45: Complex Emissions Model [40CFR80.45, 2007] codifies a mathematical model of gasoline emissions for reformulated gasoline (RFG) as a function of eleven fuel properties. In this paper we propose an extended pooling problem to maximize the profit of blending reformulated gasoline on a predetermined network structure of feed stocks, intermediate storage tanks, and gasoline products subject to applicable environmental standards. A mixed-integer nonlinear programming (MINLP) model is introduced which is nonconvex due to the presence of bilinear, polynomial, and fractional power terms. A mixed-integer linear programming (MILP) relaxation of the extended pooling problem is proposed and we introduce several test cases from small to medium to large scale and solve them to global optimality. The large-scale test case involves 14 feed stocks, 5 pools, and 10 products and consists of 1104 continuous variables, 150 binary variables, and 640 nonlinear terms. The nonconvexities in the large-scale case study include 410 bilinear terms, 40 polynomial terms, and 10 terms raised to a fractional power. [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: This paper is concerned with global optimization of Bilinear and Concave Generalized Disjunctive Programs. A major objective is to propose a procedure to find relaxations that yield strong lower bounds. We first present a general framework for obtaining a hierarchy of linear relaxations for nonconvex Generalized Disjunctive Programs (GDP). This framework combines linear relaxation strategies proposed in the literature for nonconvex MINLPs with the results of the work by for Linear GDPs. We further exploit the theory behind Disjunctive Programming by proposing several rules to guide more efficiently the generation of relaxations by considering the particular structure of the problems. Finally, we show through a set of numerical examples that these new relaxations can substantially strengthen the lower bounds for the global optimum, often leading to a significant reduction of the number of nodes when used within a spatial branch and bound framework. [Copyright &y& Elsevier]

Abstract: This paper addresses the optimal design and planning of sustainable chemical supply chains (SCs) in the presence of uncertainty in the damage model used to evaluate their environmental performance. The environmental damage is assessed through the Eco-indicator 99, which includes recent advances made in life cycle assessment (LCA). The overall problem is formulated as a bi-criterion stochastic non-convex mixed-integer nonlinear program (MINLP). The deterministic equivalent of such a model is obtained by reformulating the joint chance-constraint employed to calculate the environmental performance of the SC in the space of uncertain parameters. The resulting bi-criterion non-convex MINLP is solved by applying the epsilon constraint method. To guarantee the global optimality of the Pareto solutions found, we propose a novel spatial branch and bound method that exploits the specific structure of the problem. The capabilities of our modeling framework and the performance of the proposed solution strategy are illustrated through a case study. [Copyright &y& Elsevier]

Abstract: Canonical duality theory is a potentially powerful methodology, which can be used to model complex systems with a unified solution to a wide class of discrete and continuous problems in global optimization and nonconvex analysis. This paper presents a brief review and recent developments of this theory with applications to some well-know problems, including polynomial minimization, mixed integer and fractional programming, nonconvex minimization with nonconvex quadratic constraints, etc. Results shown that under certain conditions, these difficult problems can be solved by deterministic methods within polynomial times, and NP-hard discrete optimization problems can be transformed to certain minimal stationary problems in continuous space. Concluding remarks and open problems are presented in the end. [Copyright &y& Elsevier]

In this paper a new version of the Outer Approximation for Global Optimization Algorithm by Bergamini et al. [Bergamini, M.L., Aguirre, P., & Grossmann, I.E. (2005a). Logic based outer approximation for global optimization of synthesis of process networks. Computers and Chemical Engineering 29, 1914] is proposed, in order to speed up the convergence in nonconvex MINLP models that involve bilinear and concave terms. Bounding problems are constructed replacing these nonconvex terms by piecewise linear underestimators. These problems, which correspond to mixed-integer linear programs, are solved to generate approximate solutions with improved objective value. When no further feasible solution can be found, this guarantees that the upper bound cannot be improved in the nonconvex problem, thus providing a termination criterion. The new algorithm is applied to five different synthesis problems in the areas of water networks, heat exchanger networks and distillation sequences. The results show a significant reduction in the computational cost compared with the previous version of the algorithm. [Copyright &y& Elsevier]

Abstract: Signomial discrete programming (SDP) problems occur frequently in engineering design. This paper proposes a generalized method to solve SDP problems with free variables. An SDP problem with free variables is first converted into another one containing non-negative variables, and then various non-convex signomial terms are transformed such that the original SDP problem becomes a convex integer program solvable to obtain a globally optimal solution. Compared with current SDP methods, the proposed method is capable of dealing with free variables of an SDP problem and is guaranteed to converge to a global optimum. In addition, several computationally efficient convexification rules for signomial terms are presented to enhance the efficiency of the optimization approach. Numerical examples in real applications are presented to demonstrate the usefulness of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper presents an overview of the research progress in global optimization during the last 5 years (1998–2003), and a brief account of our recent research contributions. The review part covers the areas of (a) twice continuously differentiable nonlinear optimization, (b) mixed-integer nonlinear optimization, (c) optimization with differential-algebraic models, (d) optimization with grey-box/black-box/nonfactorable models, and (e) bilevel nonlinear optimization. Our research contributions part focuses on (i) improved convex underestimation approaches that include convex envelope results for multilinear functions, convex relaxation results for trigonometric functions, and a piecewise quadratic convex underestimator for twice continuously differentiable functions, and (ii) the recently proposed novel generalized BB framework. Computational studies will illustrate the potential of these advances. [Copyright &y& Elsevier]

Accurate nonlinear dynamic models of process operations such as start-ups and shut-downs include state-dependent events that trigger discrete changes to the describing equations, and are best analyzed within a hybrid systems framework. The automated design of an optimal process operation can thus be formulated as a dynamic optimization problem with a hybrid system embedded. This paper describes recent progress on the development of suitable deterministic algorithms for the global solution of these problems. A method for constructing convex relaxations of general nonconvex nonlinear programming (NLP) problems with linear dynamic systems embedded is presented. These convex relaxations are then extended to multistage problems with model switches between the stages. Finally, integer variables are introduced to represent alternative sequences of model switches. The ability to construct convex relaxations enables existing nonconvex mixed nonlinear programming (MINLP) algorithms to be applied to find the global solution of the resulting mixed integer dynamic optimization (MIDO) problems. [Copyright &y& Elsevier]

It is often possible to use different convexification techniques with different transformations in global optimization. In ‘Optimization Eng. (submitted for publication)’, a new global optimization technique based on convexifying signomial terms is presented. The technique is based on the solution of a sequence of convexified approximate subproblems. The choice of transformation functions is clearly essential. It is not enough to use convexifications that will result in convex and underestimating problems, if an effective optimization approach is wanted. The transformations should be such that they make the resulting problems convex but at the same time do not change the problem more than necessary. It will be shown in this article that for certain problems the choice of transformations has a clear influence on the efficiency of the proposed optimization approach. Using other transformations than what is proposed in ‘Optimization Eng. (submitted for publication)’ will, in some examples, give solution times that are shorter by an order of magnitude. The concept of power convex functions (Generalized Concavity Optimization Econ. (1981) 153) will be used as a measure of the quality of the transformations. In this paper, the new transformation functions are also shown to be very successful in a heat exchanger network synthesis application. [Copyright &y& Elsevier]

This paper presents a new method for multiphase equilibria calculation by direct minimization of the Gibbs free energy of multicomponent systems. The methods for multiphase equilibria calculation based on the equality of chemical potentials cannot guarantee the convergence to the correct solution since the problem is non-convex (with several local minima), and they can find only one for a given initial guess. The global optimization methods currently available are generally very expensive. A global optimization method called Tunneling, able to escape from local minima and saddle points is used here, and has shown to be able to find efficiently the global solution for all the hypothetical and real problems tested. The Tunneling method has two phases. In phase one, a local bounded optimization method is used to minimize the objective function. In phase two (tunnelization), either global optimality is ascertained, or a feasible initial estimate for a new minimization is generated. For the minimization step, a limited-memory quasi-Newton method is used. The calculation of multiphase equilibria is organized in a stepwise manner, combining phase stability analysis by minimization of the tangent plane distance function with phase splitting calculations. The problems addressed here are the vapor–liquid and liquid–liquid two-phase equilibria, three-phase vapor–liquid–liquid equilibria, and three-phase vapor–liquid–solid equilibria, for a variety of representative systems. The examples show the robustness of the proposed method even in the most difficult situations. The Tunneling method is found to be more efficient than other global optimization methods. The results showed the efficiency and reliability of the novel method for solving the multiphase equilibria and the global stability problems. Although we have used here a cubic equation of state model for Gibbs free energy, any other approach can be used, as the method is model independent. [Copyright &y& Elsevier]

The paper focuses on the refinery-wide planning operations under uncertainties in product demand and price via robust optimization framework coupled with global optimization. Industrial/simulation data sets are used to build explicit nonlinear surrogate models for correlating the yield/property of products and the operational conditions of secondary processing units. A large-scale nonconvex mixed integer nonlinear programming (MINLP) model is formulated. The product demand and sale price uncertainties are incorporated into the proposed model via the "interval" and "interval + ellipsoidal" uncertainty set, respectively, to obtain the robust counterpart optimization model. A global optimization framework which combines the enhanced normalized multiparametric disaggregation technique (ENMDT) and the optimality-based bound tightening is developed. The proposed model and the global optimization algorithm are applied to an industrial refinery site with three illustrative cases. The results show the value of formulating nonlinear models for secondary processing units and the benefits from applying ENMDT-based algorithm. [ABSTRACT FROM AUTHOR]

• Comprehensive consideration of all kinds of uncertainties in the refinery hydrogen systems to simulate the actual operation of hydrogen networks. • A holistic modeling framework which integrates stochastic programming with flexibility constraints to show different conservativeness toward multi-scale uncertainties. • A good trade-off between the economic performance and the robustness of operation. • A tailored global optimization algorithm based on multiparametric disaggregation technique that reduces the optimality gap by orders of magnitude for large-scale process network problems with numerous bilinear terms. • The quantification of the value of stochastic solution (VSS) as the key measure for assessing the benefits of the stochastic programming. Robust design of hydrogen systems for large-scale refineries under multi-scale uncertainties has great potential for energy saving and cost reduction. The operation of hydrogen network is greatly affected by the rapidly changing market, deteriorating crude feedstock and varying operating conditions. In this paper, we propose a two-stage stochastic programming with flexibility constraints modeling framework that accounts for multi-scale uncertainties in an integrated strategy, aiming to achieve a good trade-off between the economic performance and the robustness of operation. A tailored-made global optimization algorithm based on multiparametric disaggregation technique is developed to tackle the computational challenge of the resulting MINLP problem with numerous bilinear terms. To illustrate the applicability of the proposed modeling framework and solution algorithm, studies on the optimal design of an industrial hydrogen system are presented. Multi-scenario operation strategy increases the operational flexibility and greatly reduces the total annualized cost in terms of the value of stochastic solution. [ABSTRACT FROM AUTHOR]

• A disjunctive optimization model for shell and tube heat exchanger is developed. • The model includes automatically selection of heat transfer enhancement techniques. • Detailed geometrical components of exchanger can be obtained after optimization. • Optimal solutions include the investigation of local and global optimums. • Performance and benefits of proposed model are demonstrated. Heat transfer enhancement (HTE) is an efficient technology to improve the performance of shell and tube heat exchangers (STHEs). While there exist many commercial software packages, heat exchanger design still highly depends on users' experiences, resulting in long computing time and inferior solutions. Therefore, a systematic optimization methodology is required in order to achieve an efficient and accurate design solution. This paper presents a generalized disjunctive programming (GDP) model for the optimization of STHE design. It is formulated as a mixed integer non-linear programming (MINLP) problem, involving selection for 12 technology combinations (four tube-side techniques, three shell-side techniques), and all discrete decisions for each selection are modeled by disjunctions. The model is then applied to minimize the total capital cost. Both global optimization solver BARON, and general MINLP solver DICOPT are tested. The results show that the developed method provides a better design solution compared with conventional STHE design procedures. [ABSTRACT FROM AUTHOR]