Scheduling of crude oil operations under demand uncertainty: A robust optimization framework coupled with global optimization

Scheduling of crude oil operations is an important component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transform the problem into a challenging, nonconvex, mixed‐integer nonlinear programming (MINLP) optimization model. In practice, uncertainties are unavoidable and include demand fluctuations, ship arrival delays, equipment malfunction, and tank unavailability. In the presence of these uncertainties, an optimal schedule generated using nominal parameter values may often be suboptimal or even become infeasible. In this article, the robust optimization framework proposed by Lin et al. and Janak et al. is extended to develop a deterministic robust counterpart optimization model for demand uncertainty. The recently proposed branch and bound global optimization algorithm with piecewise‐linear underestimation of bilinear terms by Li et al. is also extended to solve the nonconvex MINLP deterministic robust counterpart optimization model and generate robust schedules. Two examples are used to illustrate the capability of the proposed robust optimization approach, and the extended branch and bound global optimization algorithm for demand uncertainty. The computational results demonstrate that the obtained schedules are robust in the presence of demand uncertainty. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2373–2396, 2012     

Continuous‐time modeling and global optimization approach for scheduling of crude oil operations

Scheduling of crude oil operations is a critical and complicated component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. Moreover, blending with less expensive crudes can significantly increase profit margins. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transforms the problem into a challenging, nonconvex, and mixed‐integer nonlinear programming (MINLP) optimization model. Two primary contributions have been made. First, the authors developed a novel unit‐specific event‐based continuous‐time MINLP formulation for this problem. Then they incorporated realistic operational features such as single buoy mooring (SBM), multiple jetties, multiparcel vessels, single‐parcel vessels, crude blending, brine settling, crude segregation, and multiple tanks feeding one crude distillation unit at one time and vice versa. In addition, 15 important volume‐based or weight‐based crude property indices are also considered. Second, they exploited recent advances in piecewise‐linear underestimation of bilinear terms within a branch‐and‐bound algorithm to globally optimize the MINLP problem. It is shown that the continuous‐time model results in substantially fewer bilinear terms. Several examples taken from the work of Li et al. are used to illustrate that (1) better solutions are obtained and (2) ε‐global optimality can be attained using the proposed branch‐and‐bound global optimization algorithm with piecewise‐linear underestimations of the bilinear terms. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Global superstructure optimization for the design of integrated process water networks

We propose a general superstructure and a model for the global optimization for integrated process water networks. The superstructure consists of multiple sources of water, water‐using processes, wastewater treatment, and pre‐treatment operations. Unique features are that all feasible interconnections are considered between them and multiple sources of water can be used. The proposed model is formulated as a nonlinear programing (NLP) and as a mixed integer nonlinear programing (MINLP) problem for the case when 0–1 variables are included for the cost of piping and to establish optimal trade‐offs between cost and network complexity. To effectively solve the NLP and MINLP models to global optimality we propose tight bounds on the variables, which are expressed as general equations. We also incorporate the cut proposed by Karuppiah and Grossmann to significantly improve the strength of the lower bound for the global optimum. The proposed model is tested on several examples. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Operational strategy and planning for raw natural gas refining complexes: Process modeling and global optimization

Optimal operational strategy and planning of a raw natural gas refining complex (RNGRC) is very challenging since it involves highly nonlinear processes, complex thermodynamics, blending, and utility systems. In this article, we first propose a superstructure integrating a utility system for the RNGRC, involving multiple gas feedstocks, and different product specifications. Then, we develop a large‐scale nonconvex mixed‐integer nonlinear programming (MINLP) optimization model. The model incorporates rigorous process models for input and output relations based on fundamentals of thermodynamics and unit operations and accurate models for utility systems. To reduce the noncovex items in the proposed MINLP model, equivalent reformulation techniques are introduced. Finally, the reformulated nonconvex MINLP model is solved to global optimality using state of the art deterministic global optimization approaches. The computational results demonstrate that a significant profit increase is achieved using the proposed approach compared to that from the real operation. © 2016 American Institute of Chemical Engineers AIChE J, 63: 652–668, 2017     

Integrated gasoline blending and order delivery operations: Part I. short‐term scheduling and global optimization for single and multi‐period operations

Gasoline is one of the most valuable products in an oil refinery and can account for as much as 60–70% of total profit. Optimal integrated scheduling of gasoline blending and order delivery operations can significantly increase profit by avoiding ship demurrage, improving customer satisfaction, minimizing quality give‐aways, reducing costly transitions and slop generation, exploiting low‐quality cuts, and reducing inventory costs. In this article, we first introduce a new unit‐specific event‐based continuous‐time formulation for the integrated treatment of recipes, blending, and scheduling of gasoline blending and order delivery operations. Many operational features are included such as nonidentical parallel blenders, constant blending rate, minimum blend length and amount, blender transition times, multipurpose product tanks, changeovers, and piecewise constant profiles for blend component qualities and feed rates. To address the nonconvexities arising from forcing constant blending rates during a run, we propose a hybrid global optimization approach incorporating a schedule adjustment procedure, iteratively via a mixed‐integer programming and nonlinear programming scheme, and a rigorous deterministic global optimization approach. The computational results demonstrate that our proposed formulation does improve the mixed‐integer linear programming relaxation of Li and Karimi, Ind. Eng. Chem. Res., 2011, 50, 9156–9174. All examples are solved to be 1%‐global optimality with modest computational effort. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2043–2070, 2016     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

Data‐driven mathematical modeling and global optimization framework for entire petrochemical planning operations

In this work we develop a novel modeling and global optimization‐based planning formulation, which predicts product yields and properties for all of the production units within a highly integrated refinery‐petrochemical complex. Distillation is modeled using swing‐cut theory, while data‐based nonlinear models are developed for other processing units. The parameters of the postulated models are globally optimized based on a large data set of daily production. Property indices in blending units are linearly additive and they are calculated on a weight or volume basis. Binary variables are introduced to denote unit and operation modes selection. The planning model is a large‐scale non‐convex mixed integer nonlinear optimization model, which is solved to ε‐global optimality. Computational results for multiple case studies indicate that we achieve a significant profit increase (37–65%) using the proposed data‐driven global optimization framework. Finally, a user‐friendly interface is presented which enables automated updating of demand, specification, and cost parameters. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3020–3040, 2016     

Global optimization for sustainable design and synthesis of algae processing network for CO2 mitigation and biofuel production using life cycle optimization

Global optimization for sustainable design and synthesis of a large‐scale algae processing network under economic and environmental criteria is addressed. An algae processing network superstructure including 7800 processing routes is proposed. Based on the superstructure, a multiobjective mixed‐integer nonlinear programming (MINLP) model is developed to simultaneously optimize the unit cost and the unit global warming potential (GWP). To efficiently solve the nonconvex MINLP model with separable concave terms and mixed‐integer fractional terms in the objective functions, a global optimization strategy that integrates a branch‐and‐refine algorithm based on successive piecewise linear approximations is proposed and an exact parametric algorithm based on Newton's method. Two Pareto‐optimal curves are obtained for biofuel production and biological carbon sequestration, respectively. The unit annual biofuel production cost ranges from $7.02/gasoline gallon equivalent (GGE) to $9.71/GGE, corresponding to unit GWP's of 26.491 to 16.52 kg CO₂‐eq/GGE, respectively. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3195–3210, 2014     

Global optimization of large‐scale mixed‐integer linear fractional programming problems: A reformulation‐linearization method and process scheduling applications

Mixed‐integer linear fractional program (MILFP) is a class of mixed‐integer nonlinear programs (MINLP) where the objective function is the ratio of two linear functions and all constraints are linear. Global optimization of large‐scale MILFPs can be computationally intractable due to the presence of discrete variables and the pseudoconvex/pseudoconcave objective function. We propose a novel and efficient reformulation–linearization method, which integrates Charnes–Cooper transformation and Glover's linearization scheme, to transform general MILFPs into their equivalent mixed‐integer linear programs (MILP), allowing MILFPs to be globally optimized effectively with MILP methods. Extensive computational studies are performed to demonstrate the efficiency of this method. To illustrate its applications, we consider two batch scheduling problems, which are modeled as MILFPs based on the continuous‐time formulations. Computational results show that the proposed approach requires significantly shorter CPU times than various general‐purpose MINLP methods and shows similar performance than the tailored parametric algorithm for solving large‐scale MILFP problems. Specifically, it performs with respect to the CPU time roughly a half of the parametric algorithm for the scheduling applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4255–4272, 2013     

Decomposition strategy for the global optimization of flexible energy polygeneration systems

The optimal design and operation of flexible energy polygeneration systems using coal and biomass to coproduce power, liquid fuels, and chemicals are investigated. This problem is formulated as a multiperiod optimization problem, which is a potentially large‐scale nonconvex mixed‐integer nonlinear program (MINLP) and cannot be solved to global optimality by state‐of‐the‐art global optimization solvers, such as BARON, within a reasonable time. A duality‐based decomposition method, which can exploit the special structure of this problem, is applied. In this work, the decomposition method is enhanced by the introduction of additional dual information for faster convergence. The enhanced decomposition algorithm (EDA) guarantees to find an ε‐optimal solution in a finite time. The case study results show that the EDA achieves much faster convergence than both BARON and the original decomposition algorithm, and it solved the large‐scale nonconvex MINLPs to ε‐optimality in practical times. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3080–3095, 2012     

A mathematical programming approach for cyclic production and cleaning scheduling of multistage continuous plants

The objective of this paper is to address the cyclic scheduling of cleaning and production operations in multiproduct multistage plants with performance decay. A mixed-integer nonlinear programming (MINLP) model based on continuous time representation is proposed that can simultaneously optimize the production and cleaning scheduling. The resulting mathematical model has a linear objective function to be maximized over a convex solution space thus allowing globally optimal solutions to be obtained with an outer approximation algorithm. Case studies demonstrate the applicability of the model and its potential benefits in comparison with a hierarchical procedure for the production and cleaning scheduling problem.     

Fair profit allocation in supply chain optimization with transfer price and revenue sharing: MINLP model and algorithm for cellulosic biofuel supply chains

A mixed‐integer nonlinear programming (MINLP) formulation to simultaneously optimize operational decisions as well as profit allocation mechanisms in supply chain optimization, namely material transfer prices and revenue share policies among the supply chain participants is proposed. The case of cellulosic bioethanol supply chains is specifically considered and the game‐theory Nash bargaining solution approach is employed to achieve fair allocation of profit among the collection facilities, biorefineries, and distribution centers. The structural advantages of certain supply chain participants can be taken into account by specifying different values of the negotiation‐power indicators in the generalized Nash‐type objective function. A solution strategy based on a logarithm transformation and a branch‐and‐refine algorithm for efficient global optimization of the resulting nonconvex MINLP problem is proposed. To demonstrate the application of the proposed framework, an illustrative example and a state‐wide county‐level case study on the optimization of a potential cellulosic bioethanol supply chain in Illinois are presented. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3211–3229, 2014     

Optimal design of reverse-osmosis networks for wastewater treatment

An optimization study of reverse-osmosis networks (RON) for wastewater treatment has been carried out by describing the system as a nonconvex mixed-integer nonlinear problem (MINLP). A mixed-integer linear problem (MILP) is derived from the original nonlinear problem by the convex relaxation of the nonconvex terms in the MINLP to provide bounds for the global optimum. The MILP model is solved iteratively to supply different initial guesses for the nonconvex MINLP model. It is found that such a procedure is effective in finding local optimum solutions in reasonable time and overcoming possible convergence difficulties associated with MINLP local search methods. Examples of water desalination and wastewater treatment from the pulp and paper industry are considered as case studies to illustrate the proposed solution strategy.     

Centralized–decentralized optimization for refinery scheduling

This paper presents a novel decomposition strategy for solving large scale refinery scheduling problems. Instead of formulating one huge and unsolvable MILP or MINLP for centralized problem, we propose a general decomposition scheme that generates smaller sub-systems that can be solved to global optimality. The original problem is decomposed at intermediate storage tanks such that inlet and outlet streams of the tank belong to the different sub-systems. Following the decomposition, each decentralized problem is solved to optimality and the solution to the original problem is obtained by integrating the optimal schedule of each sub-systems. Different case studies of refinery scheduling are presented to illustrate the applicability and effectiveness of the proposed decentralized strategy. The conditions under which these two types of optimization strategies (centralized and decentralized) give the same optimal result are discussed.     

A new superstructure optimization paradigm for process synthesis with product distribution optimization: Application to an integrated shale gas processing and chemical manufacturing process

We propose a novel process synthesis framework that combines product distribution optimization of chemical reactions and superstructure optimization of the process flowsheet. A superstructure with a set of technology/process alternatives is first developed. Next, the product distributions of the involved chemical reactions are optimized to maximize the profits of the effluent products. Extensive process simulations are then performed to collect high‐fidelity process data tailored to the optimal product distributions. Based on the simulation results, a superstructure optimization model is formulated as a mixed‐integer nonlinear program (MINLP) to determine the optimal process design. A tailored global optimization algorithm is used to efficiently solve the large‐scale nonconvex MINLP problem. The resulting optimal process design is further validated by a whole‐process simulation. The proposed framework is applied to a comprehensive superstructure of an integrated shale gas processing and chemical manufacturing process, which involves steam cracking of ethane, propane, n‐butane, and i‐butane. © 2017 American Institute of Chemical Engineers AIChE J, 63: 123–143, 2018     

Sensor network design for maximizing process efficiency: An algorithm and its application

Sensor network design (SND) is a constrained optimization problem requiring systematic and effective solution algorithms for determining where best to locate sensors. A SND algorithm is developed for maximizing plant efficiency for an estimator‐based control system while simultaneously satisfying accuracy requirements for the desired process measurements. The SND problem formulation leads to a mixed integer nonlinear programming (MINLP) optimization that is difficult to solve for large‐scale system applications. Therefore, a sequential approach is developed to solve the MINLP problem, where the integer problem for sensor selection is solved using the genetic algorithm while the nonlinear programming problem including convergence of the “tear stream” in the estimator‐based control system is solved using the direct substitution method. The SND algorithm is then successfully applied to a large scale, highly integrated chemical process. © 2014 American Institute of Chemical Engineers AIChE J, 61: 464–476, 2015     

Optimization of large‐scale water transfer networks: Conic integer programming model and distributed parallel algorithms

The optimization of a multi‐echelon water transfer network (WTN) and the associate transportation and inventory systems with demand uncertainty is addressed in article. Optimal network structure, facility locations, operation capacities, as well as the inventory and transportation decisions can be simultaneously determined by the mixed integer nonlinear programming (MINLP) model which includes bilinear, square root and nonlinear fractional terms. By exploiting the properties of this model, we reformulate the MINLP problem as a conic integer optimization model. To overcome the memory and computing bandwidth limitations caused by the huge number of active nodes in the branch‐and‐bound search tree, novel distributed parallel optimization algorithms based on Lagrangean relaxation and message passing interface as well as their serial versions are proposed to solve the resulting conic integer programming model. A regional WTN in China is studied to demonstrate the applicability of the proposed model and the performance of the algorithms. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1566–1581, 2017     

Integrated Scheduling and Dynamic Optimization of Sequential Batch Processes with Online Implementation

An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed‐integer dynamic optimization problem or a large‐scale mixed‐integer nonlinear programming (MINLP) problem by discretizing the dynamic models. To reduce the computational complexity, we first decompose all dynamic models from the integrated problem, which is then approximated by a scheduling problem based on the flexible recipe. The recipe candidates are expressed by Pareto frontiers, which are determined offline by using multiobjective dynamic optimization to minimize the processing cost and processing time. The operational recipe is then optimized simultaneously with the scheduling decisions online. Because the dynamic models are encapsulated by the Pareto frontiers, the online problem is a mixed‐integer programming problem which is much more computationally efficient than the original MINLP problem, and allows the online implementation to deal with uncertainties. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2379–2406, 2013     

Simultaneous mixed-integer dynamic optimization for environmentally benign electroplating

Hoist scheduling, especially cyclic hoist scheduling (CHS), is used to maximize the manufacturing productivity of electroplating processes. Water-reuse network design (WRND) for the electroplating rinsing system targets the optimal water allocation, such that fresh water consumption and wastewater generation are minimized. Currently, there is still a lack of studies on integrating CHS and WRND technologies for electroplating manufacturing. In this paper, a multi-objective mixed-integer dynamic optimization (MIDO) model has been developed to integrate CHS and WRND technologies for simultaneous consideration of productivity and water use efficiency for environmentally benign electroplating. The orthogonal collocation method on finite elements is employed to convert the MIDO problem into a mixed-integer nonlinear programming (MINLP) problem. The efficacy of the methodology is demonstrated by solving a real electroplating example. It demonstrates that the computational methods of production scheduling, process design, and dynamic optimization can be effectively integrated to create economic and environmental win-win situations for the electroplating industry.     

Optimization-based design of reactive distillation columns using a memetic algorithm

The design optimization of reactive distillation columns (RDC) is characterized by complex nonlinear constraints, nonlinear cost functions, and the presence of many local optima. The standard approach is to use MINLP solvers that work on a superstructure formulation where structural decisions are represented by discrete variables and lead to an exponential increase in the computational effort. The mathematical programming (MP) methods which solve the continuous sub-problems provide only one local optimum which depends strongly on the initialization. In this contribution a memetic algorithm (MA) is introduced and applied to the global optimization of four different formulations of a computational demanding real-world design problem. An evolution strategy addresses the global optimization of the design decisions, while continuous sub-problems are efficiently solved by a robust MP solver. The MA is compared to MINLP techniques. It is the only algorithm that finds the global solution in reasonable times for all model formulations.