Optimal storage design for a multi-product plant: A non-convex MINLP formulation

We discuss a tank design problem for a multi product plant, in which the optimal cycle time and the optimal campaign size are unknown. A mixed-integer nonlinear programming (MINLP) formulation is presented, where non-convexities are due to the tank investment cost, storage cost, campaign setup cost and variable production rates. The objective of the optimization model is to minimize the sum of the production cost per ton per product produced. A continuous-time mathematical programming formulation is proposed and several extensions are discussed. The model is implemented in GAMS and computational results are reported for the two global MINLP solver BARON and LINDOGlobal as well as several nonlinear solvers available in GAMS.     

Nonlinear robust optimization for process design

A novel robust optimization framework is proposed to address general nonlinear problems in process design. Local linearization is taken with respect to the uncertain parameters around multiple realizations of the uncertainty, and an iterative algorithm is implemented to solve the problem. Furthermore, the proposed methodology can handle different categories of problems according to the complexity of the problems. First, inequality‐only constrained optimization problem as studied in most existing robust optimization methods can be addressed. Second, the proposed framework can deal with problems with equality constraint associated with uncertain parameters. In the final case, we investigate problems with operation variables which can be adjusted according to the realizations of uncertainty. A local affinely adjustable decision rule is adopted for the operation variables (i.e., an affine function of the uncertain parameter). Different applications corresponding to different classes of problems are used to demonstrate the effectiveness of the proposed nonlinear robust optimization framework. © 2017 American Institute of Chemical Engineers AIChE J, 64: 481–494, 2018     

ϵ-OA for the solution of bi-objective generalized disjunctive programming problems in the synthesis of nonlinear process networks

There has been an increasing interest in multicriteria optimization (MCO) of nonlinear process network problems in recent years. Several mathematical models have been developed and solved using MCO methodologies including ϵ-constraint, weighted sum, and minimum distance. In this paper, we investigate the bi-objective nonlinear network synthesis problem and propose an effective algorithm, ϵ-OA, based on augmented ϵ-constraint and logic-based outer approximation (OA). We provide theoretical characterization of the proposed algorithm and show that the solutions generated are efficient. We illustrate the effectiveness of our novel algorithm on two benchmark problems. The ϵ-OA is compared to the straightforward use of OA with augmented ϵ-constraint algorithm (ϵ-con + OA), the augmented ϵ-constraint without OA (ϵ-MINLP), and the traditional ϵ-constraint (T-ϵ-con). Based on the results, our novel algorithm is very effective in solving the bi-objective generalized disjunctive programming problems in the synthesis of process networks.     

Membrane system design for multicomponent gas mixtures via mixed-integer nonlinear programming

An optimal design strategy for membrane networks separating multicomponent gas mixtures based on an approximate permeator model and mixed-integer nonlinear programming (MINLP) is proposed. A permeator system superstructure is used to embed a very large number of possible network configurations and allows the permeator feed-side pressure to be fixed or a design variable. A MINLP design model is developed to minimize the total annual process cost by simultaneous optimization of the permeator configuration and operating conditions. Case studies for the separation of acid gases (CO₂ and H₂S) from crude natural gas mixtures with spiral-wound permeators are presented. Permeator configurations are derived for different number of separation stages for both continuous and discrete membrane areas. The method is sufficiently robust to handle product compositions that vary five orders of magnitude. The proposed approach provides an efficient methodology for preliminary screening of multi-stage membrane separation systems for multicomponent gas mixtures.     

A novel MINLP-based representation of the original complex model for predicting gasoline emissions

The Environmental Protection Agency (EPA) introduced Reformulated Gasoline (RFG) requirements as a measure to reduce emissions from gasoline-powered vehicles in certain geographic areas. As part of this effort, the EPA developed empirical models for predicting emissions as a function of gasoline properties and established statutory baseline emissions from a representative set of gasolines. All reformulated gasoline requires certification via this model, known as the Complex Model, and all refiners and importers calculate emissions performance reductions from the statutory baseline gasoline. The current representation of the Complex Model is extremely difficult to implement within refinery operations models or to use in combination with models for designer gasoline. RFG and boutique fuels are key driving forces in the North American refining industry.The RFG models introduce increasingly complex constraints with the major limitation that they are implicitly defined through a series of complicated disjunctions assembled by the EPA in the form of spreadsheets. This implicit and cumbersome representation of the emissions predictive models renders rigorous optimization and sensitivity analysis very difficult to address directly. In this paper, we discuss how the federal government requirements for reformulated gasoline can be restated as a set of mixed-integer nonlinear programming (MINLP) constraints with the aid of disjunctive programming techniques. We illustrate the use of this model with two simple example fuel blending problems.     

Optimization-based method for calculating water networks with user specified characteristics

This paper addresses problem of designing water usage network that consists of fixed flow rate water using processes. A design method is founded on the solution of mixed-integer linear programming (MILP) model of network superstructure. The application of optimization to solve basic formulation of network synthesis has been reported in some works. However, this approach applies certain extensions of the standard formulation that allow accounting for several industrial scenarios. In particular, it is possible to apply various performance indices and imposing conditions on continuous variables as well as on network topology. Multiple contaminant case is easily accounted for. At least but not at last, the method is able to generate several solutions of identical values of major performance indices but of different structure and other features. All these possibilities are available within single optimization framework. Several examples are given to illustrate advantages of the approach.     

Combine operations research with molecular biology to stretch pharmacogenomics and personalized medicine—A case study on HIV/AIDS

The dramatic reduction in morbidity and mortality associated with the use of highly active antiretroviral therapy has created new challenges for clinicians: AIDS has become a chronic, potentially life-threatening, condition in many clinical instances. In this paper, a novel system engineering approach based on mixed-integer linear programming (MILP) is presented to support HIV/AIDS clinicians when formulating real-world therapeutic plans for heavily treatment-experienced patients under variable settings. Our results suggest that, while current practices (standard protocols and/or subjective recommendations based on the clinician's experience) can generally provide satisfactory management of drug resistance in the short-term, optimization-based therapy planning has a far greater potential to achieve this goal over expanded time horizons thereby changing paradigms and rethinking best practices in the HIV/AIDS clinical arena. Moreover, the ability of this methodology to address other viral pathologies (e.g., hepatitis B and C virus) can make this work appeal to a broader audience.     

Simultaneous process and control system design for grade transition in styrene polymerization

We present a comprehensive approach to the simultaneous design and control of a continuous stirred tank reactor (CSTR) for styrene solution polymerization that must be able to produce different polymer grades. The resulting tool allows simultaneous selection of the polymerization equipment, the multivariable feedforward-feedback controller's structure and tuning parameters, the steady states and the transition paths between them. For this purpose a multiobjective optimization is implemented to minimize the annualized reactor cost, the operating costs, the production of off-specification polymer and the transition time between steady states. Trade-offs between the sometimes conflicting objectives are dealt with by the optimization. Unlike many previous grade transition studies, steady states are not known a priori. The only known parameters are the target molecular weights to be produced at each steady state. We have analyzed three different scenarios, and propose practical criteria for selecting the most reasonable optimum when the solution is not unique.     

A new Lagrangian decomposition approach applied to the integration of refinery planning and crude-oil scheduling

The aim of this paper is to introduce a methodology to solve a large-scale mixed-integer nonlinear program (MINLP) integrating the two main optimization problems appearing in the oil refining industry: refinery planning and crude-oil operations scheduling. The proposed approach consists of using Lagrangian decomposition to efficiently integrate both problems. The main advantage of this technique is to solve each problem separately. A new hybrid dual problem is introduced to update the Lagrange multipliers. It uses the classical concepts of cutting planes, subgradient, and boxstep. The proposed approach is compared to a basic sequential approach and to standard MINLP solvers. The results obtained on a case study and a larger refinery problem show that the new Lagrangian decomposition algorithm is more robust than the other approaches and produces better solutions in reasonable times.     

Optimal placement of gas detectors: A P‐median formulation considering dynamic nonuniform unavailabilities

A stochastic programming formulation (SPqt), based on the P‐median problem, is proposed for determining the optimal placement of detectors in mitigation systems while considering nonuniform dynamic detector unavailabilities. Unlike previously proposed formulations, SPqt explicitly considers backup detection levels. This allows the modeller to determine the maximum degree of the nonlinear products to be used based on the trade‐off between computational complexity and solution accuracy. We analyze this trade‐off on formulation SPqt results by using 4 real data sets for the gas detector placement problem while using unavailability values obtained from real industry gas detector data. For this data, our results show that two detection levels are sufficient to find objective values within 1% of the optimal solution. Using two detection levels reduces the nonlinear formulation to a quadratic formulation. Three solution strategies are proposed for this quadratic formulation and then compared from the computational efficiency perspective. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2728–2739, 2016