Nonlinear Programming Strategy Research Articles

Closed-loop scheduling optimization strategy based on particle swarm optimization with niche technology and soft sensor method of attributes-applied to gasoline blending process

Gasoline blending scheduling optimization can bring significant economic and efficient benefits to refineries. However, the optimization model is complex and difficult to build, which is a typical mixed integer nonlinear programming (MINLP) problem. Considering the large scale of the MINLP model, in order to improve the efficiency of the solution, the mixed integer linear programming - nonlinear programming (MILP-NLP) strategy is used to solve the problem. This paper uses the linear blending rules plus the blending effect correction to build the gasoline blending model, and a relaxed MILP model is constructed on this basis. The particle swarm optimization algorithm with niche technology (NPSO) is proposed to optimize the solution, and the high-precision soft-sensor method is used to calculate the deviation of gasoline attributes, the blending effect is dynamically corrected to ensure the accuracy of the blending effect and optimization results, thus forming a prediction-verification-reprediction closed-loop scheduling optimization strategy suitable for engineering applications. The optimization result of the MILP model provides a good initial point. By fixing the integer variables to the MILP-optimal value, the approximate MINLP optimal solution can be obtained through a NLP solution. The above solution strategy has been successfully applied to the actual gasoline production case of a refinery (3.5 million tons per year), and the results show that the strategy is effective and feasible. The optimization results based on the closed-loop scheduling optimization strategy have higher reliability. Compared with the standard particle swarm optimization algorithm, NPSO algorithm improves the optimization ability and efficiency to a certain extent, effectively reduces the blending cost while ensuring the convergence speed.

Nonlinear Optimization Strategies for Process Separations and Process Intensification

AbstractAdvanced nonlinear programming (NLP) strategies based on equation‐oriented (EO) process models are leading to significant improvements in computer‐aided process engineering. The EO paradigm allows the development of large, integrated optimization platforms that expand the scope of continuous optimization tasks in process engineering. In particular, these platforms deploy significantly faster NLP strategies than in commercial simulation tools. Moreover, they exploit exact derivatives and system structure in order to consider much larger and more challenging systems. Finally, they allow the incorporation of much more general models, such as multi‐level optimization and complementarity constraints. For process optimization this allows the treatment of extended models for complex phase equilibrium and process separations. These advances facilitate the optimization of novel integrated systems that arise in process intensification. Several separation case studies are presented that illustrate these optimization concepts and demonstrate their effectiveness for hybrid membrane/distillation separations and reactive distillation systems that typify novel systems in process intensification.

Introducing KIPET: A novel open-source software package for kinetic parameter estimation from experimental datasets including spectra

This paper presents KIPET (Kinetic Parameter Estimation Toolkit) an open-source toolbox for the determination of kinetic parameters from a variety of experimental datasets including spectra and concentrations. KIPET seeks to overcome limitations of standard parameter estimation packages by applying a unified optimization framework based on maximum likelihood principles and large-scale nonlinear programming strategies for solving estimation problems that involve systems of nonlinear differential algebraic equations (DAEs). The software is based on recent advances proposed by Chen et al. (2016) and puts their original framework into an accessible framework for practitioners and academics. The software package includes tools for data preprocessing, estimability analysis, and determination of parameter confidence levels for a variety of problem types. In addition KIPET introduces informative wavelength selection to improve the lack of fit. All these features have been implemented in Python with the algebraic modeling package Pyomo. KIPET exploits the flexibility of Pyomo to formulate and discretize the dynamic optimization problems that arise in the parameter estimation algorithms. The solution of the optimization problems is obtained with the nonlinear solver IPOPT and confidence intervals are obtained through the use of either sIPOPT or a newly developed tool, k_aug. The capabilities as well as ease of use of KIPET are demonstrated with a number of examples.

Improving Reliability in Nonlinear Hyperspectral Unmixing by Multidimensional Structural Optimization

Nonlinear unmixing algorithms are playing a key role in modern earth observation analysis thanks to their ability to characterize complex phenomena occurring in the instantaneous field of view. When unmixing hyperspectral images according to nonlinear mixture models by means of state-of-the-art methods, actual abundances of the elements in the scene can be only indirectly estimated. Thus, the reliability of the investigation can be dramatically jeopardized, hence degrading the accuracy of the characterization of the surface composition. In order to overcome this issue, we propose in this paper a nonlinear programming scheme that aims at providing direct estimation of the end members fractions. The method we introduce is based on a structural optimization approach where the abundances are directly assessed, so that no epistemic uncertainties are injected in the framework. Experimental results show that the proposed method is able to deliver accurate and reliable estimates of these quantities in hyperspectral images.

Distributed Resource Allocation for Energy Efficiency in OFDMA Multicell Networks With Wireless Power Transfer

In this paper, an energy-efficient resource allocation problem is investigated for the wireless power transfer (WPT)-enabled OFDMA multicell networks. In the considered system, multiple base stations (BSs) with a large number of antennas are responsible to provide WPT in the downlink, and the users can recycle and utilize the received energy for uplink data transmission. The role of BS is to execute WPT; thus, there are no data transmissions in the downlink. A time-division protocol is considered to divide the time of downlink WPT and uplink wireless information transfer into separate time slots. With the objective to improve the energy efficiency, we propose the time, subcarrier, and power allocation schemes and antenna selection algorithms. As the perfect channel state information (CSI) is hard to obtain in the practical systems, we also take the case where only estimated CSI is available into consideration when executing resources allocation decisions and analyze the corresponding performance. Due to the non-convexity of the formulated optimization problem, we first apply the nonlinear programming scheme to convert it to a convex optimization problem. Then, an efficient alternating direction method of multipliers-based distributed resource allocation algorithm is applied to address the transformed problem. Performance evaluations are conducted to demonstrate the advantages of the proposed schemes.

Optimal integrated facility for waste processing

A mixed-integer nonlinear programming strategy is proposed to design integrated facilities to simultaneously recover power and nutrients from organic waste. The facilities consider anaerobic digestion of different types of manure (cattle, pig, poultry, and sheep). The products from this step are biogas and a nutrient-rich effluent. The biogas produced is cleaned and used in a gas turbine to produce power while the hot flue gas obtained from combustion produces steam that is fed to a steam turbine to produce additional power. The nutrient-rich effluent is processed to recover the nutrients using different technologies that include filtration, coagulation, centrifugation, and struvite precipitation in stirred and fluidized bed reactors. This processing step provides a mechanism to prevent phosphorus or nitrogen release to the environment and to avoid the development of eutrophication processes. It is found that struvite production in fluidized beds is the technology of choice to recover nutrients from all manure sources. Furthermore, power production depends strongly on manure composition and exhibits high cost variability (from 4,000€/kW in the case of poultry manure to 25,000€/kW in the case of cattle and pig manure).

Integrated Optimization Strategies for Dynamic Process Operations

Process systems engineering faces increasing demands and opportunities for better process modeling and optimization strategies, particularly in the area of dynamic operations. Modern optimization strategies for dynamic optimization trace their inception to the groundbreaking work Pontryagin and his coworkers, starting 60 years ago. Since then the application of large-scale non-linear programming strategies has extended their discoveries to deal with challenging real-world process optimization problems. This study discusses the evolution of dynamic optimization strategies and how they have impacted the optimal design and operation of chemical processes. We demonstrate the effectiveness of dynamic optimization on three case studies for real-world reactive processes. In the first case, we consider the optimal design of runaway reactors, where simulation models may lead to unbounded profiles for many choices of design and operating conditions. As a result, optimization based on repeated simulations typically fails, and a simultaneous, equationbased approach must be applied. Next we consider optimal operating policies for grade transitions in polymer processes. Modeled as an optimal control problem, we demonstrate how product specifications lead to multistage formulations that greatly improve process performance and reduce waste. Third, we consider an optimization strategy for the integration of scheduling and dynamic process operation for general continuous/batch processes. The method introduces a discrete time formulation for simultaneous optimization of scheduling and operating decisions. For all of these cases we provide a summary of directions and challenges for future integration of these tasks and extensions in optimization formulations and strategies.

Advanced optimization strategies for integrated dynamic process operations

Modern approaches for dynamic optimization trace their inception to Pontryagin's Maximum Principle 60 years ago. Since then the application of large-scale nonlinear programming strategies has been extended to deal with challenging real-world process optimization problems. This study discusses and demonstrates the effectiveness of dynamic optimization on three case studies on real-world chemical processes. In the first case, we consider the optimal design of runaway reactors, where simulation models may lead to unbounded profiles for many choices of design and operating conditions. As a result, optimization based on repeated simulations typically fails, and a simultaneous, equation-based approach must be applied. Second, we consider optimal operating policies for grade transitions in polymer processes. Modeled as an optimal control problem, we demonstrate how incorporation of product specification bands leads to multi-stage formulations that greatly improve process performance and significantly reduce off-grade product. Third, we consider an optimization strategy for the integration of scheduling and dynamic process operation for general continuous/batch processes. The method introduces a discrete time formulation for simultaneous optimization of scheduling and operating decisions. Finally, we provide a concise summary of directions and challenges for future extension of these optimization formulations and solution strategies.

Level set shape and topology optimization of finite strain bilateral contact problems

SummaryThis paper presents a method for the optimization of multicomponent structures comprised of 2 and 3 materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit level set method, which allows for both shape and topology changes. The mechanical model assumes finite strains, a nonlinear elastic material behavior, and a quasi‐static response. Identification of overlapping surface position is handled by a coupled parametric representation of contact surfaces. A stabilized Lagrange method and an active set strategy are used to model frictionless contact and separation. The mechanical model is discretized by the extended FEM, which maintains a clear definition of geometry. Face‐oriented ghost penalization and dynamic relaxation are implemented to improve the stability of the physical response prediction. A nonlinear programming scheme is used to solve the optimization problem, which is regularized by introducing a perimeter penalty into the objective function. Design sensitivities are determined by the adjoint method. The main characteristics of the proposed method are studied by numerical examples in 2 dimensions. The numerical results demonstrate improved design performance when compared to models optimized with a small strain assumption. Additionally, examples with load path dependent objectives display nonintuitive designs.

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

Evolution handoff strategy for real-time video transmission over practical cognitive radio networks

The transmission delay of real-time video packet mainly depends on the sensing time delay (short-term factor) and the entire frame transmission delay (long-term factor). Therefore, the optimization problem in the spectrum handoff process should be formulated as the combination of microscopic optimization and macroscopic optimization. In this paper, we focus on the issue of combining these two optimization models, and propose a novel Evolution Spectrum Handoff (ESH) strategy to minimize the expected transmission delay of real-time video packet. In the micro-optimized model, considering the tradeoff between Primary User's (PU's) allowable collision percentage of each channel and transmission delay of video packet, we propose a mixed integer non-linear programming scheme. The scheme is able to achieve the minimum sensing time which is termed as an optimal stopping time. In the macro-optimized model, using the optimal stopping time as reward function within the partially observable Markov decision process framework, the EHS strategy is designed to search an optimal target channel set and minimize the expected delay of packet in the long-term real-time video transmission. Meanwhile, the minimum expected transmission delay is obtained under practical cognitive radio networks' conditions, i.e., secondary user's mobility, PU's random access, imperfect sensing information, etc‥ Theoretical analysis and simulation results show that the ESH strategy can effectively reduce the transmission delay of video packet in spectrum handoff process.

Nonlinear programming strategies for dynamic chemical process optimization

Problem formulations and algorithms are considered for optimization problems with differential-algebraic equation (DAE) models. In particular, we provide an overview of direct methods, based on nonlinear programming (NLP), and indirect, or variational, methods. We further classify each method and tailor it to the appropriate applications. For direct methods, we briefly describe current approaches including the sequential approach (or single shooting), multiple shooting method, and the simultaneous collocation (or direct transcription) approach. In parallel to these strategies we discuss NLP algorithms for these methods and discuss optimality conditions and convergence properties. In particular, we present the simultaneous collocation approach, where both the state and control variable profiles are discretized. This approach allows a transparent handling of inequality constraints and unstable systems. Here, large scale nonlinear programming strategies are essential and a novel barrier method, called IPOPT, is described. This NLP algorithm incorporates a number of features for handling large-scale systems and improving global convergence. The overall approach is Newton-based with analytic second derivatives and this leads to fast convergence rates. Moreover, it allows us to consider the extension of these optimization formulations to deal with nonlinear model predictive control and real-time optimization. To illustrate these topics we consider a case study of a low density polyethylene (LDPE) reactor. This large-scale optimization problem allows us to apply off-line parameter estimation and on-line strategies that include state estimation, nonlinear model predictive control and dynamic real-time optimization.

An efficient 3D topology optimization code written in Matlab

This paper presents an efficient and compact Matlab code to solve three-dimensional topology optimization problems. The 169 lines comprising this code include finite element analysis, sensitivity analysis, density filter, optimality criterion optimizer, and display of results. The basic code solves minimum compliance problems. A systematic approach is presented to easily modify the definition of supports and external loads. The paper also includes instructions to define multiple load cases, active and passive elements, continuation strategy, synthesis of compliant mechanisms, and heat conduction problems, as well as the theoretical and numerical elements to implement general non-linear programming strategies such as SQP and MMA. The code is intended for students and newcomers in the topology optimization. The complete code is provided in Appendix C and it can be downloaded from http://top3dapp.com .

Modeling of the non-catalytic semi-batch esterification of palm fatty acid distillate (PFAD)

Biodiesel fuel is one of the most attractive alternatives to the traditional diesel fuel derived from a petroleum refinery. Development of a reliable model for the biodiesel production process requires maximizing economics and enhancing safety in the commercial operation of biodiesel plants. We propose a model which represents effectively the non-catalytic biodiesel production reaction. In the modeling of the reaction, we employ a nonlinear programming scheme to estimate reaction kinetic parameters which minimize a specified objective function. The behavior of the methanol during the reaction is investigated both experimentally and numerically. Imperfect mixing in the liquid phase at the initial reaction stage causes a little discrepancy between the experimental data and results of simulations. Overall, the proposed model represents the biodiesel production reaction effectively.

Dynamic Optimization of Aeration Operations for a Benchmark Wastewater Treatment Plant

AbstractThis study considers the optimization of aeration operations of a challenging benchmark wastewater treatment plant (WWTP), described by the Benchmark Simulation Model 1 (BSM1). The objective is to minimize aeration energy cost while maintaining effluent quality within regulation-specified limits. For this study, the optimization model based on BSM1 was developed using the AMPL language and IPOPT nonlinear programming (NLP) solver. Optimal air volume and the corresponding dissolved oxygen (DO) setpoint were obtained at steady state conditions. Finally, optimal dynamic aeration operations were obtained under dry weather conditions, using an efficient nonlinear programming strategy. This result showed significant improvements over conventional strategies based on setpoints alone.

An efficient nonlinear programming strategy for PCA models with incomplete data sets

AbstractProcessing plants can produce large amounts of data that process engineers use for analysis, monitoring, or control. Principal component analysis (PCA) is well suited to analyze large amounts of (possibly) correlated data, and for reducing the dimensionality of the variable space. Failing online sensors, lost historical data, or missing experiments can lead to data sets that have missing values where the current methods for obtaining the PCA model parameters may give questionable results due to the properties of the estimated parameters. This paper proposes a method based on nonlinear programming (NLP) techniques to obtain the parameters of PCA models in the presence of incomplete data sets. We show the relationship that exists between the nonlinear iterative partial least squares (NIPALS) algorithm and the optimality conditions of the squared residuals minimization problem, and how this leads to the modified NIPALS used for the missing value problem. Moreover, we compare the current NIPALS‐based methods with the proposed NLP with a simulation example and an industrial case study, and show how the latter is better suited when there are large amounts of missing values. The solutions obtained with the NLP and the iterative algorithm (IA) are very similar. However when using the NLP‐based method, the loadings and scores are guaranteed to be orthogonal, and the scores will have zero mean. The latter is emphasized in the industrial case study. Also, with the industrial data used here we are able to show that the models obtained with the NLP were easier to interpret. Moreover, when using the NLP many fewer iterations were required to obtain them. Copyright © 2010 John Wiley & Sons, Ltd.

The simulation design and analysis of a Flexible Manufacturing System with Automated Guided Vehicle System

This paper presents the simulation design and analysis of a Flexible Manufacturing System (FMS) with an Automated Guided Vehicle system (AGVs). To maximize the operating performance of FMS with AGVs, many parameters must be considered, including the number, velocity, and dispatching rule of AGV, part-types, scheduling, and buffer sizes. Of the various critical factors, we consider the following three: (1) minimizing the congestion; (2) minimizing the vehicle utilization; and (3) maximizing the throughput. In this paper, we consider the systematic analysis methods that combine a simulation-based analytic and optimization technique that is Multi-Objective Non-Linear Programming (MONLP) and Evolution Strategy (ES). MONLP determines the design parameters of the system through multi-factorial and regression analyses. ES is used to verify each parameter for simulation-based optimization. A validation test for the two methods is conducted. This method-based approach towards design yields the correct experimental results, ensures confidence in the specification of design parameters and supports a robust framework for analysis.

Hydrodynamics and Axial Dispersion in a Gas−Liquid−(Solid) EL-ALR with Different Sparger Designs

The gas−liquid−(solid) three-phase hydrodynamics in an external-loop airlift reactor (EL-ALR) with an upward pipe 0.47 m in diameter and 2.5 m in height, two external loop downward pipes 0.08 m in diameter and 2.5 m in height, were investigated using four different gas sparger designs. The microconductivity probe and the three-dimensional (3-D) laser Doppler anemometry (LDA) techniques were, respectively, implemented to measure the local gas holdup in the riser (αGr) and liquid phase velocity in the downcomer (ULd) using air as the gas phase, water as the liquid phase, and alginate gel beads as the solid phase, over a wide range of operation conditions. The tracer age distribution was measured using the pulse-pursuit response technology. Axial dispersion model (ADM) was used to estimate the model parameter Peclet number (Pe) values as a fitted parameter with the measured data, using the gold partition method for nonlinear programming strategy inequation restrict conditions. The ADM gave better fits to the experimental data at high axial locations and lower superficial gas velocity (UG) for an EL-ALR used with a large L/DR ratio. A synergistic effect of ULd, αGr, Pe, solids loading (SL), and sparger designs on the performance of an EL-ALR was observed in our experiments. The sparger designs were determined to have a noticeable effect on the αGr and Pe in the lower gas velocity and lower solid loading ranges (UG < 0.025 m/s and SL < 2%), but only a slight effect in the high gas velocity and high solid loading ranges (UG > 0.030 m/s and SL > 3%). However, the effect of sparger designs on the ULd is greater in the gas velocity from 0.025 m/s to 0.045 m/s. For the lower solids loading, the increase of orifice diameter leads to a decrease in αGr. This is in accordance with what was presented in the gas−liquid two-phase system. Moreover, the influence of orifice diameters of the spargers is negligible for solids loading of >3%. Although the Pe values decreased with the operating gas velocity, the gas velocity change from 0.03 m/s to 0.04 m/s yielded lower Pe values, as a result of the reduced bubble size. As the gas velocity further increased to 0.06 m/s, the αGr and the ULd values increased, while the Pe values negligibly increased. For a gas−liquid two-phase system, Pe decreases with the orifice diameter and, for 1% of solids, Pe is also lower for sparger P-2 (ϕ 0.6 mm) than for sparger P-1 (ϕ 0.3 mm). For higher amounts of solids (3%), Pe does not have a defined trend. In addition to the gas velocity and sparger design effects, the solids loading had the effect of decreasing the ULd values, while such effect became small and flattened at high solid loadings. The ULd values, especially with VO = 100%, are ~20% lower in three-phase flow than that in two-phase flow. In addition, the ULd profiles in three-phase flow are flatter than that in two-phase flow with VO = 50%−100%, actually showing a parabolic shape rather than the almost linear one encountered in two-phase flow. This is very important for design and optimum operation that are used to systemically investigate the synergistic effect of ULd, αGr, Pe, solid loading (SL), and sparger designs on hydrodynamic performance of an EL-ALR.

Nonlinear Model Predictive Control applied to E. Coli Cultures

This paper proposes a nonlinear model predictive control scheme with particular application to the regulation of acetate concentration in order to maximize the biomass growth during fed-batch cultures of E. Coli. A reference feed rate which enables to maintain the acetate concentration at a specified level is first determined by means of optimal conditions. This feed rate is further used as the reference control trajectory within the NMPC algorithm. Finally, to avoid discretization problems during NMPC application, the on-line optimization is moved into a nonlinear programming strategy using the control vector parameterization approach (CVP). Some simulation results obtained on a fed-batch E. Coli bioreactor validate the efficiency of the proposed control strategy.

Multiplier convergence in trust-region methods with application to convergence of decomposition methods for MPECs

We study piecewise decomposition methods for mathematical programs with equilibrium constraints (MPECs) for which all constraint functions are linear. At each iteration of a decomposition method, one step of a nonlinear programming scheme is applied to one piece of the MPEC to obtain the next iterate. Our goal is to understand global convergence to B-stationary points of these methods when the embedded nonlinear programming solver is a trust-region scheme, and the selection of pieces is determined using multipliers generated by solving the trust-region subproblem. To this end we study global convergence of a linear trust-region scheme for linearly-constrained NLPs that we call a trust-search method. The trust-search has two features that are critical to global convergence of decomposition methods for MPECs: a robustness property with respect to switching pieces, and a multiplier convergence result that appears to be quite new for trust-region methods. These combine to clarify and strengthen global convergence of decomposition methods without resorting either to additional conditions such as eventual inactivity of the trust-region constraint, or more complex methods that require a separate subproblem for multiplier estimation.