Successive Quadratic Programming Algorithm Research Articles

Simulation and optimization of VPSA system based on pseudo transient continuation method

AbstractIn order to address the challenge of optimization of pressure swing adsorption systems, an optimization framework based on pseudo transient continuation method was used and a corresponding library with several models was established for simulation of more complex processes. Then, two vacuum pressure swing adsorption processes for oxygen and nitrogen production were considered as case studies and the results based on the single discretization and pseudo transient method were compared and analyzed in detail. Besides, a new strategy was proposed for the stability and efficiency of simulation. Finally, reduced successive quadratic programming and time relaxation algorithm were used for the optimization of the two systems, respectively, and the results showed that the time relaxation algorithm based on the pseudo transient framework has a strong advantage in saving optimization time cost compared with the former.

A competitive inexact nonmonotone filter SQP method: convergence analysis and numerical results

We propose an inexact nonmonotone successive quadratic programming (SQP) algorithm for solving nonlinear programming problems with equality constraints and bounded variables. Regarding the value of the current feasibility violation and the minimum value of its linear approximation over a trust region, several scenarios are envisaged. In one scenario, a possible infeasible stationary point is detected. In other scenarios, the search direction is computed using an inexact (truncated) solution of a feasible strictly convex quadratic program (QP). The search direction is shown to be a descent direction for the objective function or the feasibility violation in the feasible or infeasible iterations, respectively. A new penalty parameter updating formula is proposed to turn the search direction into a descent direction for an -penalty function. In certain iterations, an accelerator direction is developed to obtain a superlinear local convergence rate of the algorithm. Using a nonmonotone filter strategy, the global convergence of the algorithm and a superlinear local rate of convergence are guaranteed. The main advantage of the algorithm is that the global convergence of the algorithm is established using inexact solutions of the QPs. Furthermore, the use of inexact solutions instead of exact solutions of the subproblems enhances the robustness and efficiency of the algorithm. The algorithm is implemented using MATLAB and the program is tested on a wide range of test problems from the CUTEst library. Comparison of the obtained numerical results with those obtained by testing some similar SQP algorithms affirms the efficiency and robustness of the proposed algorithm.

Optimal design of microtube recuperators for an indirect supercritical carbon dioxide recompression closed Brayton cycle

This paper presents a baseline design and optimization approach developed in Aspen Custom Modeler (ACM) for microtube shell-and-tube exchangers (MSTEs) used for high- and low-temperature recuperation in a 10 MWe indirect supercritical carbon dioxide (sCO2) recompression closed Brayton cycle (RCBC). The MSTE-type recuperators are designed using one-dimensional models with thermal-hydraulic correlations appropriate for sCO2 and properties models that capture considerable nonlinear changes in CO2 properties near the critical and pseudo-critical points. Using the successive quadratic programming (SQP) algorithm in ACM, optimal recuperator designs are obtained for either custom or industry-standard microtubes considering constraints based on current advanced manufacturing techniques. The three decision variables are the number of tubes, tube pitch-to-diameter ratio, and tube diameter. Five different objective functions based on different key design measures are considered: minimization of total heat transfer area, heat exchanger volume, metal weight, thermal residence time, and maximization of compactness. Sensitivities studies indicate the constraint on the maximum number of tubes per shell does affect the number of parallel heat exchanger trains but not the tube selection, total number of tubes, tube length and other key design measures in the final optimal design when considering industry-standard tubes. In this study, the optimally designed high- and low-temperature recuperators have 47,000 3/32 in. tubes and 63,000 1/16 in. tubes, respectively. In addition, sensitivities to the design temperature approach and maximum allowable pressure drop are studied, since these specifications significantly impact the optimal design of the recuperators as well as the thermal efficiency and the economic performance of the entire sCO2 Brayton cycle.

Link optimization for energy‐constrained wireless networks with packet retransmissions

AbstractWith the objective to minimize the energy consumption for packet based communications in energy‐constrained wireless networks, this paper establishes a theoretical model for the joint optimization of the parameters at the physical layer and data link layer. Multilevel quadrature amplitude modulation (MQAM) and automatic repeat request (ARQ) techniques are considered in the system model. The optimization problem is formulated into a three dimensional nonlinear integer programming (NIP) problem with the modulation order, packet size, and retransmission limit as variables. For the retransmission limit, a simple search method is applied to degenerate the three dimensional problem into a two dimensional NIP problem, for which two optimization algorithms are proposed. One is the successive quadratic programming (SQP) algorithm, combining with the continuous relaxation based branch‐and‐bound method, which can obtain the global optimal solution since the continuous relaxation problem is proved to be hidden convex. The other is a low‐complexity sub‐optimal iterative algorithm, combining with the nearest‐neighboring method, which can be implemented with a polynomial complexity. Numerical examples are given to illustrate the optimization solution, which suggests that the joint optimization of the physical/data link layer parameters contributes noticeably to the energy saving in energy‐constrained wireless networks. Copyright © 2010 John Wiley & Sons, Ltd.

Optimization and Design of a Cascaded DC/DC Converter Devoted to Grid-Connected Photovoltaic Systems

The integration of photovoltaic (PV) modules in buildings causes problems with shadows that can strongly reduce the energy produced by these systems. Moreover, most PV modules are designed for stand-alone applications that have output voltage adapted to lead batteries. Indeed, this historical sizing of PV modules can be discussed in the case of grid-connected systems. In this paper, a cascaded dc/dc converter based on boost chopper is proposed. First, the advantages and the limits of this topology will be shown. Second, this topology will be optimized to maximize the efficiency or minimize the volume. The originality of this optimization is that the converters' parameters and the arrangement of the PV cells are variable parameters. Indeed, the optimization is done on the entire system. To realize these optimizations, semiempiric models of losses and volumes of different components of a boost chopper were developed. The optimization uses a successive quadratic programming algorithm. Considering the optimization results over the whole range of the specifications, a flexible solution is developed and experimental results are presented. Finally, optimized topologies connected to several PV are evaluated at different situations of typical shadows.

A Hybrid Optimization Method for Constrained Optimal Control Problem

A new hybrid algorithm by integrating a nested partitions (NP) method with successive quadratic programming (SQP) is presented for global optimization of general optimal control problems involving lumped parameter system. The control parameterization technique first employed to reduce the control problem into a parameter selection problem. Then, in the global phase a vicinity of global optimizer is approximated by an appropriate NP method. Subsequently, the SQP algorithm in the local phase promotes the accuracy of final solution. The effectiveness of the hybrid NP-SQP algorithm is also illustrated by means of numerical simulations. I. INTRODUCTION In the early years of optimal control theory traditional methods based on calculus of variations could furnish some relatively simple problems with an analytical solution. As the analytical solution might not always be available, researchers have been interested in computational method for optimal control problems, yet when reliable and powerful computers became everywhere available, it was the end of an era. The software environments have become a platform for implementation of many practical methods to solve arising control problems. The iterative traditional methods both directly (3) or indirectly (using the Pontryagin's minimum principle) (8) rely on gradient information, and perform efficiently for convex problems, otherwise the performance of these methods highly depend on selected initial solution. As an alternative to approximate a solution for complex nonconvex problems, many metaheuristic methods have been proposed (4). In general, these methods iteratively sample amongst potential solutions, and the search is directed using the value of the objective function only, hence reducing the need for gradient information. Moreover, as metaheuristic methods globally search for optima, they are usually characterized as global optimizer due to their capability to efficiently arrive at the vicinity of a global optimum. Nested partitions (NP) (10) is an exemplary method in this category, where concisely described in the third section. We use this method to globally search for optimal control for the class of the control problems described in the next section. Then, in the subsequent sections we propose the hybrid NP-SQP algorithm. II. THE CONTROL PROBLEMS In this study, we consider a general optimal control problem where the system of dynamics is described by a first-order ordinary differential equation (ODE),

Limit analysis of FRP strengthened masonry arches via nonlinear and linear programming

The collapse load of masonry arches strengthened with FRP materials is determined. The arch is made of quadrangular blocks and the nonlinearity of the problem (no-tension material, frictional sliding and crushing) is concentrated at the interface between the blocks. Two methods are used to solve the problem. In the first method, a nonlinear programming problem (NLP) is formulated and is solved by using the successive quadratic programming algorithm (SQP) and combinatorial analysis. This method finds the optimal solution in the analysed cases. In the second method, a linear programming problem (LP) is formulated and is solved with classical techniques. LP approximates the optimal solution to any desired degree of accuracy. Although the number of variables of LP is much larger than that of NLP, LP process time can result much lower than NLP process time. Numerical examples are provided in order to show the advantages of the two methods and the effectiveness of FRP strengthening for different arch geometries.

Modeling of the α-lactalbumin and β-lactoglobulin protein separation

This work used the General Rate Model (GRM) to evaluate the experimental data of α-lactalbumin (α-la) and β-lactoglobulin (β-lg) mass transfer using size exclusion chromatography (SEC). The chromatographic simulation has become necessary in large scale production processes. Mathematical models have been used for the optimization and control of different operating conditions of the process, as well as providing calculations for the process scale-up. For the SEC experiments, the aqueous biphasic system was composed of polyethylene glycol 1500 g/mol, potassium phosphate and whey protein isolate. The polymeric phase was enriched with α-la and the saline phase with β-lg. The experiments were conducted using a glass column packed with the Sephadex G-25 ® gel. Both proteins were quantified by reverse phase liquid chromatography. The experimental data were fitted by non-linear regression, using the successive quadratic programming algorithm. The mass transfer model utilized represented adequately the SEC experimental results.

Model-Based Cost Minimization in Noncatalytic Biodiesel Production Plants

In this work, we have formulated a series of nonlinear programming models based on first principles and rigorous thermodynamic predictions, to perform economic evaluation for different scheme alternatives in supercritical methanol transesterification for biodiesel production. The model includes thermodynamic predictions with a group contribution equation of state that have been favorably compared, in this work, to the available experimental data for the different mixtures at different operating conditions. The resulting nonlinear programming problem for cost minimization has been solved with a successive quadratic programming algorithm. Numerical results indicate that the use of a heat pump within the noncatalytic biodiesel production scheme significantly reduces operating costs, making this technology economically competitive as compared to conventional ones.

A successive quadratic programming algorithm for SDP relaxation of Max-Bisection

A successive quadratic programming algorithm for solving SDP relaxation of Max-Bisection is provided and its convergence result is given. The step-size in the algorithm is obtained by solving n easy quadratic equations without using the linear search technique. The numerical experiments show that this algorithm is rather faster than the interior-point method.

Convergence Depth Control for Process System Optimization

Convergence and solution time are important considerations in process system optimization. Another nontrivial task is the definition of termination criteria. However, setting the convergence tolerance is difficult and bewildering for users. Observed behaviors of algorithms when solving many optimization problems include tardiness in deciding convergence or failure of the optimization, and incapability of giving approximate solutions as they fail to converge. Here, we propose convergence depth control (CDC) for process system optimization. It is designed to take advantage of the achievement estimation of the optimization process to discover the proper time to terminate the optimization algorithm. Criteria based on CDC prefer to provide an approximate solution with acceptable optimality. Achievability and rationality of the criteria have been analyzed. To demonstrate the effectiveness of this method, we apply the Reduced-Hessian Successive Quadratic Programming (RSQP) algorithm with convergence depth contro...

Model-based optimization of a sequencing batch reactor for biological nitrogen removal

An optimal operating mode for a sequencing batch reactor was determined via a model-based optimization. Synthetic wastewater containing mainly organic matter (as glucose) and nitrogen (as ammonium chloride) was treated without any addition of an external carbon source to accomplish denitrification step. A simplified model was used to describe process dynamics, comprised of six ordinary differential equations and an empirical correlation for oxygen consumption rate. Batch cycle time was the chosen objective function to be minimized for a fixed volume of waste to be treated. Furthermore, as SBR operation is divided in two major phases – aerobic and anoxic, to achieve total pollutants removal within minimum time, these phases can be repeatedly alternated. To ensure availability of organic matter necessary for denitrification, these two phases were combined with feed steps. Different feed strategies were tested using one, two or three feed steps. A successive quadratic programming algorithm was used, and maximum values for final COD, nitrate and ammonium concentrations, as well as maximum feed pump flow rate were some the process constraints. One step feed strategy was indicated by the optimization leading to a batch cycle time of 5 h.

Successive quadratic programming multiuser detector

Abstract Based on the semidefinite programming relaxation of the CDMA maximum likelihood multiuser detection problem, a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, the suboptimal solution of the multiuser detection problem in obtained. Compared to the interior point methods previously reported based on semidefinite programming, simulations demonstrate that the successive quadratic programming algorithm often yields the similar BER performances of the multiuser detection problem. But the average CPU time of this approach is significantly reduced.

The Application of Successive Quadratic Programming Algorithm to Multiuser Detection in CDMA

In this paper, based on the semidefinite programming relaxation of the CDMA maximum likelihood (ML) multiuser detection problem, a detection strategy by the successive quadratic programming algorithm is presented. Coupled with the randomized cut generation scheme, we obtain the suboptimal solution of multiuser detection problem. Comparing with the reported interior point methods based on semidefinite programming, simulations demonstrate that the successive quadratic programming algorithm often yields the similar BER performances of the multiuser detection problem. But the average CPU time of this approach is significantly reduced.

Control and Optimization of a Three Phase Industrial Hydrogenation Reactor

Three phase catalytic reactors are very important industrial reactors with complex steady state and dynamic behavior. In fact, the interaction among the gas, solid and liquid phases with the kinetic, mass and heat transfer mechanisms lead the system to have a challenging behavior. That is the case for the o-cresol hydrogenation to obtain 2-methyl-cyclohexanol, which is carried out in a three phase catalyst slurry reactor. A determinist mathematical model was developed using the mass and energy conservation equations for each phase, so that a system of differential equations is generated. In order to identify some suitable control structures an extensive dynamic behavior analysis was carried out. The controller implemented was a multivariable predictive controller based on the philosophy of Dynamic Matrix Control (DMC). The problem of optimization was solved through non-linear programming making use of the Successive Quadratic Programming (SQP) algorithm.

An optimization strategy for nonlinear simulated moving bed chromatography: Multi-level optimization procedure (MLOP)

This paper presents a multi-level optimization strategy to obtain optimum operating conditions (four flow-rates and cycle time) of nonlinear simulated moving bed chromatography. The multi-level optimization procedure (MLOP) approaches systematically from initialization to optimization with two objective functions (productivity and desorbent consumption), employing the standing wave analysis, the true moving bed (TMB) model and the simulated moving bed (SMB) model. The procedure is constructed on a non-worse solution property advancing level by level and its solution does not mean a global optimum. That is, the lower desorbent consumption under the higher productivity is successively obtained on the basis of the SMB model, as the two SMB-model optimizations are repeated by using a standard SQP (successive quadratic programming) algorithm. This approach takes advantage of the TMB model as well as surmounts shortcomings of the TMB model in the general case of any nonlinear adsorption isotherm using the SMB model. The MLOP is evaluated on two nonlinear SMB cases characterized by i) quasi-linear/non-equilibrium and ii) nonlinear/nonequilibrium model. For the two cases, the MLOP yields a satisfactory solution for high productivity and low desorbent consumption within required purities.

Modeling and optimization of a fluidized catalytic cracking process under full and partial combustion modes

A process optimization system, which consists of a steady-state process model, a model parameter estimator and a process optimizer for a fluidized catalytic cracking (FCC) process under full and partial combustion modes, is presented in this paper. First, mathematical modeling was carried out for the reactor, regenerator, main-fractionator, and most of auxiliary units including the feed pre-heater, catalyst cooler, air blower, wet gas compressor, stack gas expander, boilers, and valves. Then, the resulting steady-state model was utilized to develop the model parameter estimator and the process optimizer both of which adopt a successive quadratic programming algorithm to efficiently locate the optimum solutions. The parameter estimator can estimate up to 52 model parameters in order to validate the process model by reducing process–model mismatch. The process optimizer maximizes the economic objective function defined as the difference between the total value of products and the cost of feedstock and utility under 30 operating constraints. The developed optimization system was applied to several optimization cases to maximize the economic profit of the FCC process operated in the full and partial combustion modes and the optimization results were extensively compared and analyzed between the combustion modes. It is expected that the proposed steady-state model, parameter estimation and optimization methods can be utilized to optimize and design modem-type FCC processes under full and partial combustion modes.

Transportation Network Optimization Problems with Stochastic User Equilibrium Constraints

A comprehensive study of static transportation network optimization problems with stochastic user equilibrium constraints is presented. It is explicitly demonstrated that the formulation of the fixed-point problem—in terms of link flows for the general stochastic user equilibrium problem in which the Jacobian matrix of link travel cost functions may not be symmetric—possesses a unique solution with mild conditions. By developing a sensitivity analysis method for the stochastic user equilibrium problem, the study proves that the perturbed equilibrium link flows are continuously differentiable implicit functions with respect to perturbation parameters. Accordingly, it can be concluded that the proposed unified bilevel programming model, which can characterize transportation network optimization problems subject to stochastic user equilibrium constraints, is a smooth optimization problem. In addition, the study presents a single-level continuously differentiable optimization formulation that is equivalent to the unified bilevel programming model. Furthermore, as a unified solution method, a successive quadratic programming algorithm based on the sensitivity analysis method is used to solve the transportation network optimization problems with stochastic user equilibrium constraints. Finally, two examples are used to demonstrate the proposed models and algorithm.

A tailored optimization strategy for PDE-based design: application to a CVD reactor

We describe a tailored strategy for nonlinear programming (NLP) with partial differential equation (PDE) models. This approach is based on a reduced space Successive Quadratic Programming (rSQP) algorithm, and it allows the reuse of existing PDE-based modeling codes. This approach leads to an efficient simultaneous strategy, where the NLP and the PDE model are solved at the same time. A number of refinements were made to the NLP algorithm to enhance its performance and reliability for large, nonlinear models. This study considers PDE-based optimization problems to demonstrate the effectiveness of this approach. In particular, we apply this approach to MPSalsa, a finite element PDE Solver developed at Sandia National Laboratories, and consider a chemical vapor deposition (CVD) reactor model as the optimization application. Here, our goal is optimize the operating conditions to produce a thin film of gallium nitride with a spatially uniform thickness. To minimize nonuniformity of the film, a novel NLP formulation is described and evaluated based on constraint aggregation. In addition to the design optimization strategy, we incorporate a stability analysis of the optimal design to assure that it is a stable steady state.

Optimal design of a system for large in vivo experiments on the effects of 50-Hz magnetic fields

This paper describes toroids for a large in vivo experiment on the effects of the magnetic field produced by electric power systems. The toroids are designed to be housed in structures that comply with the experimental protocol requirements and with the experiment specifications. The toroids were designed by using the integral approach for field and vector potential computation and a deterministic approach based on a successive quadratic programming algorithm for their optimization. The paper presents and discusses the results.