Sequential Quadratic Programming Method Research Articles

Optimization of a type of elastic metamaterial for broadband wave suppression

The optimal design is studied for a type of one-dimensional dissipative metamaterial to achieve broadband wave attenuation at low-frequency ranges. The complex dispersion analysis is made on a super-cell consisting of multiple mass-in-mass unit cells. An optimization algorithm based on the sequential quadratic programming method is used to design the wave suppression of target frequencies by coupling multiple separate narrow bandgaps into a broad bandgap. A new objective function is proposed in the optimization process for a continuous bandgap. Then, the continuous frequency range with low-wave transmissibility is optimized to achieve the maximal width of bandgap. The stiffness optimization of super-cell gives the broad bandgap from 10 Hz to 22.9 Hz at low-frequency ranges. In addition, numerical simulations are conducted for a type of dissipative metamaterial composed of a finite number of periodicities. The level of vibration isolation can be tuned by adjusting a critical value in the optimization scheme. The wave suppression in the numerical simulation well coincides with the obtained bandgaps and verifies the optimization results.

A Comprehensive Design of Six-Axis Force/Moment Sensor.

Strain gage type six-axis force/moment (F/M) sensors have been largely studied and implemented in industrial applications by using an external data acquisition board (DAQ). The use of external DAQs will ill-affect accuracy and crosstalk due to the possibility of voltage drop through the wire length. The most recent research incorporated DAQ within a relatively small F/M sensor, but only for sensors of the capacitance and optical types. This research establishes the integration of a high-efficiency DAQ on six-axis F/M sensor with a revolutionary arrangement of 32 strain gages. The updated structural design was optimized using the sequential quadratic programming method and validated using Finite Element Analysis (FEA). A new, integrated DAQ system was designed, tested, and compared to commercial DAQ systems. The proposed six-axis F/M sensor was examined with the calibrated jig. The results show that the measurement error and crosstalk have been significantly reduced to 1.15% and 0.68%, respectively, the best published combination at this moment.

Non-linear biobjective EE-SE optimization for NOMA-MIMO systems under user-rate fairness and variable number of users per cluster

The trade-off between energy efficiency (EE) and spectrum efficiency (SE) in downlink (DL) multiple-input and multiple-output (MIMO) non-orthogonal multiple access (NOMA) systems under equal-rate constraint has been investigated. The maximum fairness of the NOMA-MIMO system is attained when it is assured the same data rate for all active users in the system. The SE-EE trade-off was formulated as a multi-objective (MOO) problem. The optimization problem was solved by using primarily ∊-Constraint (∊-C) scalarization method combined with nonlinear programming (NLP) techniques, as sequential quadratic programming (SQP) and Dinkelback method (DK). The proposed iterative-analytical ∊-C-DK and ∊-C-SQP methods were able to achieve optimal EE-SE solutions at the Pareto frontier. Besides, both proposed iterative-analytical optimization methods are compared with a greedy local search heuristic method, by combining the ∊-C with the Hill Climbing (HC) heuristic and weighted sum (WS) scalarization method. Numerical results have demonstrated the ability of the ∊-C method in finding a diversity of EE-SE NOMA-MIMO solutions in the Pareto frontier. Furthermore, the proposed ∊-C-SQP method is able to attain a much more variety of solutions in the Pareto frontier in a remarkably reduced computational time.

Reactor Model of Counter-Current Continuous Catalyst-Regenerative Reforming Process toward Real Time Optimization

A new kinetic model involving 44 lumped pseudocomponents and 70 reactions for catalytic reforming was developed to satisfy real-time optimization of the commercial counter-current continuous catalyst-regenerative reforming units. The reaction kinetic model was constructed with the equation oriented method, using the orthogonal collocation method to transform the differential equations of the kinetic model into algebraic equations with variables. The sequential quadratic programming method is used to solve the equation oriented model in this study. The validation results showed that the good agreement of material compositions and catalyst coke content at the exit of the fourth reactor, as well as the temperature and pressure at the exit of each reactor, was obtained between simulated values and industrial values. Moreover, the reactor kinetic model is also used to predict the influence of process parameters which is consistent with the trend in actual industrial production. The model makes it possible to find optimal conditions in real-time optimization.

Nonlinear Steady-State Optimization of Large-Scale Gas Transmission Networks

The major optimization problem of the gas transmission system is to determine how to operate the compressors in a network to deliver a given flow within the pressure bounds while using minimum compressor power (minimum fuel consumption or maximum network efficiency). Minimization of fuel usage is a major objective to control gas transmission costs. This is one of the problems that has received most of the attention from both practitioners and researchers because of its economic impact. The article describes the algorithm of steady-state optimization of a high-pressure gas network of any structure that minimizes the operating cost of compressors. The developed algorithm uses the “sequential quadratic programming (SQP)” method. The tests carried out on the real network segment confirmed the correctness of the developed algorithm and, at the same time, proved its computational efficiency. Computational results obtained with the SQP method demonstrate the viability of this approach.

Life-Cycle Optimization of the Carbon Dioxide Huff-n-Puff Process in an Unconventional Oil Reservoir Using Least-Squares Support Vector and Gaussian Process Regression Proxies

SummaryIn this work, we investigate the efficient estimation of the optimal design variables that maximize net present value (NPV) for the life-cycle production optimization during a single-well carbon dioxide (CO2) huff-n-puff (HnP) process in unconventional oil reservoirs. A synthetic unconventional reservoir model based on Bakken Formation oil composition is used. The model accounts for the natural fracture and geomechanical effects. Both the deterministic (based on a single reservoir model) and robust (based on an ensemble of reservoir models) production optimization strategies are considered. The injection rate of CO2, the production bottomhole pressure (BHP), the duration of injection and the production periods in each cycle of the HnP process, and the cycle lengths for a predetermined life-cycle time can be included in the set of optimum design (or well control) variables. During optimization, the NPV is calculated by a machine learning (ML) proxy model trained to accurately approximate the NPV that would be calculated from a reservoir simulator run. Similar to the ML algorithms, we use both least-squares (LS) support vector regression (SVR) and Gaussian process regression (GPR). Given a set of forward simulation runs with a commercial compositional simulator that simulates the miscible CO2 HnP process, a proxy is built based on the ML method chosen. Having the proxy model, we use it in an iterative-sampling-refinement optimization algorithm directly to optimize the design variables. As an optimization tool, the sequential quadratic programming (SQP) method is used inside this iterative-sampling-refinement optimization algorithm. Computational efficiencies of the ML proxy-based optimization methods are compared with those of the conventional stochastic simplex approximate gradient (StoSAG)-based methods. Our results show that the LS-SVR- and GPR-based proxy models are accurate and useful in approximating NPV in the optimization of the CO2 HnP process. The results also indicate that both the GPR and LS-SVR methods exhibit very similar convergence rates, but GPR requires 10 times more computational time than LS-SVR. However, GPR provides flexibility over LS-SVR to access uncertainty in our NPV predictions because it considers the covariance information of the GPR model. Both ML-based methods prove to be quite efficient in production optimization, saving significant computational times (at least 4 times more efficient) over a stochastic gradient computed from a high-fidelity compositional simulator directly in a gradient ascent algorithm. To our knowledge, this is the first study presenting a comprehensive review and comparison of two different ML-proxy-based optimization methods with traditional StoSAG-based optimization methods for the production optimization problem of a miscible CO2 HnP.

Effects of Van Der Waals Forces on the Vibration of Stacked Multilayered Graphene/Black Phosphorus Heterostructures

In this paper, the vibration of a stacked multilayered graphene/black phosphorus (G/BP) heterostructure is investigated via the mesh-free method. The shape function and its derivatives are addressed by the moving least squares (MLS) approach. Optimization of the sequential quadratic programming method is adopted to calculate the distance between the arbitrary layers. Therefore, coefficients of the van der Waals (vdW) interaction between arbitrary layers of heterostructures are obtained. Then the frequencies and mode shapes of the multilayered G/BP heterostructure, considering the vdW interaction between arbitrary layers, are compared with considering only the vdW interaction among adjacent layers. The effects of the number of layers and aspect ratio of the G/BP heterostructure on the frequencies are investigated. The results demonstrate that coefficients of the vdW interaction, considering the arbitrary layers, are larger than those considering only adjacent layers. The difference between natural frequencies considering arbitrary layers and those considering adjacent layers is not clear for the low-order cases. Alternatively, the difference between natural frequencies obtained considering arbitrary layers and those considering adjacent layers are obvious for high-order cases. This paper provides a useful method to optimize the vdW interaction between multilayered G/BP heterostructures and can adequately simulate their vibration behaviors.

Total least squares adjustment in inequality constrained partial errors-in-variables models: optimality conditions and algorithms

The partial errors-in-variables (PEIV) model is a structured form of errors-in-variables (EIV) model reformulated by collecting all the independent random elements of the coefficient matrix. When some reliable inequality constraints are taken into account, the adjustment results of inequality constrained PEIV (ICPEIV) model are probably improved. In this contribution, we first present the optimality conditions for inequality constrained weighted total least squares (ICWTLS) solution in ICPEIV model. Then we modified the existing linear approximation (LA) approach to make it suitable for cross-correlated data. The sequential quadratic programming (SQP) method is proposed based on the optimality conditions. Since the Hessian matrix is difficult to compute in the SQP algorithm and it converges slowly or even not converges when the Hessian matrix is indefinite positive, the damped quasi-Newton (DQN) SQP method is proposed. Finally, three examples are given to show the feasibility and performance of the proposed algorithms.

Primal Superlinear Convergence of Sqp Methods in Piecewise Linear-Quadratic Composite Optimization

This paper mainly concerns with the primal superlinear convergence of the quasi-Newton sequential quadratic programming (SQP) method for piecewise linear-quadratic composite optimization problems. We show that the latter primal superlinear convergence can be justified under the noncriticality of Lagrange multipliers and a version of the Dennis-Moré condition. Furthermore, we show that if we replace the noncriticality condition with the second-order sufficient condition, this primal superlinear convergence is equivalent with an appropriate version of the Dennis-Moré condition. We also recover Bonnans’ result in (Appl. Math. Optim. 29, 161–186, 1994) for the primal-dual superlinear of the basic SQP method for this class of composite problems under the second-order sufficient condition and the uniqueness of Lagrange multipliers. To achieve these goals, we first obtain an extension of the reduction lemma for convex Piecewise linear-quadratic functions and then provide a comprehensive analysis of the noncriticality of Lagrange multipliers for composite problems. We also establish certain primal estimates for KKT systems of composite problems, which play a significant role in our local convergence analysis of the quasi-Newton SQP method.

Flutter Optimization of a Wing–Engine System with Passive and Active Control Approaches

In the present study, the flutter performance of a composite thin-walled beam wing–engine system is optimized by implementing two different control approaches: 1) passive open-loop and 2) active closed-loop control. Sequential quadratic programming and genetic algorithm methods are applied in the optimization process. In the passive control method, variable stiffness is acquired by constructing laminates of thin-walled beam with curvilinear fibers having prescribed paths. The goal is to exploit the desirable fiber paths with improved flutter performance to determine an optimized wing–engine aeroelastic configuration. In the active control strategy, piezo-composite actuators and the linear quadratic Gaussian algorithm are used to improve the flutter characteristics. A novel optimization strategy based on the total energy of the aeroelastic system is introduced and applied in both passive and active control strategies. The minimum total aeroelastic energy is an indication of ideal optimization variables, which leads to optimum flutter performance. The governing equations are formulated based on Librescu’s thin-walled beam theory and Hamilton’s principle. An unsteady aerodynamic model based on incompressible indicial aerodynamics is applied. The governing equations of motion are solved using a Ritz-based solution methodology. Numerical results demonstrate a 16 and 46% improvement in the flutter speed of the wing–engine system using the proposed passive and active control approaches, respectively. The presented results provide valuable information concerning the design of advanced lightweight and high-aspect-ratio aircraft wings with mounted engines in terms of favorable aeroelastic performance characteristics.

YAM2: Yet another library for the [formula omitted] variables using sequential quadratic programming

The M2 variables are devised to extend MT2 by promoting transverse masses to Lorentz-invariant ones and making explicit use of on-shell mass relations. Unlike simple kinematic variables such as the invariant mass of visible particles, where the variable definitions directly provide how to calculate them, the calculation of the M2 variables is undertaken by employing numerical algorithms. Essentially, the calculation of M2 corresponds to solving a constrained minimization problem in mathematical optimization, and various numerical methods exist for the task. We find that the sequential quadratic programming method performs very well for the calculation of M2, and its numerical performance is even better than the method implemented in the existing software package for M2. As a consequence of our study, we have developed and released yet another software library, YAM2, for calculating the M2 variables using several numerical algorithms. Program summaryProgram title: YAM2CPC Library link to program files:https://doi.org/10.17632/4g7wfd5fpb.1Developer’s repository link:https://github.com/cbpark/YAM2Licensing provisions: BSD 3-ClauseProgramming language: C ++Nature of problem: The value and the solution of the M2 variables can be obtained from the optimality and feasibility conditions of the nonlinearly constrained minimization problem in numerical optimization. To perform the calculation properly, one should employ suitable numerical algorithms with the appropriate formulation of the variables, having in mind the algorithmic efficiency and the computational cost.Solution method: There exist various numerical methods for solving constrained optimization problems. We have chosen the sequential quadratic programming method with the derivative-dependent quasi-Newton algorithm since it performs very efficiently to find the local minimum using derivative information. The method has been codified by using the implementation of the numerical algorithms in the NLopt library [1]. The new library also includes the routines using other algorithms for calculating M2, such as the augmented Lagrangian method.

Application of sequential quadratic programming for obtaining optimal obstacle avoidance posture and end position of a 7-axis robotic manipulator

This paper used sequential quadratic programming (SQP) method to obtain the optimal obstacle avoidance posture and end position of a 7-axis robotic manipulator. By applying restraining conditions, obstacle information, and finishing point coordinates, a homogeneous transformation matrix was firstly used to construct a space for limited movement for the first and sixth axes of the robotic manipulator. Subsequently, we determined whether the terminal point was within reach of the robotic manipulator and calculated the angle of each axis. Finally, the MATLAB software was used to conduct a simulation and verification. In this study, the SQP method was used to introduce inequality constraints into the computation and conducted the iterative method. The simulation results revealed that the method can obtain avoidance of obstacle postures and select optimal values from the iteration results of multiple initial values to avoid the local optimal problem. Overall, the research findings are that the functions and applicability of the 7-axis robotic manipulator can be extended in industry when applied in future intelligent manufacturing.

Base position optimization of mobile manipulators for machining large complex components

• A BP optimization method for mobile manipulator considering both kinematics and stiffness performance is proposed. • A performance index MSPI is proposed to evaluate the robot's global stiffness performance. • A multi-constrained BP optimization model with maximum MSPI is established. • A sparse uniform grid decomposition + SQP solution method that can accurately obtain the optimal BP is designed. • Simulation and experiment verify the effectiveness of the BP optimization method. With good mobility and high flexibility, the mobile manipulator shows a broad application prospect in the machining of large complex components. In these applications, in order to fully utilize the capabilities of the robot, it is usually necessary to design a series of suitable working positions (i.e. robot's base position) for the mobile manipulator. However, the performance distribution of the robot in the task space is highly nonlinear, which makes it difficult to determine the optimal base positions. Therefore, this paper proposes a new base position optimization method, which can accurately find the optimal base position that takes into account both kinematics and stiffness performance. First, a task-oriented performance index MSPI (mean stiffness performance index) is proposed to evaluate the global stiffness performance of the robot. Based on MSPI, an optimization model considering multiple constraints such as joint range, joint speed, singular avoidance and collision avoidance is established. The optimization model is solved by sparse uniform grid decomposition and Sequential Quadratic Programming (SQP) method, the former is used to find a suitable initial value, the latter is used to determine the optimal base position. Finally, simulation analysis and experiments confirmed the effectiveness of the optimization method and the correctness of the performance index MSPI.

Energy and spectral efficiency trade-off in OCDMA-PON assisted by non-linear programming methods

Two important metrics for performance evaluation in optical code division multiple access networks (OCDMA) are energy efficiency (EE) and spectral efficiency (SE). Both metrics are investigated in this work through the bi-objective optimization approach by analyzing the trade-off between SE and EE. We first formulate the SE–EE optimization as a bi-objective optimization (BOO) problem with minimum rate requirement constraints. Then, considering the non-convexity of the BOO problem, it is converted into a single-objective optimization (SOO) problem by utilizing weighted sum method. Nonlinear programming methods as sequential quadratic programming method (SQP) and majoration–minimization (MaMi) are applied to solve the BOO problem, with QoS guarantees for the OCDMA networks. Resource efficiency (RE) is able to explore the trade-off between EE and SE in OCDMA networks. The optimization methods were applied and their performance-complexity trade-offs are compared with the exhaustive search (ES) method. Numerical results were performed considering practical and realistic scenarios, including a wide range of nodes, while the solutions obtained by the methods are represented in the Pareto front.

Continuation methods with the trusty time-stepping scheme for linearly constrained optimization with noisy data

The nonlinear optimization problem with linear constraints has many applications in engineering fields such as the visual-inertial navigation and localization of an unmanned aerial vehicle maintaining the horizontal flight. In order to solve this practical problem efficiently, this paper constructs a continuation method with the trusty time-stepping scheme for the linearly equality-constrained optimization problem at every sampling time. At every iteration, the new method only solves a system of linear equations other than the traditional optimization method such as the sequential quadratic programming (SQP) method, which needs to solve a quadratic programming subproblem. Consequently, the new method can save much more computational time than SQP. Numerical results show that the new method works well for this problem and its consumed time is about one fifth of that of SQP (the built-in subroutine fmincon.m of the MATLAB2018a environment) or that of the traditional dynamical method (the built-in subroutine ode15s.m of the MATLAB2018a environment). Furthermore, we also give the global convergence analysis of the new method.

Structural optimization of ultra-thin leaf spring for weakening elastic hysteresis effect and enhancing fatigue life

Small-size ultra-thin leaf spring as the key elastic sensitive member is widely used in the precision electro-mechanical products. However, owing to the unavoidable elastic hysteresis effect of leaf spring, it always suffers from a significant graceful degradation of designed deflection and subsequently fatigue fracture under the condition of cyclic loading. In order to weaken the elastic hysteresis effect, structural optimization according to sequential quadratic programming method for reducing stress concentration of leaf spring was first carried out by simulations, and then the identification of elastic hysteresis effect for optimal leaf spring was carried out by experiments. Compared with the original design, the maximum deflection deviation for single cycle is decreased from 0.026 mm to 0.002 mm. For the sake of predicting the fatigue life of optimal structure of leaf spring being on the service, a loading block with multistage variable stress amplitudes was experimentally recorded and fitted by normal probability density function, and then a statistical probability method by mathematical analysis was proposed. Compared with the original design, the predicted fatigue life of leaf spring is 736000 loading blocks, which is ten times than that before structural optimization. A structural optimization for reducing stress concentration can significantly weaken the elastic hysteresis effect and enhance the fatigue life, which is benefit for the elastic stability of leaf spring during engineering application.

Improved design of Lorentz force-type magnetic bearings for magnetically suspended gimballing flywheels

A Lorentz force-type magnetic bearing (LFMB) with good linearity is suitable for the high-precision deflection control of a magnetically suspended gimballing flywheel (MSGFW). In this paper, a novel LFMB with improved double magnetic circuits is presented. Inclined magnetization Halbach array permanent magnets (PMs) and trapezoidal PMs are utilized for improving the magnetic flux density. A mathematical model of the magnetic flux density is established based on the equivalent surface current method. To obtain the maximum magnetic flux density, the optimal magnetization angle is calculated, and the dimension parameters are optimized by the sequential quadratic programming method. A maximum magnetic flux density of 0.615 T is obtained, which is 7.9% larger than that of an LFMB with conventional double magnetic circuits. Based on simulation results, LFMB prototype magnetic flux density experiments are carried out. The results show that the magnetic flux density fluctuations of the two LFMB schemes are similar. The maximum magnetic flux density of 0.608 T is increased by 6.7% when compared with that of the LFMB with conventional double magnetic circuits at 0.57 T. The error between the simulation and the experiment is within 5%. This indicates that the LFMB with improved double magnetic circuits is promising when it comes to meet the agile maneuver requirements of the spacecraft.

A QCQP-based splitting SQP algorithm for two-block nonconvex constrained optimization problems with application

This paper discusses a class of two-block nonconvex smooth optimization problems with nonlinear constraints. Based on a quadratically constrained quadratic programming (QCQP) approximation, an augmented Lagrangian function (ALF), and a Lagrangian splitting technique into small-scale subproblems, we propose a novel sequential quadratic programming (SQP) algorithm. First, inspired by the augmented Lagrangian method (ALM), we penalize the quadratic equality constraints associated with the QCQP approximation subproblem in its objective by means of the ALF, and then split the resulting subproblem into two small-scale ones, but both of them are not quadratic programming (QP) due to the square of the quadratic equality constraints in the objective. Second, by ignoring the three-order infinitesimal arising from the squared term, the two small-scale subproblems are reduced to two standard QP subproblems, which can yield an improved search direction. Third, taking the ALF of the discussed problem as a merit function, the next iterate point is generated by the Armijo line search. As a result, a new SQP method, called QCQP-based splitting SQP method, is proposed. Under suitable conditions, the global convergence, strong convergence, iteration complexity and convergence rate of the proposed method are analyzed and obtained. Finally, preliminary numerical experiments and applications were carried out, and these show that the proposed method is promising.

Optimal chiller loading for energy conservation using a hybrid whale optimization algorithm based on population membrane systems

ABSTRACT The optimal chiller loading (OCL) is one of the most essential issues for saving energy and costs. Because of the pervasive use of chiller systems in the world, even saving a small amount of energy consumption in a chiller system can be significant. This study introduces a hybrid algorithm that could achieve similar or better results than those presented in previous studies for OCL problem. The whale optimization algorithm (WOA) is a recent promising algorithm for solving optimization problems with the small number of tuning parameters. However, it suffers from its inefficient exploitation around the best solution. To address this shortcoming, WOA-SQP was introduced that uses a sequential quadratic programming (SQP) method to exploit efficiently the search space around the best solution obtained by WOA. Although, WOA-SQP could achieve good results, but the variance of its solutions is high for different runs on the same problem. The non-deterministic distributed parallel framework of the population P system (PPS) enhances the diversity of WOA-SQP to minimize the variance of the solutions that shows the stability of the algorithm. Simulation results of the proposed algorithm on several case studies show the better performance of the proposed algorithm in comparison with the recent approaches.

Modified iterative learning controller for efficient power management of hybrid AC/DC microgrid

In this paper, modified ILC is proposed for maintaining stable voltage, frequency and for efficient power management in a hybrid micro grid (HMG). The system is modelled with solar, battery, DC loads at DC bus, wind turbine, utility grid and AC loads at AC bus. An interlinking converter (IC) is connected between the AC and DC bus to facilitate bidirectional power flow. The control of voltage at AC/DC bus and management of power are obtained in the modelled hybrid micro grid with set point weighting iterative learning controller (SPW-ILC) by controlling the interlinking converter both in autonomous and grid connected mode of operation. To minimise the error signal to the controller, the classical optimisation method of sequential quadratic programming (SQP) has been employed to improve the performance of the controller. The simulation results show that the proposed controller have better performance than other controllers under variable source and load conditions.