Sequential Quadratic Programming Algorithm Research Articles

A Stochastic Inexact Sequential Quadratic Optimization Algorithm for Nonlinear Equality-Constrained Optimization

A stochastic algorithm is proposed, analyzed, and tested experimentally for solving continuous optimization problems with nonlinear equality constraints. It is assumed that constraint function and derivative values can be computed but that only stochastic approximations are available for the objective function and its derivatives. The algorithm is of the sequential quadratic optimization variety. Distinguishing features of the algorithm are that it only employs stochastic objective gradient estimates that satisfy a relatively weak set of assumptions (while using neither objective function values nor estimates of them) and that it allows inexact subproblem solutions to be employed, the latter of which is particularly useful in large-scale settings when the matrices defining the subproblems are too large to form and/or factorize. Conditions are imposed on the inexact subproblem solutions that account for the fact that only stochastic objective gradient estimates are employed. Convergence results are established for the method. Numerical experiments show that the proposed method vastly outperforms a stochastic subgradient method and can outperform an alternative sequential quadratic programming algorithm that employs highly accurate subproblem solutions in every iteration. Funding: This material is based upon work supported by the National Science Foundation [Awards CCF-1740796 and CCF-2139735] and the Office of Naval Research [Award N00014-21-1-2532].

Training mode of university dance performers based on sequential quadratic programming algorithm

Dance performance is an art form, which needs to cultivate students’ dance skills, artistic accomplishment and stage performance ability. Sequential quadratic programming algorithm is an optimization algorithm that can be used to solve complex optimization problems. In this paper, Sequential Quadratic Programming (SQP) is applied to explore the training mode of dance performers in colleges to help dance performers develop the optimal training plan and program. Aiming at the problems existing in the training mode of dance performance talents in colleges, this paper put forward an optimization method based on SQP algorithm, and implemented its optimization scheme in actual colleges. In the planning of dance performance talent training mode, particle swarm optimization (PSO) is used to optimize SQP algorithm, so that it can have higher planning efficiency. This paper studied the goal and index system of the training of dance performance talents in colleges, generated a personalized training program, and further improved the scientific and practical effectiveness of the training mode. This paper investigated the current situation of dance performance talent training in several dance schools in a certain province of China. The survey data include practical curriculum planning, teachers’ teaching philosophy and teaching content. Combined with SQP algorithm, the teaching and training program is optimized. After evaluation, it can be concluded that the SQP algorithm optimized by PSO shows good stability and accuracy. It can calculate the optimal solution of the cultivation scheme, and when calculating the optimal solution, the running time of the Central Processing Unit (CPU) was only 5.6 s, which can further improve the efficiency of the planning. Finally, through the satisfaction and resource utilization test, it can be found that the number of people who are very satisfied with the teaching content of the dance performance talent training program optimized by SQP increased from 38.4% to 52.4%. After optimization, the average utilization rate of teaching resources reached 88.1%. It can be concluded that SQP algorithm can provide scientific basis for dance education institutions to improve the training mode of dance talents. This can help dance education institutions better improve the training mode, and improve the overall quality and dance skills of dance students.

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

Surge-Elimination Strategy for Aero-Engine Transient Control

Abstract The fundamental principle of the transient state control method for turbofan engines, which is based on the acceleration ratio of high-pressure rotational speed (N-dot), involves sacrificing a portion of the safety margin to obtain satisfactory acceleration performance. However, it could induce surge in the engine's compressor. To prevent the destructive damage caused by surge to both the engine and its components, a surge-elimination control strategy for the engine based on an N-dot controller is proposed. First, the engine mathematical model, which incorporates the effects of engine volumetric dynamics, stall zone characteristics, and combustion chamber flameout characteristics, is established to simulate surge mechanism. Subsequently, the acceleration schedule of the N-dot is calculated by employing sequential quadratic programming (SQP) algorithm to solve the multiconstraint optimization problem, while designing the transition state controller of N-dot based on a high-order filter. Finally, the surge detection logic and surge-elimination strategy based on the μ-correction method are proposed and designed to realize active control of surge elimination. The simulation results demonstrate that the N-dot control method offers significant advantages in mitigating the steady-state errors resulting from inevitable engine degradations. The surge state is effectively suppressed by the proposed surge-elimination control method, and the surge duration is significantly shorten during the acceleration phases. Furthermore, compared to the one without any surge-elimination control, the proposed method decreases the acceleration time by 5.53%.

Full-period operation optimization of the semi-regenerative reactor based on dehydrogenation reaction and deactivation kinetics

Semi-regenerative reactors are adopted in many catalytic processes. Based on industrial data, a one-dimensional pseudo-homogeneous reactor model was established for the semi-regenerative reactor of the dehydrogenation of heavy paraffins. The validation results show high accuracy of the model prediction. The Sequential Quadratic Programming (SQP) algorithm was employed for the full-period operation optimization of the reactor, resulting in a 3.04% increase in the yield of mono-olefins, but the optimized operation conditions are not consistent with common combination according to the practical production experience described in the literature. Further investigations for semi-regenerative reactors with different dehydrogenation systems show that the optimized combination of operation conditions in a full period is dependent on the depth of dehydrogenation, the rate of catalyst deactivation, and the duration of the period.

Optimizing heat source distribution in sintering molds: Integrating response surface model with sequential quadratic programming

The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an optimization approach that combines response surface models with the sequential quadratic programming algorithm to optimize the geometric parameters and heating power configuration of a heating system for sintering mold. The response surface models of the maximum temperature difference, maximum temperature, and minimum temperature of the sintering area are constructed utilizing the central composite design method. The model's reliability is rigorously confirmed through variance analysis, residual analysis, and generalization capability validation. The models demonstrate remarkable predictive accuracy within the design space. A nonlinear constrained optimization model is established based on the response surface models, and the optimal parameters are obtained after 9 iterations using the sequential quadratic programming algorithm. Under the optimal parameters, the maximum temperature difference is maintained at less than 5 °C, confirming exceptional temperature uniformity. We conduct parameter analysis based on standardized effects to determine the main influencing factors of temperature uniformity, revealing that the distance between adjacent heating rods and the power density of the inner heating rods exert significant influence. Enhanced temperature uniformity can be achieved by adopting a larger distance between heating rods and configuring the power density of the heating rods to a relatively modest level. This work introduces a practical approach to optimize the heating systems for sintering molds, with potential applications in various industrial mold optimization.

A Robot Positional Error Compensation Method Based on Improved Kriging Interpolation and Kronecker Products

This paper proposes a stable and high-accuracy model-free calibration method for unopened robotic systems, which can significantly improve the robot positional accuracy. Two improvements are made to the existing kriging-based error compensation method to achieve robustness/practicality enhancement goals: (1) The semi-variogram model is solved using the sequential quadratic programming (SQP) algorithm, and the distance weight coefficients are added to the objective function. The accuracy of semi-variogram modeling is guaranteed, thereby improving the performance and stability of error compensation. (2) The hand-eye (the pose matrix between the robot base and the laser tracker) and the tool center point (TCP) position are calibrated based on Kronecker products without relying on the spatial analyzer (SA) software to construct the robot base coordinate system separately. Thus, the calibration accuracy and efficiency are significantly improved. Experiments have been conducted, and the results reveal that the proposed method can significantly reduce the robot positional error. Furthermore, the proposed approach performs better than the existing kriging-based error compensation method without Kronecker products. The maximum, mean, and root mean square (RMS) values of the absolute positional errors are reduced by 34.48%, 8.09%, and 10.05%, respectively.

Optimization of surface texture distribution on the thrust bearing using the mass-conserving cavitation boundary condition: Theory and experiments

This study developed a numerical optimization model for the texture distribution in thrust bearings, employing the flat-headed chevron and circular dimple, and utilizing a mass-conserving cavitation boundary. A hybrid of the genetic algorithm and sequential quadratic programming algorithm is utilized. The results indicate the highest load-carrying capacity can be obtained by optimizing the texture distribution based on the flat-headed chevron. The primary mechanism is that the optimal distribution can efficiently harness the collective effect of texture, thereby effectively building up pressure. The optimal distributions of the flat-headed chevron and circular dimples exhibit asymmetric chevron and herringbone shapes, respectively. Furthermore, verification experiments show that the optimal distribution can shift the transition point to a lower rotation speed and higher normal load.

MIMO radar partially correlated waveform design based on chirp rate diversity

Waveform design is a significant topic in multiple-input-multiple-output (MIMO) radar. In this paper, we address the problem of waveform design for colocated narrowband MIMO radar transmit beampattern synthesis. The existing methods have not comprehensively considered the transmit beampattern synthesis under multiple practical constraints, such as constant modulus constraint, Doppler tolerance, high range resolution and low auto-correlation sidelobe. We consider these practical constraints and propose a novel chirp rate diversity-based linear frequency modulated (CRD-LFM) waveform design for approximating the desired MIMO radar transmit beampattern. To tackle the problem, we improve the classical two-step approach. Firstly we design the covariance matrix using the existing closed-form solution. Then we model the problem of obtaining the waveforms from the covariance matrix as a nonlinear optimization problem, and we utilize the Sequential Quadratic Programming (SQP) algorithm to solve it. The simulations demonstrate that the waveforms obtained by this method can well approximate the desired transmit beampattern and have higher range resolution. Furthermore, we verify that the suppression of auto-correlation sidelobe can be achieved using amplitude weighting, which is easily realizable in practical engineering.

Design, optimization and verification of a conical guiding origami mechanism for underwater docking station

Underwater docking station requires a conical guiding device with a large tolerance capacity and smaller volume to recover unmanned underwater vehicles (UUVs). Here, this paper innovatively introduces a conical guiding origami mechanism designed by an array and rotation approach based on a rigid origami mechanism. The Jacobian matrix method systematically calculates the degree of freedom (DOF) of the device. The variation function of dihedral angle in the folding process of the origami mechanism is derived, and the kinematics model is established within the Cartesian coordinate system. Based on this model, we established a mathematical model for optimizing the origami mechanism by considering number of units and unit volume as the design variables, subject to minimizing the underwater flow area and length. The sequential quadratic programming algorithm is employed to identify the optimum design variables. Subsequently, based on optimized results, collision simulation is carried out, and a conical guiding device tailored for an underwater docking station is successfully designed. The proposed device can be used as an underwater docking station to recover UUVs for ocean exploration. The proposed device has a large tolerance capacity, minimal shrinkage state cross-sectional area and length, excellent hydrodynamic performance, and a high spatial utilization rate.

Research on optimization method for flyby observation mission adapted to satellite on-board computation

In this paper, the optimization problem of orbital transfer strategy for orbital flyby observation missions is studied. A hybrid optimization method is proposed, which is improved to make it more suitable for satellite on-board computing. This new algorithm is designed to solve the initial value sensitivity problem of the sequential quadratic programming algorithm (SQP). It is consisted of the depth-first search algorithm (DFS) and the SQP algorithm and thus has the characteristics of fast convergence, high reliability, and good robustness. With this method, the DFS with a large step size is calculated first, and then the optimal value in the calculation result is used as the initial value of the SQP algorithm for further optimization. This method can obtain the approximate optimal solution available in engineering. The numerical simulation of an orbital transfer optimization problem is set to verify the effectiveness of the new hybrid algorithm. The simulation results compared with the genetic algorithm (GA) show that the proposed hybrid algorithm can effectively reduce the on-board resource occupation when getting similar results and thus can meet the needs of satellite on-board computing.

Optimization of working slope configuration in seasonal operations of cold regions open-pit mine

This paper proposes a method for dynamically controlling the working slope configuration in seasonal stripping open-pit coal mines. Constructing a bench group working slope model calculates the cyclic advancement time of the stripping working slope. A mathematical optimization model is then established to minimize the transport work of the overburden, and a Sequential Quadratic Programming (SQP) algorithm is employed to solve it. The method is applied to the Shengli West No. 2 open-pit coal mine, and the results show that the number of benches in the bench group is 5. The working bench width is 89 m, and the working slope advancement meets the stripping and mining engineering continuity requirements while minimizing the transport work of the overburden. The maximum advancement speed of the working slope under this configuration is 320 m/year. The paper also analyzes the working slope’s maximum advancement speed variation with changes in the bench combination form and cyclic advancement distance.

Landing trajectory and control optimization for helicopter encountering different tail rotor pitch lockups

In recent years, tail rotor failure has been a significant factor in helicopter accidents, contributing to around 30 % of all incidents. Among these failures, tail rotor pitch lockup accounts for nearly 2/3. However, there is currently a lack of research on the landing trajectory and control optimization for piloted helicopters facing tail rotor pitch lockup. Therefore, this paper aims to study the landing trajectory and pilot control strategy optimization during helicopter tail rotor pitch lockup. The findings of this research are expected to provide valuable insights and serve as a reference for subsequent real-time pilot-in-the-loop simulations and final flight tests. In this paper, we utilize the UH-60A helicopter as a prototype to establish a flight dynamics model and a pilot model. The aerodynamic forces and induced velocity of the main rotor are calculated using the blade element method and Pitt-Peters model. The rotor flap motion is simplified to a first-order harmonic quantity. We then formulate the problem of safe landing and control optimization as a nonlinear optimal control problem, with the cost function designed to reflect safety and feasibility during the flight and touchdown process. To solve the optimal control problem numerically, we use direct multiple shooting and sequential quadratic programming algorithms. Flight test data for the UH-60A, encompassing steady-state flight, dynamic response, and autorotation landing, are utilized to validate the accuracy of the flight dynamics model and the effectiveness of the optimal control algorithm. Finally, the paper investigates the safe landing trajectories and control strategies for the sample helicopter when encountering high tail rotor pitch lockup and low tail rotor pitch lockup, respectively. Simulation results demonstrate that when the tail rotor is stuck at a high pitch, it is advisable for pilots to execute a high-power state landing by maintaining the engine at high power while reducing forward speed and descent rate. Conversely, when the tail rotor is stuck at a low pitch, flying at an economical speed (in a low-power state) is advantageous, but it does not facilitate a safe landing thereafter. If the pilot attempts a conventional landing, the yaw rate at touchdown would be very high and potentially dangerous. In contrast, if an autorotation landing is executed, the landing will be safer with a much lower yaw rate at touchdown. The optimal landing trajectory and control process align with the recommendations from actual helicopter flight tests. The proposed method provides feasible pilot control strategies for safe landing when helicopters encounter various tail rotor pitch lockup situations. This research can serve as a reference for pilots before conducting actual flight tests.

Performance seeking control method for minimum pollutant emission mode for turbofan engine

The research shows that the impact of aero-engine pollutant emission on the environment cannot be ignored. In addition to fuel type and combustor structure, aero-engine exhaust pollutants are also related to engine operating conditions and control systems. In this context, taking CO and NOx as the main exhaust pollutants of the engine as the research object, a performance optimization control method of the minimum pollutant emission mode of the engine is proposed. Firstly, the CO and NOx emission characteristics of the engine under different operating conditions at sea level are calculated by CFD numerical simulation method, and the engine component-level model applicable to all flight envelope and all conditions is established according to the characteristic data. Secondly, in order to improve computational efficiency, an airborne model with high accuracy and real-time performance is established through the deep neural network. Compared to the component-level model, the average relative error of each performance parameter is less than 0.5 %, and the real-time performance is improved by about 12 times. Finally, the optimization principle of the minimum pollutant emission mode is discussed. The feasible sequential quadratic programming (FSQP) algorithm is selected, and the fuel quantity and throat area of the tail nozzle are taken as control variables. Numerical simulations are performed in the typical mission envelope. Simulation results show that the CO emission index decreases by 5 % and the NOx emission index decreases by more than 6.5 % through performance optimization control of the minimum pollutant emission mode under the premise of ensuring constant engine thrust and meeting other constraints.

Cooperative optimal train operation algorithm for utilizing regenerative braking energy

The efficient use of regenerative braking energy between trains can significantly reduce the net traction energy consumption in urban rail transit systems, and has attracted considerable attention in recent years. An effective way of using regenerative braking energy is to adjust the train's coasting or cruising phase to an acceleration phase to match the braking phase of a nearby train within the same substation. This paper formulates the train driving phase adjustment problem as a cooperative optimal control problem, where a novel energy constraint is introduced to ensure efficient use of regenerative braking energy during the adjusted phase with optimal traction effort. By applying the control parameterisation method and elaborate handling of the energy constraint and the non-smooth control bound constraint, we transform the formulated problem into a nonlinear programming problem. We then use the sequential quadratic programming algorithm to solve the resulting problem, with the gradients of the cost and constraint functions computed using the sensitivity method. Numerical examples based on real-world data for a subway line show the effectiveness of the proposed method and its advantages over a genetic algorithm in terms of energy savings and computational efficiency.

Research on energy management and control for six-wheel-drive electric bus rapid transit with photovoltaic-battery-supercapacitor

Electric Bus Rapid Transit is an effective solution to traffic congestion and environmental pollution. At present, Electric Bus Rapid Transit needs to be equipped with a large number of power batteries, which brings the key problems of long charging time, short driving range, and high comprehensive utilization cost. To solve the above problems, a novel six in-wheel motors driving Electric Bus Rapid Transit scheme with photovoltaic cells, lithium-ion batteries and supercapacitors (SWEBRT-PBS) is studied, constrained by the cost and comprehensive energy efficiency of vehicle. First, the system architecture for hybrid energy storage system composed of photovoltaic cells, lithium-ion batteries and supercapacitors (PBS) is analyzed. The life cycle cost function for PBS based on the degradation cost of lithium-ion batteries and the electricity cost of each energy source is proposed. The dynamic programming algorithm is employed to optimize the life cycle cost function of PBS, and then to obtain the optimal size of matches for supercapacitors. Second, the fixed step disturbance observation method is adopted to ensure stable power output in the maximum power point tracking controller of photovoltaic cells based on the vehicle application environment. Third, the power control rules are extracted based on the optimization results of dynamic programming algorithm, and the power allocation strategy for PBS with dynamic programming algorithm joint rules is formulated. Fourth, the overall efficiency function for driving system is established and optimized based on the sequential quadratic programming algorithm. The collaborative optimization strategy for SWEBRT-PBS is developed based on the corresponding optimization results, PBS operating modes and vehicle operating modes. The results show that the SWEBRT-PBS can reduce the number of lithium-ion batteries, thereby reducing the vehicle mass by 1.27 % and increasing the vehicle space utilization by 1.81 %. In addition, the comprehensive energy efficiency of vehicle can be improved by 28.79 %.

Configuration Optimization of a Skippable Anti-Ship Missile Considering Initial Kinematic Parameters

Skimming the sea at ultralow altitudes can be achieved by repeatedly touching and bouncing off water surface (commonly referred to as skipping), thus giving birth to skippable anti-ship missiles. However, the high impact load during skipping poses a safety hazard to the structure. Whether a missile can rebound primarily depends on the initial kinematic parameters, which also influence the impact load along with the configuration parameters. Therefore, it is important to optimize both of them. Due to the differences in types and complicated coupling of these parameters, the optimization problem becomes highly complex. In this paper, the grouped sequential quadratic programming (GSQP) algorithm is proposed to reduce the nonlinearity and nonconvexity of the problem. By bringing together the global search capability of cooperative co-evolutionary algorithm and the local search strength of GSQP, a combined optimization framework using decomposition strategies is constructed. With the support of fluid–structure interaction models, the optimization is performed to reduce impact load for the missile. The results demonstrate that simultaneously optimizing the configuration and initial kinematic parameters yields a reduction of 12.2% in the impact load on the premise of successful skipping. This research provides a valuable reference for the design of future skippable anti-ship missiles.

Application of the LPPL model in the identification and measurement of structural bubbles in the Chinese stock market

This study proposes innovative methods for determining the starting point and estimating the parameters of the LPPL model for predicting stock market bubbles. These methods address the challenges in determining the starting point of irregularly staged bubbles and the issues of multiple local optima or no solutions in previous prediction algorithms. The proposed LPPL model, incorporating innovative algorithms, is applied to the Chinese A-share market from 2018 to 2021. The starting points of structural bubbles are determined using the difference and grid search methods, and the sequential quadratic programming (SQP) algorithm is used to estimate the parameters of the LPPL model. The study measures and warns about structural bubbles in the A-share market. The results demonstrate that the LPPL model with the innovative algorithm can accurately measure staged and structural bubbles in the A-share market and provide reasonably accurate warnings of bubble bursts, which have been confirmed by the market multiple times.

Optimization of membrane thickness for proton exchange membrane electrolyzer considering hydrogen production efficiency and hydrogen permeation phenomenon

Reducing the membrane thickness of Proton exchange membrane (PEM) electrolyzer was found to efficiently promote the hydrogen production rate. However, it can also aggravate the phenomenon of hydrogen permeation, leading to an increased hydrogen content on the anode side and posing a risk of explosions. Thus, optimal design of the membrane thickness of PEM electrolyzer systems is crucial to ensure both safe and efficient hydrogen production. In this paper, we propose two optimization problems for the membrane thicknesses, aiming at achieving a balance between the hydrogen content on the anode side and the hydrogen production rate under constant and varying power input conditions. First, the theoretical model of a PEM electrolyzer is established, and a photovoltaic-PEM electrolyzer system is considered to provide varying power input conditions. Then, the two optimization problems are formulated and resolved using the sequential quadratic programming (SQP) and particle swarm optimization (PSO) algorithms, respectively. Our results reveal that the optimal membrane thickness decreases as the constant input power increases. This suggests that high/low power inputs require thin/thick membranes. For varying power input, we collected one year of solar radiation intensity data from four different regions in China. The findings demonstrate that the selection of the optimal membrane thickness depends not only on the average solar radiation intensity but also on its seasonal variations. By applying these strategies, we effectively optimize the membrane thickness in PEM electrolyzer systems, thereby enhancing the efficiency and safety of hydrogen production. The outcomes provide valuable insights for selecting the appropriate membrane thickness in regions with varying solar radiation intensities and accounting for seasonal variations in solar radiation.

A parameter optimization method of multi-layer nested slit resonator for the converter transformer noise in high voltage direct current converter station

We propose a parameter optimization method of multi-layer nested slit resonator (MNSR) for the converter transformer noise in a high voltage direct current (HVDC) converter station. With the optimization objective of achieving quasi-perfect sound absorption at the target frequencies and the structural parameters of MNSR as the optimization variables, the optimization model of the structural parameters of MNSR is established and then solved by the sequential quadratic programming algorithm (SQP). The theoretical and simulation results of the four validation cases show that the optimized MNSR can achieve quasi-perfect sound absorption at all target frequencies, which is consistent with the optimization objective. The parameter optimization design method provides an efficient method to design a dual-frequency quasi-perfect sound absorber for the converter transformer noise.