Sequential Quadratic Programming Approach Research Articles

Efficient power allocation with individual QoS guarantees in future small-cell networks

Small-cell is a key technology for next generation mobile networks to cope with the explosive growth of data traffic. In this paper, our objective is to enhance the sum rate of the small-cell networks. We optimize the uplink transmission subject to guaranteeing the quality of services (QoS) requirement of each user and the maximum transmit power constraint at each node. A new sequential quadratic programming (SQP) based solution is proposed to solve the non-convex optimization problem. Further, a low complexity sub-optimal scheme is also proposed. It is found that under the proposed SQP approach, the sum rate of the system increases with increasing the available transmit power and decreases with increasing the minimum rate requirement. Simulation results show that the proposed SQP approach significantly outperforms the sub-optimal scheme in terms of system sum capacity.

ICM method for topology optimization of multimaterial continuum structure with displacement constraint

A new topology optimization method is formulated for lightweight design of multimaterial structures, using the independent continuous mapping (ICM) method to minimize the weight with a prescribed nodal displacement constraint. Two types of independent topological variable are used to identify the presence of elements and select the material for each phase, to realize the interpolations of the element stiffness matrix and total weight. Furthermore, an explicit expression for the optimized formulation is derived, using approximations of the displacement and weight given by first- and second-order Taylor expansions. The optimization problem is thereby transformed into a standard quadratic programming problem that can be solved using a sequential quadratic programming approach. The feasibility and effectiveness of the proposed multimaterial topology optimization method are demonstrated by determining the best load transfer path for four numerical examples. The results reveal that the topologically optimized configuration of the multimaterial structure varies with the material properties, load conditions, and constraint. Firstly, the weight of the optimized multimaterial structure is found to be lower than that composed of a single material. Secondly, under the precondition of a displacement constraint, the weight of the topologically optimized multimaterial structure decreases as the displacement constraint value is increased. Finally, the topologically optimized multimaterial structures differ depending on the elastic modulus of the materials. Besides, the established optimization formulation is more reliable and suitable for use in practical engineering applications with structural performance parameters as constraint.

Look-Ahead Traffic-Based Optimal Velocity Planning for Parallel HEVs

Abstract This paper proposes a real-time look-ahead velocity planning and torque distribution ratio prediction for parallel hybrid electric vehicles(HEVs) with consideration of traffic conditions in minimization of fuel and electricity consumptions. Firstly, mathematical models that could depict vehicle dynamics and surrounding look-ahead traffic dynamics for vehicle following scenario are built. Then, a receding horizon optimization problem that trades off fuel and electricity consumptions with dynamics model constraints is formulated. The proposed nonlinear model predictive control optimal problem is decoupled by multiple shooting and solved by a sequential quadratic programming approach to obtain numerical solutions. Simulations are conducted in MATLAB/Simulink platform with different emulated real-world traffic scenarios. Simulation results demonstrate the effectiveness of proposed control performance.

A new trust region–sequential quadratic programming approach for nonlinear systems based on nonlinear model predictive control

ABSTRACTIn this article, a superlinearly convergent trust region–sequential quadratic programming approach is first proposed, developed and investigated for nonlinear systems based on nonlinear model predictive control. The method incorporates a combination algorithm that allows both the trust region technique and the sequential quadratic programming method to be used. If the attempted search of the trust region method is not accepted, the line search rule will be adopted for the next iteration. Also, having to resolve the quadratic programming subproblem for nonlinear constrained optimization problems is avoided. This gives the potential for fast convergence in the neighbourhood of an optimal solution. Moreover, additional characteristics of the algorithm are that each quadratic programming subproblem is regularized and the quadratic programming subproblem always has a consistent point. The main result is illustrated on a nonlinear system with a variable parameter and a bipedal walking robot system through simulations and is utilized to achieve rapidly stability. Numerical results show that the trust region–sequential quadratic programming algorithm is feasible and effective for a nonlinear system with a variable parameter and a bipedal walking robot system. Therefore, the simulation results demonstrate the usefulness of the trust region–sequential quadratic programming approach with nonlinear model predictive control for real-time control systems.

Hierarchical Direct Yaw-Moment Control System Design for In-Wheel Motor Driven Electric Vehicle

In this study, a hierarchical structured direct yaw-moment control (DYC) system, which consists of a main-loop controller and a servo-loop controller, is designed to enhance the handling and stability of an in-wheel motor driven driven electric vehicle (IEV). In the main loop, a Fractional Order PID (FO-PID) controller is proposed to generate desired external yaw moment. A modified Differential Evolution (M-DE) algorithm is adopted to optimize the controller parameters. In the servo-loop controller, the desired external yaw moment is optimally distributed to individual wheel torques by using sequential quadratic programming (SQP) approach, with the tire force boundaries estimated by Unscented Kalman Filter (UKF) based on a fitted empirical tire model. The IEV prototype is virtually modelled by using Adams/Car collaborating with SolidWorks, validated by track tests, and serves as the control plant for simulation. The feasibility and effectiveness of the designed control system are examined by simulations in typical handling maneuver scenarios.

Decoupling the constraints for process simulation in large-scale flowsheet optimization

A distinct advantage of sequential quadratic programming (SQP) is global convergence that ensures convergence from a remote starting point. When the constraints are highly nonlinear such as in flowsheet optimization, however, locally convergent Newton's method used in SQP as the equation-solving tool may deteriorate the behavior of convergence. Our recognition that this issue remains to be resolved motivated us to study a two-tier SQP approach where the constraints for process simulation consisting of nonlinear equations are decoupled from the KKT system in order to block the adverse influence of nonlinearity on global convergence. Our equation oriented (EO) process simulator (Ishii and Otto, 2011) is employed to decouple the constraints and for maintaining feasibility of the decoupled constraints. The effectiveness and potential of the two-tier SQP approach for reliably and efficiently solving large-scale flowsheet optimization problems are numerically illustrated with fully thermally coupled distillation problems.

Bio-inspired computational heuristics to study models of HIV infection of CD4+ T-cell

In this work, biologically-inspired computing framework is developed for HIV infection of CD4[Formula: see text] T-cell model using feed-forward artificial neural networks (ANNs), genetic algorithms (GAs), sequential quadratic programming (SQP) and hybrid approach based on GA-SQP. The mathematical model for HIV infection of CD4[Formula: see text] T-cells is represented with the help of initial value problems (IVPs) based on the system of ordinary differential equations (ODEs). The ANN model for the system is constructed by exploiting its strength of universal approximation. An objective function is developed for the system through unsupervised error using ANNs in the mean square sense. Training with weights of ANNs is carried out with GAs for effective global search supported with SQP for efficient local search. The proposed scheme is evaluated on a number of scenarios for the HIV infection model by taking the different levels for infected cells, natural substitution rates of uninfected cells, and virus particles. Comparisons of the approximate solutions are made with results of Adams numerical solver to establish the correctness of the proposed scheme. Accuracy and convergence of the approach are validated through the results of statistical analysis based on the sufficient large number of independent runs.

Control of Three Degrees-of-Freedom Wave Energy Converters Using Pseudo-Spectral Methods

Abstract This paper presents a solution to the optimal control problem of a three degrees-of-freedom (3DOF) wave energy converter (WEC). The three modes are the heave, pitch, and surge. The dynamic model is characterized by a coupling between the pitch and surge modes, while the heave is decoupled. The heave, however, excites the pitch motion through nonlinear parametric excitation in the pitch mode. This paper uses Fourier series (FS) as basis functions to approximate the states and the control. A simplified model is first used where the parametric excitation term is neglected and a closed-form solution for the optimal control is developed. For the parametrically excited case, a sequential quadratic programming approach is implemented to solve for the optimal control numerically. Numerical results show that the harvested energy from three modes is greater than three times the harvested energy from the heave mode alone. Moreover, the harvested energy using a control that accounts for the parametric excitation is significantly higher than the energy harvested when neglecting this nonlinear parametric excitation term.

Multi-material topology optimization for the transient heat conduction problem using a sequential quadratic programming algorithm

ABSTRACTTransient heat conduction analysis involves extensive computational cost. It becomes more serious for multi-material topology optimization, in which many design variables are involved and hundreds of iterations are usually required for convergence. This article aims to provide an efficient quadratic approximation for multi-material topology optimization of transient heat conduction problems. Reciprocal-type variables, instead of relative densities, are introduced as design variables. The sequential quadratic programming approach with explicit Hessians can be utilized as the optimizer for the computationally demanding optimization problem, by setting up a sequence of quadratic programs, in which the thermal compliance and weight can be explicitly approximated by the first and second order Taylor series expansion in terms of design variables. Numerical examples show clearly that the present approach can achieve better performance in terms of computational efficiency and iteration number than the solid isotropic material with penalization method solved by the commonly used method of moving asymptotes. In addition, a more lightweight design can be achieved by using multi-phase materials for the transient heat conductive problem, which demonstrates the necessity for multi-material topology optimization.

Local optimum in multi-material topology optimization and solution by reciprocal variables

It is revealed that the local optimum is particularly prone to occur in multi-material topology optimization using the conventional SIMP method. To overcome these undesirable phenomena, reciprocal variables are introduced into the formulation of topology optimization for minimization of total weight with the prescribed constraint of various structural responses. The SIMP scheme of multi-phase materials is adopted as the interpolation of the elemental stiffness matrix, mass matrix and weight. The sensitivities of eigenvalue and weight with respect to design variables are derived. Explicit approximations of natural eigenvalue and weight are given with the help of the first and second order Taylor series expansion. Thus, the optimization problem is solved using a sequential quadratic programming approach, by setting up a sub-problem in the form of a quadratic program. The filtering technique by solving the Helmholtz-type partial differential equation is performed to eliminate the checkerboard patterns and mesh dependence. Numerical analysis indicates that it is beneficial to avoid the local optimum by using the reciprocal SIMP formulation. Besides, the structure composed of multi-materials can achieve a lighter design than that made from the exclusive base material. The effectiveness and capability of the proposed method are also verified by nodal displacement constraint and multiple constraints.

Reliability-based design optimization using SORM and SQP

In this work a second order approach for reliability-based design optimization (RBDO) with mixtures of uncorrelated non-Gaussian variables is derived by applying second order reliability methods (SORM) and sequential quadratic programming (SQP). The derivation is performed by introducing intermediate variables defined by the incremental iso-probabilistic transformation at the most probable point (MPP). By using these variables in the Taylor expansions of the constraints, a corresponding general first order reliability method (FORM) based quadratic programming (QP) problem is formulated and solved in the standard normal space. The MPP is found in the physical space in the metric of Hasofer-Lind by using a Newton algorithm, where the efficiency of the Newton method is obtained by introducing an inexact Jacobian and a line-search of Armijo type. The FORM-based SQP approach is then corrected by applying four SORM approaches: Breitung, Hohenbichler, Tvedt and a recent suggested formula. The proposed SORM-based SQP approach for RBDO is accurate, efficient and robust. This is demonstrated by solving several established benchmarks, with values on the target of reliability that are considerable higher than what is commonly used, for mixtures of five different distributions (normal, lognormal, Gumbel, gamma and Weibull). Established benchmarks are also generalized in order to study problems with large number of variables and several constraints. For instance, it is shown that the proposed approach efficiently solves a problem with 300 variables and 240 constraints within less than 20 CPU minutes on a laptop. Finally, a most well-know deterministic benchmark of a welded beam is treated as a RBDO problem using the proposed SORM-based SQP approach.

An inverse problem methodology for design and optimization of an interior permanent magnetic BLDC motor

In the theory of inverse problem, the parameters identification by optimization is considered as one of its main applications. This paper presents an optimal design of a slotted permanent magnet Brushless DC (BLDC) motor with surface mounted magnets. The inverse problem method is applied by using a thriving solver afforded by the nonlinear optimization toolbox of Matlab ‘Fmincon’, this function is based on Active-Set and Sequential Quadratic Programming approaches with calculation of the Hessian from Quasi-Newton algorithm. The optimal magnetic field density considered as the main objective is obtained by picking several parameters and analyzing their effects. The proposed approach is highlighted by using the obtained parameters in the design of the motor. The Finite element method is applied on the motor for numerical analysis by using FEMM magnetic coupled with Matlab code. Effectiveness and robustness of the proposed approach are verified by a comparison between the initial and optimized design.

Optimal design of continuous time irrational filter with a set of fractional order gammatone components via norm relaxed sequential quadratic programming approach

This paper proposes a continuous time irrational filter structure via a set of the fractional order Gammatone components instead of via a set of integer order Gammatone components. The filter design problem is formulated as a nonsmooth and nonconvex infinite constrained optimization problem. The nonsmooth function is approximated by a smooth operator. The domain of the constraint functions is sampled into a set of finite discrete points so the infinite constrained optimization problem is approximated by a finite constrained optimization problem. To find a near globally optimal solution, the norm relaxed sequential quadratic programming approach is applied to find the locally optimal solutions of this nonconvex optimization problem. The current or the previous locally optimal solutions are kicked out by adding the random vectors to them. The locally optimal solutions with the lower objective functional values are retained and the locally optimal solutions with the higher objective functional values are discarded. By iterating the above procedures, a near globally optimal solution is found. The designed filter is applied to perform the denoising. It is found that the signal to noise ratio of the designed filter is higher than those of the filters designed by the conventional gradient descent approach and the genetic algorithm method, while the required computational power of our proposed method is lower than those of the conventional gradient descent approach and the genetic algorithm method. Also, the signal to noise ratio of the filter with the fractional order Gammatone components is higher than those of the filter with the integer order Gammatone components and the conventional rational infinite impulse response filters.

Decentralized price-driven grid balancing via repurposed electric vehicle batteries

The share of electricity generated from intermittent renewable sources, e.g., wind and solar grows rapidly. This affects grid stability and power quality. If the share of renewable power generation is to be increased further, additional flexibilities must be introduced.Aggregating small, distributed loads and energy storage facilities is a good medium-term option. In this paper, the suitability of decentralized and on-site optimized storage system consisting of repurposed electric vehicle batteries for grid balancing is investigated. Battery operation is controlled via an optimization procedure, which relies on a one-way communicated pseudo-cost function (PCF). Day-ahead electricity stock market prices are used as the PCF.Based on one year simulations, a sequential quadratic programming (SQP) approach is compared to a dynamic programming (DP) and an integer linear programming (ILP) approach with respect to runtime and control objective. All approaches lead to very similar results, however ILP leads to the shortest runtimes. ILP is then used to investigate the grid balancing potential using last decade's hourly day-ahead prices. Higher market data resolutions featuring quarter-hours introduced in 2014 lead to higher earnings. For hourly day-ahead prices the optimal capacity-to-power ratio of the battery is approximately 6 h while for quarter-hourly prices it is about 3 h.

Efficient shape optimization for fluid–structure interaction problems

An approach for the shape optimization of fluid–structure interaction (FSI) problems is presented. It is based on a partitioned solution procedure for fluid–structure interaction, a shape representation with NURBS, and sequential quadratic programming approach for optimization within a parallel environment with MPI as direct coupling tool. The optimization procedure is accelerated by employing reduced order models based on a proper orthogonal decomposition method with snapshots and Kriging. After the verification of the FSI optimization, the functionality and efficiency of the reduced order modeling as well as the corresponding optimization procedure are investigated.

Numerical investigation of optimal yaw misalignment and collective pitch angle for load imbalance reduction of rigid and flexible HAWT blades under sheared inflow

Wind shear can strongly influence the cyclic loading on horizontal axis wind turbine blades. These load fluctuation causes a variation of power output and introduces fatigue load. Thus, individual pitch controllers have been developed that are focused on the load alleviations, however, comes at a price of actuator requirements for control. Moreover, these controllers are unable to apply to already existing wind turbines with active yaw and collective pitch control system. Therefore, the investigations for minimizing load imbalance through the adjustments of yaw misalignment and collective pitch angle are implemented for the rigid and flexible blades under the sheared inflow. By applying the optimization process based on a sequential quadratic programming approach, the optimal yaw and pitch angle can be estimated. Then, the numerical simulations for predicting the performance are performed. The results showed that the fluctuation range of the root flapwise bending moment for the rigid blades can be reduced by 84.5%, whereas the vibratory bending moment for the flexible blades can be reduced by up to approximately 82.4% in the best case. Therefore, the magnitudes of load imbalance can be minimized by the adjustment of the optimal yaw misalignment and collective pitch angle without any power loss.

Frequency Dependent Spencer Modeling of Magnetorheological Damper Using Hybrid Optimization Approach

Magnetorheological dampers have been widely used in civil and automotive industries. The nonlinear behavior of MR fluid makes MR damper modeling a challenging problem. In this paper, a frequency dependent MR damper model is proposed based on Spencer MR damper model. The parameters of the model are identified using an experimental data based hybrid optimization approach which is a combination of Genetic Algorithm and Sequential Quadratic Programming approach. The frequency in the proposed model is calculated using measured relative velocity and relative displacement between MR damper ends. Therefore, the MR damper model will be function of frequency. The mathematical model is validated using the experimental results which confirm the improvement in the accuracy of the model and consistency in the variation damping with the frequency.

Natural Preconditioning and Iterative Methods for Saddle Point Systems

The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or the discrete setting, so saddle point systems arising from the discretization of partial differential equation problems, such as those describing electromagnetic problems or incompressible flow, lead to equations with this structure, as do, for example, interior point methods and the sequential quadratic programming approach to nonlinear optimization. This survey concerns iterative solution methods for these problems and, in particular, shows how the problem formulation leads to natural preconditioners which guarantee a fast rate of convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness---in terms of rapidity of convergence---is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matri...

A sequential quadratic programming algorithm for equality-constrained optimization without derivatives

In this paper, we present a new model-based trust-region derivative-free optimization algorithm which can handle nonlinear equality constraints by applying a sequential quadratic programming (SQP) approach. The SQP methodology is one of the best known and most efficient frameworks to solve equality-constrained optimization problems in gradient-based optimization [see e.g. Lalee et al. (SIAM J Optim 8:682–706, 1998), Schittkowski (Optim Lett 5:283–296, 2011), Schittkowski and Yuan (Wiley encyclopedia of operations research and management science, Wiley, New York, 2010)]. Our derivative-free optimization (DFO) algorithm constructs local polynomial interpolation-based models of the objective and constraint functions and computes steps by solving QP sub-problems inside a region using the standard trust-region methodology. As it is crucial for such model-based methods to maintain a good geometry of the set of interpolation points, our algorithm exploits a self-correcting property of the interpolation set geometry. To deal with the trust-region constraint which is intrinsic to the approach of self-correcting geometry, the method of Byrd and Omojokun is applied. Moreover, we will show how the implementation of such a method can be enhanced to outperform well-known DFO packages on smooth equality-constrained optimization problems. Numerical experiments are carried out on a set of test problems from the CUTEst library and on a simulation-based engineering design problem.

Stochastic numerical treatment for thin film flow of third grade fluid using unsupervised neural networks

In the present study, novel soft computing techniques are developed for numerical treatment of non-linear thin film flow (TFF) problem of third grade fluids using artificial neural networks (ANNs), particle swarm optimization (PSO), sequential quadratic programming (SQP), and their hybrid combinations. The strength of universal function approximation capabilities of ANNs is exploited in formulation of mathematical model of the problem based on an unsupervised error. The training of the design parameter of the networks is performed with PSO, SQP, and hybrid approach PSO–SQP. The proposed schemes are evaluated on four variants of the two cases of TFF problems by taking different values of material parameter and Stokes number. The reliability and effectiveness of the proposed approaches are validated through the results of statistical analyses based on sufficient large number of independent runs.