Sequential Quadratic Programming Solver Research Articles

Design of evolutionary computational intelligent solver for nonlinear corneal shape model by Mexican Hat and Gaussian wavelet neural networks

In this study, an integrated computational intelligence algorithm is implemented for the numerical treatment of the two-point boundary value problems that arise in the nonlinear corneal shape (NCS) model through the exploitation of wavelet neural networks including Mexican-Hat (MHWNNs) and Gaussian-wavelet (GWNNs) through global genetic algorithms (GAs) then hybridization with local sequential quadratic programming (SQP) solvers, i.e. MHWNNs-GAs, GWNNs-GAs, MHWNNs-GA-SQP, and GWNNs-GA-SQP respectively. The GWNNs and MHWNNs are applied to calculate the mean squared error of mathematical modeling of the proposed problem through objective functions while optimization of the fitness functions is initially conducted with an efficiency of global search GAs and then the efficacy of local search technique SQP for fine-tuning. A comparison of the proposed solutions of MHWNNs-GAs, GWNNs-GAs, MHWNNs-GA-SQP, and GWNNs-GA-SQP solvers with a reference solution of Adam’s method shows that the proposed schemes have better accuracy, stability, efficiency consistency on an independent number of runs analyzed through complexity analysis and different statistical operators.

A comparative study of sensitivity computations in ESDIRK-based optimal control problems

This paper compares the impact of iterated and direct approaches to sensitivity computation in fixed step-size explicit singly diagonally implicit Runge–Kutta (ESDIRK) methods when applied to optimal control problems (OCPs). We strictly use the principle of internal numerical differentiation (IND) for the iterated approach, i.e., reusing iteration matrix factorizations, the number of Newton-type iterations, and Newton iterates, to compute the sensitivities. The direct method computes the sensitivities without using the Newton schemes. We compare the impact of these sensitivity computations in OCPs for the quadruple tank system (QTS). We discretize the OCPs using multiple shooting and solve these with a sequential quadratic programming (SQP) solver. We benchmark the iterated and direct approaches against a base case. This base case applies the ESDIRK methods with exact Newton schemes and a direct approach for sensitivity computations. In these OCPs, we vary the number of integration steps between control intervals and evaluate the performance based on the number of SQP and QPs iterations, KKT violations, function evaluations, Jacobian updates, and iteration matrix factorizations. We also provide examples using the continuous-stirred tank reactor (CSTR), and the IPOPT algorithm instead of the SQP. For OCPs solved using SQP, the QTS results show the direct method converges only once, while the iterated approach and base case converges in all situations. Similar results are seen with the CSTR. Using IPOPT, both the iterated approach and base case converge in all cases. In contrast, the direct method only converges in all cases regarding the CSTR.

A fast and accurate domain decomposition nonlinear manifold reduced order model

This paper integrates nonlinear-manifold reduced order models (NM-ROMs) with domain decomposition (DD). NM-ROMs approximate the full order model (FOM) state in a nonlinear-manifold by training a shallow, sparse autoencoder using FOM snapshot data. These NM-ROMs can be advantageous over linear-subspace ROMs (LS-ROMs) for problems with slowly decaying Kolmogorov n-width. However, the number of NM-ROM parameters that need to be trained scales with the size of the FOM. Moreover, for “extreme-scale” problems, the storage of high-dimensional FOM snapshots alone can make ROM training expensive. To alleviate the training cost, this paper applies DD to the FOM, computes NM-ROMs on each subdomain, and couples them to obtain a global NM-ROM. This approach has several advantages: Subdomain NM-ROMs can be trained in parallel, involve fewer parameters to be trained than global NM-ROMs, require smaller subdomain FOM dimensional training data, and can be tailored to subdomain-specific features of the FOM. The shallow, sparse architecture of the autoencoder used in each subdomain NM-ROM allows application of hyper-reduction (HR), reducing the complexity caused by nonlinearity and yielding computational speedup of the NM-ROM. This paper provides the first application of NM-ROM (with HR) to a DD problem. In particular, this paper details an algebraic DD reformulation of the FOM, training a NM-ROM with HR for each subdomain, and a sequential quadratic programming (SQP) solver to evaluate the coupled global NM-ROM. Theoretical convergence results for the SQP method and a priori and a posteriori error estimates for the DD NM-ROM with HR are provided. The proposed DD NM-ROM with HR approach is numerically compared to a DD LS-ROM with HR on the 2D steady-state Burgers’ equation, showing an order of magnitude improvement in accuracy of the proposed DD NM-ROM over the DD LS-ROM.

Research on obstacle avoidance path planning of UAV in complex environments based on improved Bézier curve

Obstacle avoidance path planning is considered an essential requirement for unmanned aerial vehicle (UAV) to reach its designated mission area and perform its tasks. This study established a motion model and obstacle threat model for UAVs, and defined the cost coefficients for evading and crossing threat areas. To solve the problem of obstacle avoidance path planning with full coverage of threats, the cost coefficients were incorporated into the objective optimization function and solved by a combination of Sequential Quadratic Programming and Nonlinear Programming Solver. The problem of path planning under threat full coverage with no solution was resolved by improving the Bézier curve algorithm. By introducing the dynamic threat velocity obstacle model and calculating the relative and absolute collision cones, a path planning algorithm under multiple dynamic threats was proposed to solve the difficulties of dynamic obstacle prediction and avoidance. Simulation results revealed that the proposed Through-out method was more effective in handling full threat coverage and dynamic threats than traditional path planning methods namely, Detour or Cross Gaps. Our study offers valuable insights into autonomous path planning for UAVs that operate under complex threat conditions. This work is anticipated to contribute to the future development of more advanced and intelligent UAV systems.

Model predictive control of power plant cycling using Industry 4.0 infrastructure

This work involves the Industry 4.0 infrastructure developed at West Virginia University (WVU) for process systems applications. This infrastructure emulates an interconnected environment, enabling communication and data sharing among different components for use in academic and industrial settings. The current infrastructure encompasses a power plant model interacting with online load demand, distributed control systems, and data analytics components. The developed model of a sub-critical coal-fired power plant is employed to evaluate classical and advanced control strategies using this infrastructure under different operating conditions. Specifically, the control strategies evaluated include classical proportional–integral–derivative (PID) and advanced model predictive control (MPC) structures, focusing on the dynamic matrix control (DMC) approach with an in-house modified sequential quadratic programming (SQP) solver. The MPC approach is developed and simulated in closed loop to address setpoint tracking and load-following scenarios under power plant cycling conditions. In this infrastructure, the PI System centralizes all the information received from the power plant model and the online power demand and sends the control actions calculated by the MPC back to the power plant model for implementation. Results of the implementation of these control strategies are discussed focusing on power plant operating regions associated with cycling.

Design of Spline-Evolutionary Computing Paradigm for Nonlinear Thin Film Flow Model.

A novel design of stochastic numerical computing method is introduced for computational fluid dynamics problem governed with nonlinear thin film flow (TFF) system by exploiting the competency of polynomial splines for discretization and optimization with evolutionary computing aided with brilliance of local search. The TFF model of second grade fluid is represented with nonlinear second-order differential system. The aim of the present work is to exploit the cubic spline approach (CSA) to transform the differential equations for TFF model into an equivalent set of nonlinear equations. The approximation in mean squared error sense is introduced for the formulation of cost function for solving the nonlinear system of equations representing TFF model. The optimization of the decision variables of the cost function is carried out with global search efficacy of evolution by genetic algorithms (GAs) integrated with sequential quadratic programming (SQP) for speedy adjustments. The designed spline–evolutionary computing paradigm, CSA–GA–SQP, is evaluated for different scenarios of TFF model by variation of second grade and magnetic parameters, as well as variation in the length of splines. Results endorsed the worth of CSA–GA–SQP solver as an efficient alternative, reliable, stable, and accurate framework for the variants of nonlinear TFF systems on the basis of multiple autonomous executions. The design computing spline paradigm CSA–GA–SQP is a promising alternative numerical solver to be implemented for the solution of stiff nonlinear systems representing the complex scenarios of computational fluid dynamics problems.

Real‐time control algorithm for minimising energy consumption in parallel hybrid electric vehicles

In this work, a real-time energy management problem for a parallel hybrid electric vehicle (HEV) is proposed. The considered powertrain is built from a commercial HEV model. First, a non-linear optimal control problem under model predictive control scheme is formulated. The designed controller aims to generate the optimal power split and gear ratio schedule with respect to minimise the energy consumption of fuel and electricity. Moreover, the multiple shooting algorithm is introduced to decouple the dynamic constraints with the ability of avoiding the strong non-linearity while solving the optimisation problem. After that the optimisation problem is solved using sequential quadratic programming solver. Then, to evaluate the performance of the proposed real-time optimisation strategy on different traffic scenarios, the controller is applied to an adaptive cruise control (ACC) under connected environment. In this case, a solution of ACC with consideration of minimising energy consumption and maintaining string stability is provided. Finally, the proposed controller can be implemented in the traffic-in-the-loop platform without the knowledge of the predefined driving route. Simulations reveal that the proposed real-time control scheme shows great optimisation performance under the designed scenarios.

Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method

A novel framework for resolving discontinuous solutions of conservation laws, e.g., contact lines, shock waves, and interfaces, using implicit tracking and a high-order discontinuous Galerkin (DG) discretization was introduced in [39]. Central to the framework is an optimization problem whose solution is a discontinuity-aligned mesh and the corresponding high-order approximation to the flow that does not require explicit meshing of the unknown discontinuity surface. The method was shown to deliver highly accurate solutions on coarse, high-order discretizations without nonlinear stabilization and recover optimal convergence rates O(hp+1) even for problems with discontinuous solutions. This work extends the implicit tracking framework such that robustness is improved and convergence accelerated. In particular, we introduce an improved formulation of the central optimization problem and an associated sequential quadratic programming (SQP) solver. The new error-based objective function penalizes violation of the DG residual in an enriched test space and is shown to have excellent tracking properties. The SQP solver simultaneously converges the nodal coordinates of the mesh and DG solution to their optimal values and is equipped with a number of features to ensure robust, fast convergence: Levenberg-Marquardt approximation of the Hessian with weighted elliptic regularization, backtracking line search based on the ℓ1 merit function, and rigorous convergence criteria. We use the proposed method to solve a range of inviscid conservation laws of varying difficulty. We show the method is able to deliver accurate solutions on coarse, high-order meshes and the SQP solver is robust and usually able to drive the first-order optimality system to tight tolerances.

Inverse Simulation for Gas Turbine Engine Control through Differential Algebraic Inequality Formulation

Abstract Modern day gas turbines are prime movers in land, air and sea. They have stringent performance requirements to meet the complex mission objectives. Optimal control strategies can help them meet their performance objectives more efficiently. A novel inverse simulation method for optimal control and system analysis studies using Differential Algebraic Equality/Inequality (DAE/DAI) technique is brought out in this paper with a case study. The gas turbine model together with safety constraints and performance specifications is represented as a high index DAI/DAE system. The solution for this DAE/DAI system is obtained using a new numerical approach that is capable of handling both equality and inequality constraints on system dynamics. The algorithm involves direct numerical integration of a DAI formulation in a time stepping manner using Sequential Quadratic Programming (SQP) solver that detects and satisfy active constraints at each time step (mesh point). In this unique approach the model and the constraints are always solved together. The method ensures stable solution at each time step, local minimum at each iteration of simulation and provides a regularised basis to the solver. Compared to other existing computationally intensive techniques in usage, this approach is easy, ensures continuous constraint satisfaction and provides a viable option for Model Predictive Control (MPC) of gas turbine engines.

Gradient-based constrained well placement optimization

A novel well placement gradient approximation methodology is developed based on performing finite difference approximations of augmented Lagrangian derivatives within the adjoint formulation. The methodology is efficient because it requires only a pair of (forward and backward) simulations to yield a cost function sensitivity with respect to well placement coordinates. The approximated derivative is used within a Sequential Quadratic Programming (SQP) solver ensuring fast convergence and efficient constraint-handling. An extensive error analysis is performed to identify the gradient approximation errors associated with different perturbation ranges. This analysis provides information regarding the appropriate perturbation step size range needed to maintain a consistent gradient approximation while reducing errors associated with the simulation and the discretized nature of the reservoir. We validate the efficiency of the approach by solving for optimal well placement and comparing the results against two major gradient-based well placement approaches from the literature. For these cases, the methodology developed in this work delivers higher or similar final objective values while providing better performance in terms of fewer cost function evaluations. Finally, the methodology is used to find the optimal configuration of multiple deviated producers both in a binary channelized case and in a case based on the Brugge reservoir. These applications show that the proposed methodology can handle cases with more complex grid and production scenarios that require derivative information for the location of deviated wellbores in continuous space.

Optimal placement and control variable setting of power flow controllers in multi-terminal HVDC grids for enhancing static security

This research proposes an approach to select an optimal place and control variable setting for recently proposed Power Flow Controller (PFC)s including series, cascaded, and interline PFCs in Multi-Terminal High-Voltage DC (MT-HVDC) grids based on sensitivity analysis technique to enhance static security. To do so, appropriate static power injection models of the PFCs are obtained. Accordingly, sensitivity relationships between the defined power performance index and each PFCs control variable are obtained. It is for the optimal PFCs placement purpose in order to utilize maximum capacities of the transmission grid. Optimal settings for the PFC as well as the controllable voltage source converters are computed in turn by applying sequential quadratic programming solver to the developed security-based DC optimal power-flow problem which includes several corrective constraints. The study scope is single contingencies affecting HVDC lines with the objective of eliminating the consequent overloaded HVDC lines and thereby enhancing the MT-HVDC grid security by controlling the power flows within the MT-HVDC grid. Static simulations are performed considering two generic four-terminal and eighth-terminal MT-HVDC test grids in order to demonstrate the proposed methods effectiveness and authenticate its robustness. The obtained results indicate that the MT-HVDC grid can remain secure under single HVDC line contingencies in most cases by implementing the proposed method.

Multicontact Postures Computation on Manifolds

We propose a framework to generate static robot configurations satisfying a set of physical and geometrical constraints. This is done by formulating nonlinear constrained optimization problems over non-Euclidean manifolds and solving them. To do so, we present a new sequential quadratic programming (SQP) solver working natively on general manifolds, and propose an interface to easily formulate the problems, with the tedious and error-prone work automated for the user. We also introduce several new types of constraints for having more complex contacts or working on forces/torques. Our approach allows an elegant mathematical description of the constraints and we exemplify it through formulation and computation examples in complex scenarios with humanoid robots.

Multifunctional design of heterogeneous cellular structures

Mesoscale cellular structures with different desired physical properties are promising for a broad spectrum of applications. The availability of Additive Manufacturing (AM) technology has significantly relaxed the fabricating limitation of cellular structures. It enables the design of cellular structure with complex cell topologies and relative density distribution. In this paper, a multifunctional design method for heterogeneous cellular structures is proposed. To introduce this method, Function-Performance-Property-Design parameter model is proposed at first. This proposed model can help designers to analyze the complex relations between focused functions and their related design parameters. Based on the proposed F-P-P-D model, the template of compromise Decision Support Problem (DSP) is applied to generate the optimization formulation which can generally consider the performances defined for several different functions. To solve the defined optimization problem, a multifunctional design simulation infrastructure is proposed for the designed heterogeneous cellular structures. Based on this simulation infrastructure, both the value of the objective function and its gradients can be evaluated. Then, Sequential Quadratic Programming (SQP) solver can be applied to solve the defined optimization formulation. The optimal relative density of cellular structures can be achieved and converted to the heterogeneous cellular structures at the end. A case study is provided at the end of this paper. For this case study, two different cell topologies and several different combinations of optimization parameters are used. A brief discussion is made to conclude the effects of cell topologies and other optimization parameters on the optimization results. Generally, the result of this design case validates the efficiency of the proposed design method. This method provides a useful design tool for users to take advantage of heterogeneous cellular structures for multifunctional purposes.

Power Quality Characteristics of a Multilevel Current Source With Optimal Predictive Scheme From More-Electric-Aircraft Perspective

Revolutionary design power architectures into electric aircraft system are being actively discussed to cope with the issues of a present state-of-the-art technology. The two demanding objectives in more-electric-aircraft (MEA) concept are power quality enhancement and increased level of redundancy despite of higher on-board power supply requirement throughout aircraft operation. In addressing the open challenges, this study outlines an operational characteristics of a three-phase multilevel shunt active filter (SAF) deployed for distribution power system in emerging MEA. The introduced shunt active filter is based on modular multilevel converter configuration for harmonic-current compensation purposes. On this foundation, a current control strategy for SAF is designed with a finite-control-set model predictive control technique. The developed solution provides several merits into aircraft electrical network as easy implementation on embedded platforms, controllable feature with a wide range of current frequencies, producing exact current harmonic replica onto the supply side over a given prediction horizon, and modular design with redundancy functionality. Dedicated predictive control system helps to better execution-time efficiency together with low sensitivity over the constraints imposed upon the optimization formulation through an integrated perturbation analysis and sequential quadratic programming solver. Simulation and experimental verifications for the three-phase four-level shunt active power filter are discussed, where robust behavior of handling harmonic currents with respect to the supply impedance and fundamental frequency variations is achieved, when the harmonic distortion levels fulfill the IEEE Standard 519 recommendations.

Heterogeneous multi-agent optimization framework with application to synthesizing optimal nuclear waste blends

Multi-agent optimization method is a nature-inspired framework that supports the cooperative search of an optimal solution of an optimization problem by a group of algorithmic agents connected through an environment with certain predefined information sharing protocol. In this work, we propose a novel heterogeneous multi-agent optimization (HTMAO) framework. The proposed framework is validated using a set of benchmark problems a real-world synthesizing radioactive waste blending problem. The optimal radioactive waste blending problem is formulated as a mixed integer nonlinear programming. The total frit used for vitrification process is minimized subject to thermodynamic properties and process model constraints. The model simultaneously determines the optimal decisions that include the combination of the waste tanks that form each waste blend and the amount of frit needed for the vitrification of each waste blend. In developing the HTMAO framework, efficient ant colony optimization algorithms; efficient simulated annealing; efficient genetic algorithm; and sequential quadratic programming solver are considered as algorithmic agents. We illustrate this approach through a real-world case study of the optimal radioactive waste blending of Hanford site in Southern Washington where nuclear waste is stored.

Nonlinear Model Predictive Control for Unmanned Aerial Vehicles

This paper discusses the derivation and implementation of a nonlinear model predictive control law for tracking reference trajectories and constrained control of a quadrotor platform. The approach uses the state-dependent coefficient form to capture the system nonlinearities into a pseudo-linear system matrix. The state-dependent coefficient form is derived following a rigorous analysis of aerial vehicle dynamics that systematically accounts for the peculiarities of such systems. The same state-dependent coefficient form is exploited for obtaining a nonlinear equivalent of the model predictive control. The nonlinear model predictive control law is derived by first transforming the continuous system into a sampled-data form and and then using a sequential quadratic programming solver while accounting for input, output and state constraints. The boundedness of the tracking errors using the sampled-data implementation is shown explicitly. The performance of the nonlinear controller is illustrated through representative simulations showing the tracking of several aggressive reference trajectories with and without disturbances.

Trajectory feasibility evaluation using path prescribed control of unmanned aerial vehicle in differential algebraic equations framework

ABSTRACTMission simulation is a critical activity in the development and operation of Unmanned Aerial Vehicles (UAVs). It is important to ascertain the feasibility of a trajectory in a mission. In this work, an algorithm has been developed for feasibility study of a trajectory of a UAV using prescribed path optimal control through an inverse simulation method. This has been done under a Differential Algebraic Equations (DAE)/Inequalities (DAI) framework. The UAV model together with constraints is represented as a high index DAE system. The trajectory that UAV shall take is prescribed as one of the constraint equations. The solution for the DAE system is obtained using a variation of the alpha method that is capable of handling both equality and inequality constraints on system dynamics. The algorithm involves direct numerical integration of a DAI formulation in a time-stepping manner using a Sequential Quadratic Programming (SQP) solver that detects and satisfy active path constraints at each time step (mesh point). In this unique approach, the model and the constraints are always solved together. The method ensures stable solution at each time step, local minimum at each iteration of simulation and provides a regularised basis to the solver. A typical UAV trajectory has been simulated and demonstrated in this paper. This new approach can be used for path planning of UAVs before the actual control law is designed for flight control computer. Compared to other existing computationally intensive techniques, this approach is computationally simple, ensures continuous constraint satisfaction and provides a viable option for model predictive control of UAVs.

Feasibility refinement in sequential quadratic programming using parametric sensitivity analysis

In this paper we present results that extend the sequential quadratic programming (SQP) algorithm with an additional feasibility refinement based on parametric sensitivity derivatives. The refinement is applicable without restriction on the problem dimensions in sparse SQP solvers. Parametric sensitivity analysis is a tool for post optimality analysis of the solution of a nonlinear optimization problem. For the refinement approach we apply this technique on the quadratic subproblems in order to improve the overall algorithm. The sensitivity derivatives required for this approach can be computed without noticeable computational effort as the system of linear equations to be solved coincides with the system already solved for the search direction computation. For similar algorithms in the context of post optimality analysis a linear rate of convergence has been proven and therefore an extrapolation method is applied to speed up the process. The presented algorithm has been integrated into the nonlinear program (NLP) solver WORHP and we perform a numerical study to evaluate different termination criteria for the proposed algorithm. Furthermore, numerical results on the CUTEst test set are shown.

An efficient second-order SQP method for structural topology optimization

This article presents a Sequential Quadratic Programming (SQP) solver for structural topology optimization problems named TopSQP. The implementation is based on the general SQP method proposed in M...

Probabilistic constraints via SQP solver: application to a renewable energy management problem

This paper aims at illustrating the efficient solution of nonlinear optimization problems with joint probabilistic constraints under multivariate Gaussian distributions. The numerical solution approach is based on Sequential Quadratic Programming (SQP) and is applied to a renewable energy management problem. We consider a coupled system of hydro and wind power production used in order to satisfy some local demand of energy and to sell/buy excessive or missing energy on a day-ahead and intraday market, respectively. A short term planning horizon of 2 days is considered and only wind power is assumed to be random. In the first part of the paper, we develop an appropriate optimization problem involving a probabilistic constraint reflecting demand satisfaction. Major attention will be payed to formulate this probabilistic constraint not directly in terms of random wind energy produced but rather in terms of random wind speed, in order to benefit from a large data base for identifying an appropriate distribution of the random parameter. The second part presents some details on integrating Genz’ code for Gaussian probabilities of rectangles into the environment of the SQP solver SNOPT. The procedure is validated by means of a simplified optimization problem which by its convex structure allows to estimate the gap between the numerical and theoretical optimal values, respectively. In the last part, numerical results are presented and discussed for the original (nonconvex) optimization problem.