Sequential Quadratic Programming Algorithm Research Articles

Optimization of an adaptive droop control and powers allocation for a distributed generator under loads and grid uncertainties

Microgrids (MGs) provide a promising means of action to manage different distributed energy systems and energy consumers within required electrical limits and to participate in system services. To address these characteristics, this paper investigates an optimal control based on the optimization of powers allocation and adaptive fuzzy logic droop control for a MG based on a renewable distributed generator ensuring ancillary services. In fact, a sequential quadratic programming algorithm is used as an optimization function. The optimization strategy is successfully performed and mainly has two purposes. The first one is for the optimization of the powers coefficients to determine the required quantities of reactive and active powers to be absorbed or injected to the power grid, in order to ameliorate the levels of its frequency and voltage. The second purpose is the optimization of the membership-function parameters of the adaptive fuzzy logic droop controllers to compensate the powers to be exchanged with the power grid. In addition to the optimization task, the MG is managed by a power management algorithm based on the fuzzy logic technology. The strategy is developed and simulated using MATLAB/Simulink. The simulation results demonstrate the efficacity of the optimization method and the power management supervisor.

Optimization Model of Raw Material Selection Process for Complex Industry Based on Improved Sequential Quadratic Programming Algorithm

Raw materials for industrial production mainly come from nature with wide sources and uneven quality, while production requires strictly with the materials’ quality and their quality indicators are very mutual coupling. In actual production, unreasonable combination and formula often exist in the process of raw material selection, impeding the improvement of production efficiency, quality, energy-saving, and emission reduction. Unfortunately, research on this actual issue is currently vacant, so the main object of this paper is to address the selection of raw materials and formulations in actual production. Based on the designed logical combination algorithm and improved SQP algorithm, this study established the batch combination model and formula calculation model from the perspective of optimal combination and formula. Finally, a practical example of actual production is given to demonstrate the utility and application of this research.

Multi-objective macrogeometry optimization of gears: Comparison between sequential quadratic programing and genetic algorithm

Deciding a gear pair’s macrogeometry parameters requires consideration of the factors such as cost of production, gear strength, and noise contributing parameters. A practical engineering problem is encountered when best possible gear geometry is needed for a fixed center distance to achieve the conflicting objectives. Further, constraints of practical utility on input parameters need to be taken into consideration for deciding the design space. This work represents comprehensive compilation of formulations of these often-conflicting objectives and constraints as non-linear functions and selection of an appropriate optimization technique to achieve a feasible design through a case study of a helical gear pair in high load carrying capacity mesh. For comparison of the quality of results and computational efficiency between gradient based and gradient free algorithms, Sequential Quadratic Programming and Genetic algorithm were used. The differences in the formulations of the objective functions for two algorithms were analyzed and addressed. Quadratic mutation rates and random crossovers were used to prevent premature convergence of Genetic Algorithm. Significant possible improvement in the base design was observed with both the algorithms.

Optimal design of an autonomous underwater helicopter's shape based on combinatorial optimization strategy

In this study, the shape of the autonomous underwater helicopter (AUH) was optimized. AUH is a new type of disc autonomous underwater vehicle with good maneuverability and flexibility. In this paper, an optimization mathematical model is established, which takes the resistance coefficient as the optimization objective and the internal volume and the actual engineering demand as the constraints. The optimization mathematical model of AUH is solved by using two combinatorial optimization strategies. Two combinatorial optimization strategies use experimental design algorithm and multi Island genetic algorithm (MIGA) as global search algorithm, and sequential quadratic programming algorithm as local search algorithm. And based on the back propagation (BP) neural network, the sample points are trained and fitted, and the cloud map of the resistance coefficient distribution in the design space is obtained. The optimization results show that compared with the initial resistance coefficient, the first optimal solution reduces by 9.14%, and the second optimal solution reduces by 9.53%. So the resistance performance of AUH is significantly improved, which proves the feasibility of the method proposed in this paper. This provides theoretical support for the shape optimization design of AUH, which will improve the motion performance of AUH in practical engineering applications.

Dynamic flow optimization for a three-loop fluid heat dissipation system in spacecraft

Dynamic optimization of the fluid loop is critical for the active thermal control system (ATCS) for future spacecraft. In this paper, the dynamic heat transfer model of a three-loop fluid heat dissipation system is constructed by the transient heat current modeling method to analyze the optimal control problem of dynamic flow allocation. A sequential quadratic programming (SQP) algorithm combined with the exact external penalty function method is designed to solve the difficulty of temperature path constraints. Simulation results show that the proposed method effectively improves the optimization effect of temperature path constraints and significantly reduces the computational time. Compared with the results of mean allocation flow (unoptimized) and steady flow optimization, the dynamic flow allocation reduced the residual heat by 6.9% and 21.5%, respectively, while meeting all the temperature constraints. In addition, the total flow rate needs to be increased at least by 48% to meet all temperature constraints and achieve similar heat dissipation capacity, when the flow allocation was designed as steady variables. The comparison results indicate that the dynamic flow allocation effectively improves the heat dissipation efficiency of the parallel fluid loop system and ensures the payload temperatures within the constraints.

Comparing Gradient-Free and Gradient-Based Multi-Objective Optimization Methodologies on the VKI-LS89 Turbine Vane Test Case

Abstract The present paper addresses the multi-objective aerodynamic shape optimization of the two-dimensional LS-89 turbine cascade. The objective is to minimize the entropy generation at subsonic and transonic flow conditions while maintaining the same flow turning. Nineteen design variables are used to parametrize the geometry. The optimization problem is used to compare two major classes of optimization algorithms and at the same time deduce if this problem has multiple local solutions or one global optimum. A first optimization strategy uses a gradient-based Sequential Quadratic Programming (SQP) algorithm. This SQP algorithm allows to directly handle the non-linear constraints during the optimization process. An adjoint solver is used for computing the sensitivities of the flow quantities with respect to the design variables, such that the additional gradient computational cost is nearly independent of the number of design variables. In addition, the same optimization problem is performed with a gradient-free-metamodel assisted-evolutionary algorithm. A comparison of the two Pareto-fronts obtained with both methods shows that the gradient-based approach allows to find the same optimum at a reduced computational cost. Moreover, the results suggest that the considered optimization problem is uni-modal. In other terms, it is characterized by a single optimal solution.

Design robust H∞ -PID controller for a helicopter system using sequential quadratic programming algorithm

ABSTRACT This paper proposes a new methodology for designing a controller for the tracking control problem in a 2 DoF helicopter system. The control problem is formulated as a nonlinear constraint optimization problem. Also, a sequential quadratic programming algorithm is applied to tune the PID gains according to the H infinity specifications. Tuning is done by selecting relevant objective functions and constraints. A nonlinear model of the 2 DoF helicopter is linearized and decoupled into two SISO systems (i.e. Yaw and Pitch models). Two independent controllers are designed for the models. For the purpose of demonstrating the robustness and superiority of the proposed method, the method is compared with a standard H infinity. Next, the performances of both controllers are examined. That allows the effects of system uncertainties, external disturbances and different tracking command signals take place.

Feasibility of Approximate Model Optimization for Lightweight Design of Vehicle Body Structure Based on Sequential Quadratic Programming Algorithm

Feasibility of Approximate Model Optimization for Lightweight Design of Vehicle Body Structure Based on Sequential Quadratic Programming Algorithm

A dynamic optimization method for power distribution network operation with high ratio photovoltaics

With the high ratio distributed photovoltaics (PVs) penetration to the distribution network (DN), the bearing capacity, integration capacity, consuming capacity and controlling capacity of DN for PVs are all facing great challenges. Enhancing the flexible regulation and operation optimization capabilities of DN have become key factors to satisfy these new challenges. For the operation optimization problem of high ratio PVs penetration, a novel quasi-equal curtailment ratio (QCR) constraint of PVs is proposed in the dynamic optimization method for DN operation. Firstly, the uncertainty of high ratio PVs and their active power deviations are discussed. And a dynamic optimization framework of PVs based on optimal power flow (OPF) has been proposed. Secondly, the optimization model for high ratio PVs is formulated with multi-objective of maximum PVs output, minimum voltage deviation and minimum line loss, under the equality and inequality constraints of power flow, PVs power generation limit, QCR of PVs and so on. Then the multi-objective optimization problem (MOP) is transformed into a single-objective optimization problem (SOP) by weighting coefficients, and solved by sequential quadratic programming (SQP) with trust-region (TR) searching algorithm. Finally, the proposed method is tested, verified and compared with the primal dual interior point (PDIP) and traditional SQP algorithms in IEEE 33-bus, PG&E 69-bus, 292-bus and 1180-bus test cases. The experimental results show the rapidity and robustness of the proposed method.

Development of optimal speed trajectory control strategy for electric vehicles to suppress battery aging

In order to suppress the battery aging of electric vehicles (EVs), a multi-objective optimization function is established to describe the battery aging behavior based on a high-precision battery aging model, and the state–space equation is then constructed to reveal the intrinsic relationship between vehicle speed, acceleration, and battery state-of-charge (SOC). The constructed optimization model is solved by using a sequential quadratic programming (SQP) algorithm, and based on the model predictive control (MPC) theory, the efficient real-time control of vehicle speed is achieved. Simulation results show that the developed strategy extends the battery life by 10.33% compared to the baseline strategy when the traffic flow is not involved. In the case of involving the traffic flow, the optimization results of battery aging improves as the look-ahead time period increases, while the computational burden increases. The results show that the developed strategy reduces the battery aging of the target vehicle by 33.02% compared to the preceding vehicle while meeting the real-time requirement.

Simultaneous reconstruction of temperature-dependent optical and thermophysical parameters of insulation material by the GA-SQP/SQP technique

A combination genetic algorithm (GA) with sequential quadratic programming (SQP) algorithm is proposed to simultaneously identify the temperature-dependent thermal conductivity (κc(T)) and extinction coefficient (β(T)) of insulation material without any prior information of parameter distribution function. The GA is applied to obtain the initial values of κc(T) and β(T) because of its lesser dependence on initial guess, then the reconstruction results from GA are used as the initial values of SQP to reckon an optimal solution of κc(T) and β(T) and finally the established κc(T) in previous step are adopted as known parameters to reconstruct the β(T) by SQP algorithm, which is called a GA-SQP/SQP technique. The retrieval results from numerically generated temperature demonstrate that the GA-SQP/SQP technique can significantly improve the accuracy of estimated κc(T) and β(T) compared with the other traditional optimization algorithms. Corresponding experiment is performed to estimate the κc(T) and β(T) of insulation material at high temperatures by the GA-SQP/SQP technique and the results are validated.

Steady-state simulation and optimization of an air cooled chiller

In this paper, we propose a rigorous model for representing the operation of an air cooled chiller of a large office building and some simple correlations for predicting global heat exchange coefficient and pressure drop of the evaporator. The proposed models and a simplified physical one that assumes constant evaporator's heat exchange coefficient and pressure drop are used to simulate and optimize the operation of the chiller. The rigorous model shows that large variations of the order of 10% can be observed in the prediction of global heat exchange coefficient of the evaporator. We also present correlations for predicting specific enthalpies and entropies of superheated R-410, capable of representing Chemour's tabulated values within a maximum error of 2,5% for the entire expected operating region of chillers for air conditioning systems. All models are programmed as non-linear programming problems and solved by a sequential quadratic programming algorithm. Simulation and optimization results show that all physical models are easily and rapidly solved and that the more rigorous model should be preferred to optimize the operation of the chiller and to adequately predict limiting operating points and off-design situations. CPU time for all simulations was below 0,3 s using an Intel Centrino Duo type processor. Optimizing the operational point by means of the rigorous model might enable significantly reducing energy consumption depending on the disturbances affecting the operation of the chiller (e.g. of the order of 7%). We further show that the simple correlations are capable of predicting the operation of the chiller within acceptable deviations (predicting errors in compressor's power are up to 3%) and might be used to preliminarily test advanced control applications. It is also shown that evaporator's pressure drop should not be neglected as is a common practice, since prediction errors in superheating might be of the order of 3 °C. Finally, the rigorous model should be used to analyze limiting operating points and the effect of changing manipulated variables on important process constraints like superheating.

Properties of objective functions and search algorithms in multi-objective optimization problems

Objectives. A frequently used method for obtaining Pareto-optimal solutions is to minimize a selected quality index under restrictions of the other quality indices, whose values are thus preset. For a scalar objective function, the global minimum is sought that contains the restricted indices as penalty terms. However, the landscape of such a function has steep-ascent areas, which significantly complicate the search for the global minimum. This work compared the results of various heuristic algorithms in solving problems of this type. In addition, the possibility of solving such problems using the sequential quadratic programming (SQP) method, in which the restrictions are not imposed as the penalty terms, but included into the Lagrange function, was investigated.Methods. The experiments were conducted using two analytically defined objective functions and two objective functions that are encountered in problems of multi-objective optimization of characteristics of analog filters. The corresponding algorithms were realized in the MATLAB environment.Results. The only heuristic algorithm shown to obtain the optimal solutions for all the functions is the particle swarm optimization algorithm. The sequential quadratic programming (SQP) algorithm was applicable to one of the analytically defined objective functions and one of the filter optimization objective functions, as well as appearing to be significantly superior to heuristic algorithms in speed and accuracy of solutions search. However, for the other two functions, this method was found to be incapable of finding correct solutions.Conclusions. A topical problem is the estimation of the applicability of the considered methods to obtaining Pareto-optimal solutions based on preliminary analysis of properties of functions that determine the quality indices.

Closed-Loop Combustion Optimization Based on Dynamic and Adaptive Models with Application to a Coal-Fired Boiler

To increase combustion efficiency and reduce pollutant emissions, this study presents an online closed-loop optimization method and its application in a boiler combustion system. To begin with, three adaptive dynamic models are established to predict NOx emission, the carbon content of fly ash (Cfh), and exhaust gas temperature (Teg), respectively. In these models, the orders of the input variables are considered to enable them to reflect the dynamics of the combustion system under load changes. Meanwhile, an adaptive least squares support vector machine (ALSSVM) algorithm is adopted to cope with the nonlinearity and the time-varying characteristics of the combustion system. Subsequently, based on the established models, an economic model predictive control (EMPC) problem is formulated and solved by a sequential quadratic programming (SQP) algorithm to calculate the optimal control variables satisfying the constraints on the control and control moves. The closed-loop optimization system is applied on a 600 MW boiler, and the performance analysis is conducted based on the operation data. The results show that the system can effectively increase boiler efficiency by about 0.5%.

Priority‐based resource allocation in wireless powered UAV‐assisted networks

Unmanned aerial vehicles (UAVs) can be deployed to combine terrestrial and aerial networks to provide flexible connectivity to a large number of devices in three-dimensional (3D) space. Powering wireless devices through energy harvesting and wireless power transfer have been investigated to provide uninterrupted operations. Resource allocation is critical to improving the overall performance of the network. This paper focusses on a downlink network in which UAVs serve as base stations to provide connectivity to ground users. A priority-based charging of UAVs from the ground charging stations needs to be efficiently designed for the sustainable operation of the overall network. A binary linear integer programming (BLIP) problem is formulated to minimise the charging cost and maximise the number of UAVs that can be charged by charging stations. First, the BLIP is transformed into a quadratic programming problem to solve it in polynomial time. A sequential quadratic programming algorithm is developed to solve the optimisation problem. Simulation results demonstrate the effectiveness of the proposed work compared to existing solutions.

Innovative Optimal Nonstandard Tripping Protection Scheme for Radial and Meshed Microgrid Systems

The coordination of optimal overcurrent relays (OCRs) for modern power networks is nowadays one of the critical concerns due to the increase in the use of renewable energy sources. Modern grids connected to inverter-based distributed generations (IDGs) and synchronous distributed generations (SDGs) have a direct impact on fault currents and locations and then on the protection system. In this paper, a new optimal OCR coordination scheme has been developed based on the nonstandard time–current characteristics (NSTCC) approach. The proposed scheme can effectively minimize the impact of distributed generations (DGs) on OCR coordination by using two optimization techniques: genetic algorithm (GA) and hybrid gravitational search algorithm–sequential quadratic programming (GSA–SQP) algorithm. In addition, the proposed optimal OCR coordination scheme has successfully employed a new constraint reduction method for eliminating the considerable number of constraints in the coordination and tripping time formula by using only one variable dynamic coefficient. The proposed protection scheme has been applied in IEEE 9-bus and IEC MG systems as benchmark radial networks as well as IEEE 30-bus systems as meshed structures. The results of the proposed optimal OCR coordination scheme have been compared to standard and nonstandard characteristics reported in the literature. The results showed a significant improvement in terms of the protection system sensitivity and reliability by minimizing the operating time (OT) of OCRs and demonstrating the effectiveness of the proposed method throughout minimum and maximum fault modes.

Dynamic optimization analyses and algorithm design for the parallel heat exchange system in spacecraft

Dynamic optimization of the fluid loop is critical of the active thermal control system (ATCS) for future spacecraft. In this paper, the transient heat current model of the parallel heat exchanger system is constructed by the thermoelectric analogy method to analyze the optimal control problem of dynamic flow allocation. The continuous free time optimal flow control problem is transformed into a fixed-time nonlinear programming problem which can be solved by the sequential quadratic programming (SQP) algorithm through the control variable parameterization (CVP) and time-scaling methods. The simulation showed that the optimized flow allocation significantly reduced the process time required for system heat dissipation. Compared with the non-gradient particle swarm optimization (PSO) algorithm, the SQP method constructed in this paper decreased the optimization index by about 4%∼6% and the calculation time by about one order of magnitude. To diminish the sensitivity of the SQP algorithm to the initial value, this paper simplifies the model according to the system characteristics. Through the Pontryagin extremum principle, it is found and proved that, under the simplified model, the optimal flow rates are a set of time-independent variables, which significantly reduces the difficulty of the optimization problem, according to which a hybrid algorithm is designed that uses the optimal result of the simplified model as the initial value predictor. Compared with the average of using the random initial value, using the estimated initial value decreased the optimization index by more than 2% and the computation time by about 60%, under the same SQP algorithm.

Diagnostic Evaluation of Rheumatoid Arthritis (RA) in Finger Joints Based on the Third-Order Simplified Spherical Harmonics (SP3) Light Propagation Model

This work focuses on the evaluation of third-order simplified spherical harmonics (SP3) model-based image reconstruction with respect to its clinical utility to diagnose rheumatoid arthritis (RA). The existing clinical data of 219 fingers was reconstructed for both absorption and scattering maps in fingers by using the reduced-Hessian sequential quadratic programming (rSQP) algorithm that employs the SP3 model of light propagation. The k-fold cross validation method was used for feature extraction and classification of SP3-based tomographic images. The performance of the SP3 model was compared to the DE and ERT models with respect to diagnostic accuracy and computational efficiency. The results presented here show that the SP3 model achieves clinically relevant sensitivity (88%) and specificity (93%) that compare favorably to the ERT while maintaining significant computational advantage over the ERT (i.e., the SP3 model is 100 times faster than the ERT). Furthermore, it is also shown that the SP3 is similar in speed but superior in diagnostic accuracy to the DE. Therefore, it is expected that the method presented here can greatly aid in the early diagnosis of RA with clinically relevant accuracy in near real-time at a clinical setting.

An SQP Algorithm for Structural Topology Optimization Based on Majorization–Minimization Method

When applying the sequential quadratic programming (SQP) algorithm to topology optimization, using the quasi-Newton methods or calculating the Hessian matrix directly will result in a considerable amount of calculation, making it computationally infeasible when the number of optimization variables is large. To solve the above problems, this paper creatively proposes a method for calculating the approximate Hessian matrix for structural topology optimization with minimum compliance problems. Then, the second-order Taylor expansion transforms the original problem into a series of separable and easy-to-solve convex quadratic programming (QP) subproblems. Finally, the quadratic programming optimality criteria (QPOC) method and the QP solver of MATLAB are used to solve the subproblems. Compared with other sequential quadratic programming methods, the advantage of the proposed method is that the Hessian matrix is diagonally positive definite and its calculation is simple. Numerical experiments on an MBB beam and cantilever beam verify the feasibility and efficiency of the proposed method.

An efficient Bi-level hybrid multi-objective reliability-based design optimization of composite structures

This paper presents computationally an efficient multi-objective reliability-based design optimization (RBDO) method for composite structures with uncertain design parameters. The approach adopted is based on a novel hybrid decomposing-based multi-objective particle swarm optimization and sequential quadratic programming algorithms, which is coupled with bi-level modelling and optimization strategy of composite structures and RBDO using Cross entropy method. The reliability analysis considers the rare-event corresponding to the limit states, which is based on Tsai-Wu failure index. In addition, the growing requirements for composite structural design with a minimum weight, introduces significant research challenges in the RBDO approach as the weight and reliability are the two important opposing design requirements. To address this research challenges, the proposed approach involves both reliability and weight as objective functions. A laminated composite plate and benchmark problems were used to demonstrate the efficiency and accuracy of the proposed method. Results show that the proposed method provides computationally efficient and accurate evaluations of the performance of the design of composite structures in comparison to the conventional Monte Carlo simulation method and can provide a potential for solving large-scale multi-objective RBDO of composite structures design problems.