Quadratic Programming Method Research Articles

Nonlinear robust distribution planning model for perishable products based on sustainable development

With the development of social economy and the improvement of people living standards, the distribution of cold chain products has become increasingly prominent. In the process of distribution of cold chain products, due to its perishable nature, it is not only necessary to consider the efficiency and economy of transportation, but also to pay attention to risk aversion factors. Therefore, the stochastic programming of cold chain logistics based on risk aversion has become an urgent problem to be solved. Aiming to minimize the economic cost and transform the carbon emission level of cold chain transportation into carbon emission cost, a distributionally robust mean-conditional value-at-risk optimization model for the perishable goods distribution management problem is established, in which the partial distribution information of uncertain demand and transportation environment temperature was known. Then a computationally tractable equivalence model is obtained under the box ambiguity set. For the proposed nonlinear model, a trust region sequential quadratic programming method with filter is proposed to solve it. Finally, through a case study, the relationship between the stochastic programming model and the distributionally robust model is analysed.

A Time-Optimal Continuous Jerk Trajectory Planning Algorithm for Manipulators

In this paper, we propose a new optimal trajectory planning method for the manipulator to optimize its operating efficiency and ensure the smoothness of the motion process. The position sequences in joint space corresponding to a specified trajectory in task space are obtained by using the inverse kinematic algorithm, and the seventh-degree B-spline curve interpolation method is used to construct the joint trajectory with controllable start–stop kinematic parameters, and continuous velocity, acceleration and jerk. The kinematic constraints of the manipulator are transformed into the control point constraints of the B-spline curve, the sequential quadratic programming method is used to solve the optimal motion time node, and then the time-optimal continuous jerk trajectory satisfying the nonlinear kinematic constraints is planned. Simulation results show that the proposed trajectory planning method provides the ideal trajectory for the joint controller, ensuring the manipulator can smoothly track any specified trajectory in the task space in the shortest time.

Adaptive shape optimization with NURBS designs and PHT-splines for solution approximation in time-harmonic acoustics

In this paper, we propose the adaptive shape optimization algorithm based on the concept of Geometry Independent Field approximaTion paired with the Sequential Quadratic Programming method, applied to time-harmonic acoustics.Non-Uniform Rational Basis Splines are used for the geometry parametrization, and in the same manner, as in conventional isogeometric shape optimization, the control points of the optimized boundary serve as design variables. This preserves the tight link between the design, analysis, and optimization models. Polynomial splines over Hierarchical T-meshes are employed for the solution approximation, providing the capability to refine the solution locally and adaptively to the boundary changes during the optimization process in a step-by-step procedure controlled by the error tolerance. This leads to significant savings in terms of the number of degrees of freedom and computational time.The performance of the proposed method is demonstrated in three benchmark examples and the results are compared with the data from the literature, showing the high accuracy and efficiency of the technique. It is shown that an adaptive optimization scheme can bring over 90% reduction in both, the number of degrees of freedom and time, in comparison with the uniform refinement.

Improving Directional Overcurrent Relay Coordination in Distribution Networks for Optimal Operation Using Hybrid Genetic Algorithm with Sequential Quadratic Programming

In recent years, with the growing popularity of smart microgrids in distribution networks, the effective coordination of directional overcurrent relays (DOCRs) has presented a significant challenge for power system operators due to the intricate and nonlinear nature of their optimization model. Hence, this study proposes a hybrid GA-SQP algorithm to enhance the coordination of directional overcurrent relays (DOCRs) in radial and non-radial interconnected distributed power networks. The proposed approach combines the advantages of both the genetic algorithm (GA) and sequential quadratic programming (SQP) methods to optimize the objective function of relay coordination in the best manner. Thus, the proposed hybrid techniques improved the convergence of the problem and increased the likelihood of obtaining a globally optimal solution. Finally, to validate the effectiveness of the proposed algorithm, it was tested through three case studies involving the IEEE 3-Bus, 8-Bus, and modified 30-Bus distribution networks. In addition, the results were compared to those obtained using previous methods. The results obtained from the comparison of the proposed method and recent advanced research indicate that the proposed optimization approach is preeminent in terms of accuracy and total operating time as well as the continuity of the minimum margin time requirements between the primary/backup relay pairs.

Global footstep planning with greedy and heuristic optimization guided by velocity for biped robot

In order to give full play to the unique movement capabilities of biped robots that are different from traditional mobile robots, and to improve the ability to adapt to the environment, planning an appropriate global footstep sequences is an important way. In this article, we proposed Greedy and Heuristic Quadratic Programming(GH-QP) based on the Quadratic Programming(QP) method to achieve global footsteps for biped robots. Where GH-QP consists of greedy terms, heuristic terms and complementary terms. The heuristic term tries to minimize the number of steps in order to obtain the global optimal solution as quickly as possible. At the same time, we use the reference forward speed of the robot’s as the weight coefficient of the heuristic item to achieve the footsteps which is more in line with the walking trend. The greedy term minimizes the mutation caused by the heuristic term, making the footstep more inclined to the local optimum. The complementary term further enhances the greedy term to reduce the mutation between adjacent steps. We verify the effectiveness and high efficiency of our method through two sets of comparative tests. We experimentally validated our method on BHR-7P biped robot. The footstep sequences planned by our method adapts to the influence of velocity, and exerts the ability of the robot in the continuous planning process.

Enhancing Autonomous Vehicle Lateral Control: A Linear Complementarity Model-Predictive Control Approach

Model-predictive control (MPC) offers significant advantages in addressing constraint-related challenges and plays a pivotal role in self-driving car technology. Its primary goal is to achieve precise trajectory tracking while prioritizing vehicle stability and safety. However, real-time operations often face challenges related to computational demands and low computational efficiency. To address these challenges, this paper introduces a novel lateral control algorithm for self-driving vehicles, which utilizes the linear complementarity problem (LCP) instead of the conventional quadratic programming (QP) method as the MPC optimization solution. This innovative approach incorporates the electric steering system into the vehicle dynamics model, allowing for precise torque regulation of the steering motor and enhancing control accuracy. The MPC algorithm adopts the LCP solution method to calculate control signals based on the vehicle’s state, ensuring both rapid and stable vehicle control. Simulation results demonstrate that the proposed MPC algorithm, utilizing the LCP solution method, effectively addresses efficiency issues in the lateral motion of self-driving cars. This leads to improvements in both driving stability and real-time performance. Overall, this innovative approach lays a solid foundation for the practical implementation of self-driving cars.

An algorithm for solving the equilibrium points of high-dimensional nonlinear vehicle dynamic system based on a combination of genetic algorithm, sequential quadratic programming method, and continuation method

The paper proposes an algorithm that combines Genetic Algorithm, Sequential Quadratic Programming, and Continuation Method to solve the equilibrium points of a multi-degree-of-freedom vehicle nonlinear system. The algorithm’s effectiveness is demonstrated by applying it to search for equilibrium points of a 5-degree-of-freedom (5DOF) nonlinear vehicle model, which considers both longitudinal and lateral motion. The dynamic equilibrium points of front-wheel-drive, rear-wheel-drive, and all-wheel-drive vehicles with different front-wheel steering angle inputs are calculated. Taking the front-wheel-drive system as an example, the system equilibrium points are further analyzed using phase space analysis and eigenvalue analysis for verification. In addition, the impact of the driving effect on the equilibrium points bifurcation is investigated. The results show that compared with the Genetic Algorithm alone and the combination method of Genetic Algorithm and Sequential Quadratic Programming, the proposed algorithm can effectively and accurately solve the equilibrium points of the 5DOF vehicle model. The study also reveals that the driving effect significantly influences the vehicle equilibrium point bifurcation.

A Hybrid Genetic Algorithm-Based Parameter Identification Method for Nonlinear Hysteretic System with Experimental Verification

The Bouc–Wen nonlinear hysteretic model is widely used in nonlinear systems, and it is difficult to identify the parameters of Bouc–Wen model because of its high nonlinearity. In the paper, a hybrid genetic algorithm combined with sequential quadratic programming is proposed to solve the problem about the parameter identification of Bouc–Wen model. Sequential quadratic programming method has good local convergence and superlinear convergence rate. Therefore, compared with the genetic algorithm, the proposed identification method can accelerate the convergence speed in parameter recognition of Bouc–Wen model and achieve excellent recognition accuracy. Through the function test and the numerical simulation of the shear structure, it is proved that the proposed method has high convergence speed and accurate identification. In addition, the theory and method proposed in this paper are combined with Bouc–Wen model to identify parameters of overall restoring force model of the energy-dissipation structures, the identification results are in good agreement with the experimental results, verifying reliability and accuracy of the model and robustness of the proposed identification method.

Impulsive guidance of optimal pursuit with conical imaging zone for the evader

This paper addresses the problem of orbital maneuver of the pursuer to position the evader within its imaging zone, which is a spherical cone centered at the pursuer's camera with its centerline parallel to the sunlight. Two pursuit strategies are proposed respectively for the free-floating and maneuvering evader based on geometry analysis of the maneuver trajectory. Specifically, the shortest path from the evader to the conical imaging zone of the pursuer is first calculated and used to analytically design a fixed-time near-fuel-optimal guidance law for the pursuer with a fixed time interval. The magnitude of each impulse is guaranteed to be within the allowable range. Compared with the Sequence Quadratic Programming (SQP) method, the superiority in robustness and computation efficiency of this method over SQP is illustrated. Furthermore, for the maneuvering evader whose maneuver strategy is unknown to the pursuer, the proximal policy optimization (PPO) algorithm in reinforcement learning is applied to train and guide the pursuer to approach the evader intelligently. To enhance the stability and efficiency of the training process, the shortest path from the conical imaging zone to the evader is used to define a unified reward function. Since the reward function synthesizes the relative distance and sunlight angle between the pursuer and evader, reward parameters can be reduced, which is more convenient and efficient for the design and implementation of the reinforcement learning algorithm.

Optimizing Spatial Location and Service Capacity of New Schools Toward Maximum Equity in the Distribution of Educational Resources

Educational facilities are an important part of public service facilities. The scientific planning of educational facilities is conducive to the optimal allocation of educational resources and the equalization of educational services. In view of the insufficient supply and uneven spatial distribution of urban educational service facilities, this study adopted an improved two-step optimization method to maximize the equality of school accessibility by optimizing the spatial location and service capacity of urban primary schools. First, the improved p-median model was constructed, and the Teitz–Bart algorithm was used to solve the model to site new primary schools. Second, a quadratic programming method was used to optimize the service capacity of new primary schools. Finally, the two-step floating catchment area (2SFCA) method was used to analyze and evaluate the accessibility of population centers to schools before and after the site selection and service capacity optimization of new schools. The results show that the improved two-step optimization approach can effectively determine the best locations and service capacity of new schools to improve the spatial accessibility of schools and realize the fair distribution of educational resources.

A generalized Burr mixture autoregressive models for modeling non linear time series

A more flexible type of mixture autoregressive model, namely the Burr mixture autoregressive, BMAR model is studied in this article for modeling non linear time series. The model consists of a mixture of K autoregressive components with each conditional distribution of the component following a Burr distribution. The BMAR model enjoys some nice statistical properties which allow it to capture time series with: (1) unimodal or multimodal; (2) asymmetry or symmetry conditional distribution; (3) conditional heteroscedasticity; (4) cyclical or seasonal; and (5) conditional leptokurtic distribution. Sufficient and less restrictive conditions for the ergodicity of the BMAR model are derived and discussed. A more robust constrained optimization algorithm (EM – sequential quadratic programming method) is proposed for the non linear optimization problem. From the simulation studies carried out, the parameters estimation method showed satisfying results. The variance of the estimated parameters is also addressed with the missing information principle. Real datasets from two different fields of study are used to assess the performance of the BMAR model compared to other competing models. The comparison done in the empirical examples reveals the supremacy of the BMAR model in capturing the data behavior.

A Special Ordered Set of Type 2 Modeling for a Monthly Hydropower Scheduling of Cascaded Reservoirs with Spillage Controllable

This study introduces a novel approach for optimizing the monthly hydropower scheduling of cascaded reservoirs by employing a special ordered set of type 2 (SOS2) formulation within a mixed integer linear programming (MILP) model. The proposed method linearizes the relationships between hydropower output, spillage, storage, and outflow, enabling controllable spillage. The objective is to minimize spillage, maximize firm hydropower output, and maximize energy production, all in priority while considering complex constraints such as reservoir storage and discharge bounds, upstream–downstream relationship, and water balance. The approach is applied to four cascaded reservoirs on the Lancang River. Results indicate that the SOS2 formulation effectively minimizes spillage, maximizes hydropower generation, and ensures maximum firm power output. Comparisons across different gridding resolutions reveal that more grid points yield greater benefits but with a longer solution time. Furthermore, a comparison with the Successive Quadratic Programming (SQP) method highlights the superior performance of the SOS2 model in terms of objective improvement and solution efficiency. This research offers valuable insights into optimizing monthly hydropower scheduling for cascaded reservoir systems, enhancing operational efficiency and decision-making in water resources management.

An autonomous task assignment and decision-making method for coverage path planning of multiple pesticide spraying UAVs

As the approaching of Agriculture 4.0 era and advancements of new technologies of Unmanned Aerial Vehicles (UAVs) and particularly quadcopter UAVs, plant protection quadcopters are becoming increasingly popular and practical in pesticide spraying, fertilization, pollination, seeding, and other agricultural activities. One of the main problems for plant protection quadcopters is completing planning tasks efficiently and quickly. Therefore, this paper proposes an autonomous task assignment and decision-making method for coverage path planning by multiple cooperative quadcopters. The Sequential Quadratic Programming (SQP) method is adopted to acquire the optimal solution for the proposed problem. Then, a simulation platform by MATLAB Graphical User Interfaces (GUIs) is established using the Stateflow technique, and multiple ZY-UAV-680 quadrotor UAVs are employed to carry out the actual flight tests. Finally, simulations and actual flight tests are conducted to demonstrate the effectiveness of the autonomous optimal task assignment and decision-making method. The final results show that: the proposed method can divide multiple UAVs reasonably to several blocks; the time differences between the simulation test and real flight test are only 39.8 sec and 20.6 sec, and accounts for 6.6% and 3.9% of the spraying time spent on real flight test by three cooperative quadrotors, respectively; the optimal scheme can save 60.8 sec and 80.0 sec in the simulation tests and the real flight tests, which accounts for 10.8% and 13.2% of the time spent on average scheme, respectively. Therefore, it can be concluded that the simulation results can match the real flight test results quite well regardless of average scheme or optimal scheme, and the optimal scheme is more efficient and timesaving than the average scheme.

Research on Path Tracking and Yaw Stability Coordination Control Strategy for Four-Wheel Independent Drive Electric Trucks

Achieving accurate path tracking and vehicle stability control for four-wheel independent drive electric trucks under complex driving conditions, such as high speed and low adhesion, remains a major challenge in current research. Poor coordination control may cause the vehicle to deviate from its intended path and become unstable. To address this issue, this article proposes a coordinated control strategy consisting of a three-layer control framework. In the upper layer controller design, establish a linear quadratic regulator (LQR) path tracking controller to ensure precise steering control by eliminating steady-state errors through feedforward control. The middle layer controller utilizes the fractional order sliding mode control (FOSMC) yaw moment controller to calculate the additional yaw moment based on the steering angle of the upper input, utilizing the error of yaw rate and sideslip angle as the state variable. To collectively optimize the control system, establish a coordinated optimization objective function and utilize the hybrid genetic-particle swarm optimization algorithm (GA-PSO) to optimize the weight coefficient of LQR and sliding mode parameters of FOSMC, effectively improving the performance of the controller. In the lower layer torque distribution controller, use the quadratic programming method to achieve real-time optimal torque distribution based on tire utilization, which improves vehicle stability control. Through simulations conducted under four different working conditions, the proposed control scheme demonstrates a 15.54% to 23.17% improvement in tracking performance and a 10.83% to 23.88% optimization in vehicle driving stability compared to other control methods. This scheme provides a theoretical reference for path tracking and stability control in four-wheel independent drive electric trucks.

Feature matching of remote‐sensing images based on bilateral local–global structure consistency

AbstractThe goal of feature matching is to establish accurate correspondences between feature points in different images depicting the same scene. To address the polymorphism of local structures, the authors propose a mismatch removal method using bilateral local–global structural consistency. This method incorporates the problem of mismatch removal into the framework of graph matching, constructs a global affinity matrix using local structural similarity and global affine transformation consistency, and optimizes it using a constrained integer quadratic programming method. To comprehensively describe the local structure, the signature quadratic form distance (SQFD) is used to measure the consistency of the neighbourhood structure. Specifically, the weights of edges are constructed based on the SQFD of the local structure, while the matching correctness of nodes and edges between the two graphs is described using local vector similarity. Furthermore, the consistency of the global affine transformation is evaluated by assessing the consistency of the local neighbourhood affine transformation between different corresponding point pairs. In estimating the local affine transformation, a bilateral correction is performed using a total least‐squares (TLS) algorithm to measure the similarity of nodes between the two different graphs. Experimental results demonstrate that the proposed algorithm outperforms state‐of‐the‐art methods in terms of accuracy and effectiveness.

Parameter Optimization with Chebyshev Polynomials for Trajectory Design of A RLV

A trajectory optimal control problem is converted to a parameter optimization problem by approximating the states and control using piecewise Chebyshev polynomials. The Chebyshev points which control the polynomial fit is used to match the dynamics at the nodal points. Midpoint strategy significantly reduced the number of parameters to be optimized without having to sacrifice on accuracy. The resultant non- linear programming problem is solved using sequential quadratic programming method. Ascent phase trajectory optimization of a reusable launch vehicle having typical path and terminal constraints is taken as a test case.

A phase plane H∞ controller for distributed drive electric vehicles with stability enhancement based on tire road friction coefficient estimation

An H∞ control strategy based on the phase plane method (phase plane H∞ controller) tracking two degrees of freedom (DOF) ideal vehicle trajectory scheme is designed for distributed drive electric vehicles with stability enhancement. Firstly, an Extended Kalman Filter (EKF) tire road friction coefficient estimation method based on Keras neural network is presented to accurately and efficiently identify the tire road friction coefficient, taking into account the huge influence of the tire road friction coefficient on vehicle equilibrium point and stability region. Secondly, the phase plane method is applied to provide a dynamic stability boundary for the switching control strategy of direct yaw moment for different tire road friction coefficients; Furthermore, based on the dynamic stability boundary, the weighted phase stability is applied to achieve more realistic stability evaluation criteria, and the fuzzy control strategy is adopted to carry out the feedback regulator of the target side slip angle and yaw rate on the purpose of limiting its maximum value max ( β) and max ( ωr). Then the torque of the four-wheel was optimized by the quadratic programming method. Finally, the presented method is verified and the results indicate that: (1) the phase plane H∞ control has the advantage in terms of stability and maneuvering performance. More importantly, under a low tire road friction coefficient, the amplitude of the side slip angle is decreased by 26.52% over the H∞; (2) the designed EKF based on Keras neural network parameter correction has a quick and accurate performance in identifying the tire road friction coefficient, and the steady-state error does not exceed 3.25%.

Portfolio Selection Strategies in Bursa Malaysia Based on Quadratic Programming

The study aims to select the efficient portfolio on stock listed in Bursa Malaysia by using the quadratic programming method. It can help the investors to gain expected returns from the diversification portfolio. However, there are some problems that should be considered such as the measurement of inputs for Mean-Variance Models (MVM), use of portfolio models through time and consistency with management objectives in the portfolio. These problems will affect the performance of selected portfolio and cause the loss problem. Therefore, this study implements a quadratic programming approach to select an efficient portfolio on stocks listed in Bursa Malaysia. The study will choose 15 potential companies which have the best performance in the Bursa Malaysia. Quadratic programming (QP) model can solve any type of mathematical optimisation problem in the study. Therefore, investors can optimise the investment portfolio returns by using QP methods. However, we can observe the efficient frontier which is a graph that representing a list of portfolios that optimising expected return for a different level of portfolio risk so can help the investors make a good decision. The findings of this study will give important inputs, especially to the investors to maximise their portfolio return at different level of risks.

Optimasi Rata-rata Produksi Jagung di Kabupaten Limapuluh Kota Menggunakan Pemrograman Kuadratik Metode Wolfe

This research was an experimented research that purpose to form a mathematical model for optimizing average corn production in Fifty Cities District with the constraint that the harvested area should not be more than the planted area and solve the model with the Wolfe quadratic programming method. The model of mathematical in the research was a model by formed nonlinear using the method of least squares. Then use the Wolfe method to form a new linear objective function and constraints in the form of Karush Kuhn-Tucker conditions. The results showed that the optimal average corn production in Fifty Cities District was 49.00456 tons/Ha with an optimal corn harvest area of 656.256 Ha.

Research on the Vehicle Steering and Braking Stability Region

Solving the stability region in the plane motion of vehicles has become a hot research topic in vehicle handling stability under extreme conditions, but there is still a lack of research on the stability region under steering and braking conditions. In this paper, a five-degree-of-freedom (5DOF) nonlinear dynamic model of a vehicle with braking torque introduced is established, and the model is transformed into an equivalent system by using the D’Alembert principle. Then, the equilibrium points of the equivalent system are solved by using an improved hybrid algorithm combining the genetic algorithm (GA) and sequential quadratic programming (SQP) method. According to the bifurcation characteristics of the equilibrium points, the boundary of the stability region at the given initial longitudinal velocity is determined, and the three-dimensional stability region is fitted. Finally, the stability region of the equivalent system and the original system are analyzed by the energy dissipation method, and the stability region determined by the equilibrium point bifurcation method is verified by simulation. The results show that as the braking torque increases, the number of equilibrium points increase to three from one, the equilibrium bifurcation method proposed in this paper can effectively solve the stability region of the equivalent system, and the solution results are consistent with the original system stability region. When the limited braking torque is 500 N·m and the initial longitudinal velocity increases from 30 m/s to 50 m/s, the absolute value of the front wheel steering angle at the boundary point changes from less than 0.02 rad to more than 0.02 rad.