Nonlinear Constraint Optimization Research Articles

Two-Warehouse Inventory Model: Interval Valued Costs, Advanced Payment, Stock-Dependent Demand, and Partial Backlogging

A great deal of inventory costs are typically unpredictable because of the unpredictability of a competitive market. The fluctating demand from customer's and the unpredictability of the market economy make it difficult for researchers and operation research practitioners to appropriately replicate an inventory problem. In order to prevail this type of unpredictability circumstances, in this paper, we have represented the inventory parameters as interval. Using this concept, we progressed a two-warehouse inventory model for deteriorating items with a fixed Shelf life, partially backlogging shortages and interval-valued deterioration rate. In addition to this the parameters like ordering cost, purchase cost, shortage cost, deterioration cost for both the rented and owned warehouse except the backlogging parameter have been considered as interval-valued. The uncertainty in the inventory parameters motivated us to view them as interval-valued in the present research. Based on the assumptions, the cost function of this problem is a highly nonlinear constraint optimization problem. Mathematica is used to tackle this nonlinear optimization problem. A numerical example has been presented to demonstrate the computational result. Then, a sensitivity analysis has been performed to study the effect of changes of different parameters of the model on the optimal policy.

State of Health Prediction of Lithium-Ion Batteries Using Combined Machine Learning Model Based on Nonlinear Constraint Optimization

Accurate State of Health (SOH) estimation of battery systems is critical to vehicle operation safety. However, it’s difficult to guarantee the performance of a single model due to the unstable quality of raw data obtained from lithium-ion battery aging and the complexity of operating conditions in actual vehicle operation. Therefore, this paper combines a long short-term memory (LSTM) network with strong temporality, and support vector regression (SVR) with nonlinear mapping and small sample learning. A novel LSTM-SVR combined model with strong input features, less computational burden and multiple advantage combinations is proposed for accurate and robust SOH estimation. The nonlinear constraint optimization is used to assign weights to individual models in terms of minimizing the sum of squared errors of the combined models, which can combine strengths while compensating for weaknesses. Furthermore, voltage, current and temperature change curves during the battery charging were analyzed, and indirect health features (IHFs) with a strong correlation with capacity decline were extracted as model inputs using correlation analysis and principal component analysis (PCA). The NASA dataset was used for validation, and the results show that the LSTM-SVR combined model has good SOH estimation performance, with MAE and RMSE all less than 0.75% and 0.97%.

Kharitonov-Hurwitz analysis based robust decentralized PID controller for benchmark industrial processes using nonlinear constraint optimization

Kharitonov-Hurwitz analysis based robust decentralized PID controller for benchmark industrial processes using nonlinear constraint optimization

A Smooth Penalty Function Algorithm for Computing Nonlinear Inequality Constraint Optimization Problem

A Smooth Penalty Function Algorithm for Computing Nonlinear Inequality Constraint Optimization Problem

Reliable Framework for the Optimal Allocation of Harmonic Emission Limits

Power quality issues have been investigated for decades, but the changes in power grid characteristics and the trend to power-electronic-coupled installations raises additional requirements and puts harmonics into the spotlight. The increasing share of distorting installations and the change of harmonic dissipation paths emphasize the need for reliable harmonic allocation methods. The methods reported in VDE-AR-N 4130 and IEC/TR 61000-3-6 do not reliably allocate harmonic emission limits and can result in harmonic voltages exceeding the planning levels. A novel approach based on non-linear constraint optimization is presented, which promises reliable allocation and the compliance to planning levels while relying on the same input data. This paper conducts a comparison of the three methods regarding their allocation performance, reliability and suitability for embedding in a power quality grid planning process. The study case is developed based on an IEC example grid. The results indicate that the novel method avoids the shortcomings of the VDE and IEC method namely under- and over-allocation as well as their significant uncertainty and may form the basis of a reliable harmonic grid planning process.

A GNSS-aided DVL calibration method based on quaternion estimation for underwater vehicles

Doppler velocity logger (DVL) error parameters can significantly influence the navigation accuracy of DVL/strapdown inertial navigation system (SINS) integration for unmanned underwater vehicles (UUV). To improve the navigation accuracy of UUV, this study proposes a two-stage DVL calibration method aided by global navigation satellite system (GNSS) measurements. First, utilizing the velocity of GNSS/SINS integrated navigation, the scale factor error of DVL is calculated by the moduli of velocities in UUV body frame and DVL instrument frame. Then, using the measurements throughout the calibration process, the calibration problem of the installation angle is converted to a nonlinear constraint optimization problem by describing the angle as a unit quaternion. Moreover, an easy-to-implement quaternion estimation algorithm is chosen to solve the problem and obtain the optimal quaternion. Simulation and sea trial indicate that the proposed method can rapidly and accurately estimate the DVL error parameters in different scenarios, and the position accuracy of the DVL/SINS system is improved.

Skill-level classification and performance evaluation for endoscopic sleeve gastroplasty.

We previously developed grading metrics for quantitative performance measurement for simulated endoscopic sleeve gastroplasty (ESG) to create a scalar reference to classify subjects into experts and novices. In this work, we used synthetic data generation and expanded our skill level analysis using machine learning techniques. We used the synthetic data generation algorithm SMOTE to expand and balance our dataset of seven actual simulated ESG procedures using synthetic data. We performed optimization to seek optimum metrics to classify experts and novices by identifying the most critical and distinctive sub-tasks. We used support vector machine (SVM), AdaBoost, K-nearest neighbors (KNN) Kernel Fisher discriminant analysis (KFDA), random forest, and decision tree classifiers to classify surgeons as experts or novices after grading. Furthermore, we used an optimization model to create weights for each task and separate the clusters by maximizing the distance between the expert and novice scores. We split our dataset into a training set of 15 samples and a testing dataset of five samples. We put this dataset through six classifiers, SVM, KFDA, AdaBoost, KNN, random forest, and decision tree, resulting in 0.94, 0.94, 1.00, 1.00, 1.00, and 1.00 accuracy, respectively, for training and 1.00 accuracy for the testing results for SVM and AdaBoost. Our optimization model maximized the distance between the expert and novice groups from 2 to 53.72. This paper shows that feature reduction, in combination with classification algorithms such as SVM and KNN, can be used in tandem to classify endoscopists as experts or novices based on their results recorded using our grading metrics. Furthermore, this work introduces a non-linear constraint optimization to separate the two clusters and find the most important tasks using weights.

Design of an Optimal Control Strategy for Coupled Tank Systems Using Nonlinear Constraint Optimization With Kharitonov-Hurwitz Stability Analysis

Design of an Optimal Control Strategy for Coupled Tank Systems Using Nonlinear Constraint Optimization With Kharitonov-Hurwitz Stability Analysis

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.

Enhancing motion tracking accuracy of a low-cost 3D video sensor using a biomechanical model, sensor fusion, and deeplearning.

Low-cost 3D video sensors equipped with routines for extracting skeleton data facilitate the widespread use of virtual reality (VR) for rehabilitation. However, the accuracy of the extracted skeleton data is often limited. Accuracy can be improved using a motion tracker, e.g., using a recurrent neural network (RNN). Yet, training an RNN requires a considerable amount of relevant and accurate training data. Training databases can be obtained using gold-standard motion tracking sensors. This limits the use of the RNN trackers in environments and tasks that lack accessibility to gold-standard sensors. Digital goniometers are typically cheaper, more portable, and simpler to use than gold-standard motion tracking sensors. The current work suggests a method for generating accurate skeleton data suitable for training an RNN motion tracker based on the offline fusion of a Kinect 3D video sensor and an electronic goniometer. The fusion applies nonlinear constraint optimization, where the constraints are based on an advanced shoulder-centered kinematic model of the arm. The model builds on the representation of the arm as a triangle (the arm triangle). The shoulder-centered representation of the arm triangle motion simplifies constraint representation and consequently the optimization problem. To test the performance of the offline fusion and the RNN trained using the optimized data, arm motion of eight participants was recorded using a Kinect sensor, an electronic goniometer, and, for comparison, a passive-marker-based motion tracker. The data generated by fusing the Kinect and goniometer recordings were used for training two long short-term memory (LSTM) RNNs. The input to one RNN included both the Kinect and the goniometer data, and the input to the second RNN included only Kinect data. The performance of the networks was compared to the performance of a tracker based on a Kalman filter and to the raw Kinect measurements. The accuracy of the fused data was high, and it considerably improved data accuracy. The accuracy for both trackers was high, and both were more accurate than the Kalman filter tracker and the raw Kinect measurements. The developed methods are suitable for integration with immersive VR rehabilitation systems in the clinic and the home environments.

Variable thickness thin-walled rotating blades made of functionally graded porous materials

Within this study, the statics and dynamics performance of turbomachinery variable thickness rotating blades, composed of thin-walled, functionally graded metal-ceramic materials including cross-sectional distributed porosity is optimized. The pre-twisted, tapered, Thin-Wall Rotating Beams (TWRB) with constant angular velocity are considered within this context. For the optimization purpose, a genetic algorithm (GA) is implemented in a nonlinear constraint optimization problem. The goal is to exploit desirable thickness variations with improved dynamic, static, and buckling behavior of the variable thickness functionally graded material (FGM) blades. Hamilton’s principle was applied using the Euler–Lagrange dynamic system of governing equation, while the extended Galerkin’s method (EGM) was applied to solve the equations. Two variables in thickness function for each wall of the beam box (a total of eight variables) are considered in the optimization procedure. The effects of some parameters, such as the FGM volume fraction exponent, angular velocity, the pre-twist angle, porosity coefficient, and taper ratios on the mechanical behavior of the variable thickness FG beams are studied. The optimization result shows that applying the variable thickness concept can significantly increase the 1st and 2nd natural frequencies (by 60.4%, 60.22%) and reduce the weight (by 31.05%) of the system compared to the reference constant thickness beam while the increase in chordwise and flapwise deformations (by 8.16%, 9.93%) under combined loading is in an acceptable range, respectively.

Optimal Relay Coordination for DG-Based Power System Using Standard and User-Defined Relay Characteristics

The operating time of directional overcurrent relays (DOCRs) can be reduced with user-defined relay characteristics considering plug setting (PS), time multiplier setting (TMS), and relay characteristic coefficients (λ and γ). This study presents a comparative analysis of relay coordination with standard and user-defined relay characteristics. The proposed relay coordination scheme is formulated as a non-linear constraint optimization problem. The grey wolf optimization (GWO) algorithm is used to determine the optimal relay settings and total operating time of DOCRs. The performance of the proposed scheme is tested on the standard 8-bus, 9-bus, and 15-bus systems. The results show that the total operating time of DOCRs with user-defined relay characteristics is better than that with standard relay characteristics. The results of the GWO algorithm are compared with the performance of optimization techniques used in literature to solve the relay coordination problem.

Efficient UAV-based mobile edge computing using differential evolution and ant colony optimization.

Internet of Things (IoT) tasks are offloaded to servers located at the edge network for improving the power consumption of IoT devices and the execution times of tasks. However, deploying edge servers could be difficult or even impossible in hostile terrain or emergency areas where the network is down. Therefore, edge servers are mounted on unmanned aerial vehicles (UAVs) to support task offloading in such scenarios. However, the challenge is that the UAV has limited energy, and IoT tasks are delay-sensitive. In this paper, a UAV-based offloading strategy is proposed where first, the IoT devices are dynamically clustered considering the limited energy of UAVs, and task delays, and second, the UAV hovers over each cluster head to process the offloaded tasks. The optimization problem of dynamically determining the optimal number of clusters, specifying the member tasks of each cluster, is modeled as a mixed-integer, nonlinear constraint optimization. A discrete differential evolution (DDE) algorithm with new mutation and crossover operators is proposed for the formulated optimization problem, and compared with the particle swarm optimization (PSO) and genetic algorithm (GA) meta-heuristics. Further, the ant colony optimization (ACO) algorithm is employed to identify the shortest path over the cluster heads for the UAV to traverse. The simulation results validate the effectiveness of the proposed offloading strategy in terms of tasks delays and UAV energy consumption.

An Inventory Model for Non-Instantaneously Deteriorating Items with Nonlinear Stock-Dependent Demand, Hybrid Payment Scheme and Partially Backlogged Shortages

This research work presents an inventory model that involves non-instantaneous deterioration, nonlinear stock-dependent demand, and partially backlogged shortages by considering the length of the waiting time under a hybrid prepayment and cash-on-delivery scheme. The corresponding inventory problem is formulated as a nonlinear constraint optimization problem. The theoretical results for the unique optimal solution are presented, and eight special cases are also identified. Moreover, a salient theoretical result is provided: a certain condition where the optimal inventory policy may or may not involve deterioration. Finally, two numerical examples are provided using a sensitivity analysis to show the validity range of the inventory parameters.

Bionic design and analysis of a multi-posture wheelchair

Abstract. Posture transformation is an essential function for multi-posture wheelchairs. To improve the natural motion in posture transformation that is a popular problem in the design of multi-posture wheelchairs because the current wheelchair's posture transformation mechanism cannot remain consistent between the rotation center of the wheelchair and the rotation center of the human body joints. This paper proposes a sitting–standing–lying three-posture bionic transformation mechanism for a smart wheelchair. A human–wheelchair coupling model is described and analyzed according to the biomechanical characteristics of the posture transformation of human beings and their functional requirements. The configuration of the transformation mechanism is chosen by comparing the trails of the wheelchair rotation centers and the corresponding human joint rotation centers. The kinematics of the optimized configuration are discussed in detail to obtain the most bionic motion performance using the multivariable nonlinear constraint optimization algorithm. Finally, the mechanism is designed, and its posture transformation performance is simulated and verified using Adams (Automatic Dynamic Analysis of Mechanical Systems) software.

PE-A* Algorithm for Ship Route Planning Based on Field Theory

Route planning is the key to safe, efficient and intelligent navigation of maritime traffic. Autonomous route planning is a complex optimization problem, which requires both global route planning and local collision avoidance. In this paper, we propose an optimization algorithm which can consider both global route planning and local collision avoidance. Firstly, nonlinear constraint optimization models of obstacle limitation, safe water depth limitation and ship steering limitation are established. Then, the PE-A* algorithm and route planning framework are proposed by using potential energy field to accurately express the environment. Finally, the safety and feasibility of the route planned by PE-A* algorithm are discussed through simulation experiments. Simulation results show that PE-A* algorithm can realize both global route planning and local collision avoidance, and the safety and feasibility of the planned route are greatly improved. From the perspective of potential energy, this work proposes an automatic route planning algorithm and establishes a flexible mathematical model, which can add fuel consumption, time and other related engineering requirements into the model to plan the optimal route meeting the requirements.

A Fast Optimization Method for High-Speed Link Inverse Design With SVR-AS Algorithm

A fast constrained design optimization technique is introduced for the inverse design of high-speed links. The proposed method makes use of the support-vector-regression-based active subspace (SVR-AS) method to generate a lower dimensional space of active variables as a linear weighted combination of the higher dimensional design space to help simplify the optimization problem. This newly developed technique successfully transforms the complex nonlinear constraint optimization problem into a linear constraint minimization problem and provides a directly solvable function for the optimal results associated with each active variable. Furthermore, the proposed optimization algorithm can be utilized for the optimization problem with equality and inequality constraints, which contain one- and multidimensional active variables generated from the SVR-AS method. Studies of two high-speed links with channel design parameters for nonreturn-to-zero pulse and IBIS-AMI equalization settings for four-level pulse amplitude modulation, respectively, are utilized to verify the efficiency of the method. The sensitivity analysis ability of the SVR-AS method is also presented for both the one- and multidimensional active variable cases.

Design of tuned liquid sloshing dampers using nonlinear constraint optimization for across-wind response control of benchmark tall building

The present study proposes an optimal design methodology of tuned liquid sloshing dampers (TLSDs) installed in wind-excited benchmark tall building. The TLSDs design parameters were determined using proposed optimal design methodology based on nonlinear constraint optimization technique. Top floor peak acceleration was considered as the objective function and maximum value of sloshing depth of liquid as a nonlinear constraint for the design purpose. The classical nonlinear shallow water wave theory was used for the simulation of liquid sloshing, and the basic equations of nonlinear liquid sloshing were solved using the Lax Finite Difference Scheme. The governing equations of motion of combined structure-TLSDs system were expressed as state-space variables and structural response was numerically simulated. The findings were presented and assessed on the basis of a comparison between power spectral density functions, time history analysis, root mean square, peak response, and performance criteria for benchmark building with and without TLSDs. The off-tuning effect of TLSDs due to ±15% uncertainty in the building stiffness was also investigated. Further, an attempt has been made to present the control effectiveness of TLSDs in time–frequency domain (wavelet scalogram) using continuous wavelet transformation technique. The optimal TLSDs design based on the proposed methodology was found to be quite effective in serviceability-based design of benchmark tall building under wind loads and can be very useful for the practical design of TLSDs.

Optimization Design of RV Reducer Crankshaft Bearing

The crankshaft bearing is the key component of a rotate vector (RV) reducer. However, owing to the harsh working load and restricted available space, the bearing often suffers from fatigue failure. Therefore, this study proposes a novel optimization method for RV reducer crankshaft bearings. A nonlinear constraint optimization model for the design of the bearing considering the crowned roller profile is formulated and is solved by using a crow search algorithm. The goal of the optimization is to maximize the fatigue life of the bearing. The design variables corresponding to the bearing geometry and crowned roller profile are considered. The load working conditions of the bearing and structure of the RV reducer are analyzed. Various constraints, including geometry, lubrication, strength of the bearing, and structure of the RV reducer, are established. Through the optimization design, the optimum crowned roller profile suitable for the working load of the bearing is obtained, and the stress concentration between the roller and raceway is eliminated. Taking the crankshaft bearing of RV-20E and RV-110E type reducers as examples, the bearings were optimized by the proposed method. After optimization, the bearing life of the RV-20E type reducer is increased by 196%, and the bearing life of the RV-110E type reducer is increased by 168%.

Intelligent energy scheduling in a microgrid with custom power devices

The increasing penetration of distributed generators may harm power system and its control and operations. The microgrid offers a better solution for the issues in grid operation. Undergraduate electrical engineering and postgraduate power system and power electronics students need to understand the working of microgrid with renewable energy resources along with the optimization and scheduling of power quality custom power devices. To cater better understanding of the microgrid with renewable resources, wind, solar, distributed generators, distributed energy storage devices, DSTATCOM, and plug-in electric vehicle charging load are included in this work presented. In this paper, multiobjective optimization for the operation of microgrid to account for uncertainties in a stochastic energy resources management system is considered. Nonlinear constraint optimization to reduce the running cost, losses, and voltage variations is focused for the optimization. Loss sensitivity analysis is used to find the location wind, solar, distributed generators, distributed energy storage devices, and DSTATCOM. Firefly algorithm is used to optimize the size of distributed generators and DSTATCOM. Optimization reduced the loss, power taken from the grid and improves the voltages in the system. This paper is self-explanatory to the undergraduate and postgraduate students to understand the power flow analysis of microgrid with hybrid renewable energies and optimization technique.