Minimization Of Objective Function Research Articles

Reliability Analysis and Optimal Replacement Policy for Systems with Generalized Pólya Censored δ Shock Model

A fresh censored δ shock model is investigated. The arrival of random shocks follows a generalized Pólya process, and the failure mechanism of the system occurs based on the censored δ shock model. The generalized Pólya process is used for modeling because the generalized Pólya process has excellent properties, including the homogeneous Poisson process, the non-homogeneous Poisson process, and the Pólya process. Thus far, the lifetime properties of the censored δ shock model under the generalized Pólya process have not been studied. Therefore, for the established generalized Pólya censored δ shock model, the corresponding reliability function, the upper bound of the reliability function, the mean lifetime, the failure rate, and the class of life distribution are obtained. In addition, a replacement strategy N, based on the number of failures of the system, is considered using a geometric process. We determined the optimal replacement policy N* by objective function minimization. Finally, a numerical example is presented to verify the rationality of the model.

A Novel Method of Designing Random Rough Surface Considering Its Contact Force-Deformation Characteristic Requirement

Abstract The height probability distribution (HPD) of random rough surface topography has significant effect on its contact behaviors. In this paper, an optimization model to calculate the optimal HPD of random rough surface topography to make its contact force-deformation characteristic satisfy the given target force-deformation characteristic was established. In the solution to calculate the optimal HPD, using Bezier interpolation curve to represent the curve of HPD function and using the positions of the control points of Bezier interpolation curve as optimization variables were proposed. The solution was validated by numerical simulations implemented using MATLAB. The effect of the number of the control points on the minimum objective function value was investigated. Through analyzing the obtained result, we found the most appropriate number of the control points is 35. Comparison with the method using height parameters as optimization variables in literature was implemented. It was found that the proposed method is applicable to broader types of contact force-deformation characteristic requirements than the method using height parameters as optimization variables.

Evaluation of elastic constants of particle accelerator cavity materials with Resonant Ultrasound Spectroscopy

European Spallation Source is a multi-nation, interdisciplinary research facility based on the world’s most powerful neutron source that will operate with high standards of availability and reliability minimizing downtime periods. In order to meet these goals, critical component’s performance and ageing need to be constantly monitored and assessed. Resonant Ultrasound Spectroscopy (RUS) is a highly versatile non-destructive technique for the definition of elasticity matrix of materials through the measurement of resonance frequencies. RUS could benefit the characterization of particle accelerator cavity materials exposed to challenging operational environments during project’s design and commissioning phases. This paper demonstrates the methodology and the first results on the implementation of this technique on Radio-Frequency Quadrupole (RFQ) structural copper. Rectangular parallelepiped samples of polycrystal, oxygen free, high purity Cu-OF copper were prepared and RUS measured on a designed experimental set-up. The obtained resonance frequencies were used as an input for the solution of the inverse eigenvalue problem using open-source objective function minimization software. The obtained results are compared with commercially available Finite Element Method (FEM) software defining a repeatable methodology for material property and defect characterization.

A multi‐objective structural optimization method for serviceability design of tall buildings

SummaryStructural optimization design aims to identify optimal design variables corresponding to a minimum objective function with constraints on performance requirements. To this end, many optimization frameworks have been proposed to determine optimal structural systems that are subjected to seismic and wind hazards in isolation. However, some modern tall buildings are sensitive to seismic and wind excitation owing to their complex structural systems and geographic regions. Therefore, a proper structural optimization method for such buildings is required to ensure that the expected performance is achieved in a multi‐hazard scenario. This study proposes a multi‐objective serviceability design optimization methodology for buildings in multi‐hazard seismic and wind environments by combining optimality criteria and the nondominated sorting genetic algorithm II (NSGA‐II). Seismic and wind effects can be instantaneously updated due to changes in the structural dynamic properties during the optimal design process. A neural‐network‐based surrogate model with self‐updating is proposed to predict the structural natural frequency so that the overall computation time of the optimization process can be reduced. The proposed method was used to optimize a 50‐story frame‐tube building and was compared against the general genetic algorithm and general NSGA‐II to verify the feasibility and effectiveness.

Least Squares Reverse Time Migration of Ground Penetrating Radar Data Based on Modified Total Variation

As a fundamental part of ground penetrating radar (GPR) data processing, reverse time migration (RTM) can correctly position reflection waves and focusing diffraction waves on the proper spatial position. Least-squares reverse-time migration (LSRTM) is widely used in the seismic field for its ability to suppress artifacts and generate high-resolution images in comparison to conventional RTM. However, in the particular case of GPR detection methods, LSRTM is extremely susceptible to aliasing artifacts caused by under-sampling. In pursuit of enhanced precision in underground structure characterization, this paper presents the development of a new LSRTM based on modified total variation (MTV) regularization to improve imaging resolution. Initially, the objective function of LSRTM is derived by combining the Born approximation in 2-D transversal magnetic mode. Next, the adjoint equations and their gradients are solved using the Lagrange multiplier method. The objective function is then constrained by MTV regularization to ensure the precision and convergence of the LSRTM, which delivers a refined edge with reconstruction details. In the numerical experiments, in comparison to the conventional LSRTM method, the LSRTM-MTV algorithm demonstrated a 30.4% increase in computational speed and a 21.1% reduction in mean squared error (MSE). The outperformance of the proposed method is verified in detail through the image resolution and amplitude preservation in the test of synthetic data and laboratory data. Future research efforts will center on applying the proposed method to models featuring dispersive or anisotropic media that closely mimic real-world conditions and extending the application to various imaging techniques involving objective function minimization.

Soft Semi-Supervised Deep Learning-Based Clustering

Semi-supervised clustering typically relies on both labeled and unlabeled data to guide the learning process towards the optimal data partition and to prevent falling into local minima. However, researchers’ efforts made to improve existing semi-supervised clustering approaches are relatively scarce compared to the contributions made to enhance the state-of-the-art fully unsupervised clustering approaches. In this paper, we propose a novel semi-supervised deep clustering approach, named Soft Constrained Deep Clustering (SC-DEC), that aims to address the limitations exhibited by existing semi-supervised clustering approaches. Specifically, the proposed approach leverages a deep neural network architecture and generates fuzzy membership degrees that better reflect the true partition of the data. In particular, the proposed approach uses side-information and formulates it as a set of soft pairwise constraints to supervise the machine learning process. This supervision information is expressed using rather relaxed constraints named “should-link” constraints. Such constraints determine whether the pairs of data instances should be assigned to the same or different cluster(s). In fact, the clustering task was formulated as an optimization problem via the minimization of a novel objective function. Moreover, the proposed approach’s performance was assessed via extensive experiments using benchmark datasets. Furthermore, the proposed approach was compared to relevant state-of-the-art clustering algorithms, and the obtained results demonstrate the impact of using minimal previous knowledge about the data in improving the overall clustering performance.

Effect of Subsonic Compressibility and Constraints on Generation of 3-D Optimal Camber Shapes

A flat surface wing is optimized for minimum induced drag for low and high subsonic Mach numbers. Wing for transport airplane role is considered. Optimal warp is separated into twist and camber. Effect of compressibility is analysed on the camber shape generated for two different Mach numbers. Constraint of lift is firstly used for developing an objective function for drag minimization. Next the lift and wing root bending moment constraints are considered to form objective function. Analysis is made on the resulting camber and twist distributions.

Application of Nonlinear Optimization for Fault Location in Transmission Lines with Series Compensation Protected by Varistors

This paper introduces a novel approach to fault localization in transmission lines with series compensation using nonlinear optimization. The objective function minimization provides information on the fault distance and the current at which the protective varistor starts conducting. Terminal source data, the maximum current capacity of the capacitor, and the operating curve of the metal oxide varistor protection element are not required. The proposed method successfully met the predefined objectives, with a maximum error of 1.13% in simulated scenarios. In validating the method using real cases from a Brazilian energy concessionaire, the errors were below 0.5%.

Simultaneous optimization of design and maintenance for systems using multi-objective evolutionary algorithms and discrete simulation

When projecting and building new industrial facilities, getting integrated design alternatives and maintenance strategies are of critical importance to achieve the physical assets optimal performance, which is needed to be competitive in the actual global markets. Coupling Evolutionary Algorithms with Discrete Event Simulation has been explored both in relation to systems design and their maintenance strategy. However, it was not simultaneously considered when both the corrective and the preventive maintenance—consisting of achieving the optimum period of time to carry out a preventive maintenance activity—are taken into account before being considered by the authors of the present paper. This work couples Multi-objective Evolutionary Algorithms with Discrete Event Simulation in order to enhance the knowledge and efficiency of the methodology presented, which consists of exploring and optimizing simultaneously systems design alternatives and their preventive maintenance strategies. The aim consists of finding the best set of non-dominated solutions by using the system availability (first maximized objective function) with taking into consideration associated operational cost (second minimized objective function), while automatically selecting the system devices. Each solution proposed by the Multi-Objective Evolutionary Algorithm is analyzed by using Discrete Event Simulation in a procedure that looks at the effect of including periodic preventive maintenance activities all along the mission time. An industrial application case study is solved, and a comparison of the performance of five state-of-the-art and three more recently developed Multi-objective Evolutionary Algorithms is handled; moreover, the gap in the literature reviewed about the analysis regarding the effect of the discrete event simulation sampling size is faced with useful insights about the synergies of Multi-objective Evolutionary Algorithms and Discrete Event Simulation. Finally, the methodology is expanded to more complex systems which are successfully solved.

Voltage Zoning Regulation Method of Distribution Network with High Proportion of Photovoltaic Considering Energy Storage Configuration

Photovoltaics have uncertain characteristics. If a high proportion of photovoltaics are connected to the distribution network, the voltage will exceed the limit. In order to solve this problem, a voltage regulation method of a distribution network considering energy storage partition configuration is proposed. Taking the minimum total voltage deviation, the minimum total cost, the minimum total power loss, and the minimum energy storage device installation ratio as the objective function, and considering various conditions, such as voltage deviation constraint and energy storage constraint, a mathematical model of voltage regulation is established. Firstly, a high proportion of photovoltaics are connected to the distribution network, and the voltage deviation curve is obtained. The optimal k value is determined by the elbow rule. The voltage deviation curve of each node is clustered by the k-means algorithm so as to determine the energy storage device partition. The energy storage device is connected to various clustering centers, and then the weighting factor of each objective function is determined by the fuzzy comprehensive evaluation method. For comparison and analysis, (k + 1) schemes are determined through the partition configuration of (k + 1) energy storage devices. Then, the model is solved by particle swarm optimization, and the unit output result and the minimum objective function value are obtained. Finally, an example of IEEE33 is used to verify the effectiveness of the proposed model.

Optimization Method of Energy Storage Configuration for Distribution Network with High Proportion of Photovoltaic Based on Source–Load Imbalance

After a high proportion of photovoltaic is connected to the distribution network, it will bring some problems, such as an unbalanced source and load and voltage exceeding the limit. In order to solve them, this paper proposes an optimization method of energy storage configuration for a high-proportion photovoltaic distribution network considering source–load imbalance clustering. Taking the minimum total voltage deviation, the minimum total power loss and the minimum total operating cost as the objective function, and considering various constraints such as power balance constraints and energy storage operation constraints, a mathematical model for energy storage configuration optimization is established. Firstly, the source–load imbalance of the distribution network with a high proportion of photovoltaic is defined. Therefore, according to the 24 h photovoltaic and load data, the 24 h source–load imbalance can be obtained, and the optimal k value can be determined by the elbow rule, so that 24 h a day can be clustered into k periods by the k-means algorithm. Then, the fuzzy comprehensive evaluation method is used to determine the weight factors of each objective function in each period, and three scenes are determined according to the different amount of energy storage. Then, the hybrid particle swarm optimization algorithm proposed in this paper is used to solve the model, and the minimum objective function value, optimal position and optimal capacity of each energy storage grid in each scene are obtained. Finally, it is applied to an example of IEEE33. In the results, the total voltage deviation is increased by more than 10%, the total power loss is increased by more than 8% and the total operating cost is increased by more than 12%, which verifies the effectiveness of the proposed model.

A numerical approach to sequential multi-hypothesis testing for Bernoulli model

In this article, we deal with the problem of sequential testing of multiple hypotheses. The main goal is minimizing the expected sample size (ESS) under restrictions on the error probabilities. We take, as a criterion of minimization, a weighted sum of the ESSs evaluated at some points of interest in the parameter space, aiming at its minimization under restrictions on the error probabilities. We use a variant of the method of Lagrange multipliers based on the minimization of an auxiliary objective function (called Lagrangian) combining the objective function with the restrictions, taken with some constants called multipliers. Subsequently, the multipliers are used to make the solution comply with the restrictions. We develop a computer-oriented method of minimization of the Lagrangian function that provides, depending on the specific choice of the parameter points, optimal tests in different concrete settings, as in Bayesian, Kiefer-Weiss, and other settings. To exemplify the proposed methods for the particular case of sampling from a Bernoulli population, we develop a set of computer algorithms for designing sequential tests that minimize the Lagrangian function and for the numerical evaluation of test characteristics like the error probabilities and the ESS. We implement the algorithms in the R programming language. The program code is available in a public GitHub repository. For the Bernoulli model, we made a series of computer evaluations related to the optimality of sequential multi-hypothesis tests, in a particular case of three hypotheses. A numerical comparison with the matrix sequential probability ratio test is carried out. A method of solution of the multi-hypothesis Kiefer-Weiss problem is proposed and is applied for a particular case of three hypotheses in the Bernoulli model.

Inverse Evaluation of Monopile Pile–Soil Interaction Parameters Using Random Search

To deal with the uncertainties in modeling offshore wind turbines, we propose a parameter inversion method for the pile–soil interaction model based on structural health monitoring results and the numerical model. The proposed parameter inversion method has a numerical model, an objective function selected using both the numerical and identified results, and an inverse optimization using a random search algorithm in the assumed parameter space. The parameter results in the minimum optimization objective function are identified as the in situ parameter. The proposed method is confirmed to converge after some number of iterations, depending on what the initial parameter values are. However, different initial parameter cases may converge to slightly different optimal parameters, implying that the pile results are sensitive to geological parameters. Moreover, a comparison with the original design results shows design redundancy or risks. Though the proposed method has several flaws, it can shed light on the influence of parameter uncertainties on offshore wind turbines.

Simultaneous identification of groundwater pollution source and important hydrogeological parameters considering the noise uncertainty of observational data.

Groundwater pollution identification is an inverse problem. When solving the inverse problem using regular methods such as simulation-optimization or stochastic statistical approaches, requires repeatedly calling the simulation model for forward calculations, which is a time-consuming process. Currently, the problem is often solved by building a surrogate model for the simulation model. However, the surrogate model is only an intermediate step in regular methods, such as the simulation-optimization method that also require the creation and solution of an optimization model with the minimum objective function, which adds complexity and time to the inversion task and presents an obstacle to achieving fast inversion. In the present study, the extreme gradient boosting (XGBoost) method and the back propagation neural network (BPNN) method were used to directly establish the mapping relationships between the output and input of the simulation model, which could directly obtain the inversion results of the variables to be identified (pollution sources release histories and hydraulic conductivities) based on actual observational data for fast inversion. In addition, to consider the uncertainty of observation data noise, the inversion accuracy of the two machine learning methods was compared, and the method with higher precision was selected for the uncertainty analysis. The results indicated that both the BPNN and XGBoost methods could perform inversion tasks well, with a mean absolute percentage error (MAPE) of 4.15% and 1.39%, respectively. Using the BPNN, with better accuracy for uncertainty analysis, when the maximum probabilistic density value was selected as the inversion result, the MAPE was 2.13%. We obtained the inversion results under different confidence levels and decision makers of groundwater pollution prevention and control can choose different inversion results according to their needs.

Determination of Distribution Center Location using Analysis of Time-Based Set Covering Model and Maximal Covering Model Analysis

The distribution or delivery process is one factor that affect customer satisfaction as the goal of supply chain. In order for supply chain to be competitive in competition, delivery time is an important factor to manage, so that it could provide high service level value. One factor that could affects distribution or delivery is distribution center location. A strategic distribution center location would facilitate and speed up distribution process. This research discusses model for determining location of distribution center so that delivery could be made at the right amount and in the right time by analyzing of time-based using set covering model and maximal covering model. The numerical example in this research is case study on paint supply chain in Bandung which has a number of delivering clusters. Each cluster consists of a number of building material stores which are located scattered. There is one cluster that has problems in fulfilling demands and delivery times. The analysis made could be used to determine the distribution center location so that it could serve all consumer demands. Based on the calculation results, it was found that there were two distribution center locations. Two distribution centers could fulfill the objective function of cost minimization and satisfy all demands. The results of the sensitivity analysis show that there are several factors that influence the determination of location number.

Modeling Approach with Therapeutic Drug Monitoring Data to Describe Time Course of Clozapine Exposure and Positive and Negative Syndrome Scale Scores

The Positive and Negative Syndrome Scale (PANSS) is commonly used to assess the severity of the clinical symptoms of schizophrenia (SCZ). This study aimed to develop a pharmacokinetic (PK)/pharmacodynamic (PD) model based on therapeutic drug monitoring (TDM) data to characterize the relationship between clozapine exposure and the PANSS scores in patients with SCZ. TDM data for clozapine and PANSS scores from 45 patients with SCZ were included in this modeling analysis using NONMEM. Based on published data, intensive PK sampling data collected up to 12 hours postdose from 23 patients was incorporated into the PK data set to improve the fitting of absorption and disposition. For PD model development, the PANSS score was assessed at baseline, followed by 8 and 18 weeks after the initiation of clozapine dosing. Visual predictive check plots, the precision of parameter estimates, and decreases in the minimum objective function values were used for the model evaluation. A 2-compartment model with an absorption lag and a combined error model adequately described the PK of clozapine. The implementation of disease progression with placebo and drug effects improved the model's ability to describe the time course of the PANSS scores. In the final PK/PD model, Weibull and maximum effect (E max ) models were selected as disease progression models for the placebo and drug effect models, respectively. The model evaluation results supported the adequacy of the final model. A clozapine PK/PD model based on clinical settings adequately described the PANSS time course in patients with SCZ. These findings may aid the development of treatment strategies for patients with SCZ.

A nondominated sorting genetic algorithm III with three crossover strategies for the combined heat and power dynamic economic emission dispatch with or without prohibited operating zones

This paper presents a nondominated sorting genetic algorithm III with three crossover strategies (NSGA-III-TCS) for the combined heat and power dynamic economic emission dispatch (CHPDEED) problems with or without prohibited operating zones. The first strategy updates the individuals of the first nondomination rank by a modified improvisation of the harmony search algorithm, which accelerates the information exchanges of the elite individuals. The second strategy regulates the individuals of the last nondomination rank according to a modified single-point crossover of the genetic algorithm, which strengthens the convergence of the population. The third strategy adjusts the remaining individuals in terms of a modified DE/rand-to-best/1 mutation of the differential evolution algorithm, and it guides these individuals to move towards the ones which have at least one minimum objective function value, which is beneficial for expanding the distribution range of the population. NSGA-III-TCS obtains the largest average hypervolumes and shows a desirable convergence for six CHPDEED problems. NSGA-III-TCS achieves relatively high coverage rates in most cases, indicating the dominance of the Pareto sets of NSGA-III-TCS over those of the other algorithms. Also, it has relatively low average spacings for all problems, suggesting the good evenness of the Pareto sets.

A Variant Iterated Greedy Algorithm Integrating Multiple Decoding Rules for Hybrid Blocking Flow Shop Scheduling Problem

This paper studies the hybrid flow shop scheduling problem with blocking constraints (BHFSP). To better understand the BHFSP, we will construct its mixed integer linear programming (MILP) model and use the Gurobi solver to demonstrate its correctness. Since the BHFSP exists parallel machines in some processing stages, different decoding strategies can obtain different makespan values for a given job sequence and multiple decoding strategies can assist the algorithm to find the optimal value. In view of this, we propose a hybrid decoding strategy that combines both forward decoding and backward decoding to select the minimal objective function value. In addition, a hybrid decoding-assisted variant iterated greedy (VIG) algorithm to solve the above MILP model. The main novelties of VIG are a new reconstruction mechanism based on the hybrid decoding strategy and a swap-based local reinforcement strategy, which can enrich the diversity of solutions and explore local neighborhoods more deeply. This evaluation is conducted against the VIG and six state-of-the-art algorithms from the literature. The 100 tests showed that the average makespan and the relative percentage increase (RPI) values of VIG are 1.00% and 89.6% better than the six comparison algorithms on average, respectively. Therefore, VIG is more suitable to solve the studied BHFSP.

Convergence of an asynchronous block-coordinate forward-backward algorithm for convex composite optimization

AbstractIn this paper, we study the convergence properties of a randomized block-coordinate descent algorithm for the minimization of a composite convex objective function, where the block-coordinates are updated asynchronously and randomly according to an arbitrary probability distribution. We prove that the iterates generated by the algorithm form a stochastic quasi-Fejér sequence and thus converge almost surely to a minimizer of the objective function. Moreover, we prove a general sublinear rate of convergence in expectation for the function values and a linear rate of convergence in expectation under an error bound condition of Tseng type. Under the same condition strong convergence of the iterates is provided as well as their linear convergence rate.

An intervention study of VR sports games on the perceptual and motor abilities of children with incomplete intellectual development

Abstract Childhood is a critical stage for the development of perceptual and motor abilities, and strengthening the training of children with incomplete mental development at this stage will affect the development of motor skills during their growth. In this paper, we take VR technology as a starting point to build a perceptual model and introduce a convolutional sparse representation algorithm. First, a sparse representation with few non-zero elements is found to optimize a function consisting of a data fidelity term and a sparse induced penalty function. Then, the sum of the convolution of the filter and the convolution sparse feature map, i.e., the convolution operation, is computed to generate the translation invariants. Then the convolutional sparse coding method is introduced to the traditional unsupervised problem by calculating the minimization objective function and solving it in an iterative manner alternatively. Finally, the constituents of the signal are analyzed and the discrete equivalence of the convolution is derived based on the Fourier transform to derive the intervening variables. The experimental results showed that the mean value of the post-test of motor ability compared with the pre-test increased by 4.6 through an eight-week VR sports game training intervention study test on different children with incomplete mental development. Therefore, it is of great theoretical and practical significance to understand the characteristics of perceptual and motor abilities of children with incomplete intellectual development and to develop corresponding programs for VR sports game training according to their characteristics.