Minimization Of Objective Function Research Articles

Study on the effects of parameters to PET bottle thickness in blowing process

PET bottles are widely used for drinking water. PET bottles’ quality depends on their thickness. The aim of this study is to find design variables and optimal parameters of the stretching blow molding (SBM) process of PET bottles in order to increase the uniformity of bottle thickness by using the simulation technique and Taguchi method. The finite element method is used to predict the results of the SBM process. The Taguchi method is performed with six variables that belong to two main factors, which are temperature positions and parison thickness. Through the analysis process, the optimal parameters are determined and verified, with a minimum objective function result of 0.000265. On the other hand, the temperature at T4 positions and the preform thickness at Th2 sections are the main influences on the uniformity of PET bottle thickness.

Coal blending optimization in thermal power plants based on multi-strategy fusion multi-objective particle swarm optimization

ABSTRACT Rising coal price and increasingly stringent emission policy highlight the importance of balancing economic benefit and sustainable development of coal-fired power plants. In order to make the power plant operate economically and safely, and reduce the emission of pollutants as much as possible, this paper proposed a coal blending optimization framework for coal-fired power plants. This framework constructs a set of mathematical model based on the minimization objective function, including the economy, safety and environmental protection of coal. And a multi-strategy fusion multi-objective particle swarm optimization (MSF-MOPSO) method is proposed to optimize the coal blending model. The feasibility, effectiveness and superiority of the method are theoretically verified by convergence analysis and several sets of simulation experiments. And the practical application of this framework shows that under the coal blending strategy based on different weight combinations, the algorithm proposed in this paper can produce high-quality Pareto spatial distribution. Comparing with other state-of-the-art coal blending algorithms, this method can reduce the coal purchase cost by 4.42% and S O 2 emission by 5.11% at least under the same condition. It has significant environmental protection and economic benefit.

Collaborative Optimal Configuration of a Mobile Energy Storage System and a Stationary Energy Storage System to Cope with Regional Grid Blackouts in Extreme Scenarios

To address regional blackouts in distribution networks caused by extreme accidents, a collaborative optimization configuration method with both a Mobile Energy Storage System (MESS) and a Stationary Energy Storage System (SESS), which can provide emergency power support in areas of power loss, is proposed. First, a time–space model of MESS with a coupled transportation network and power grids is constructed, as a MESS is more flexible than a SESS. Considering resilience and recovery, a minimization objective function for total cost, encompassing the hybrid energy storage investment cost, the power grid operation cost, and the load shedding penalty cost, is established. Moreover, considering SESS constraints and operational constraints, a hybrid configuration model is established. Then, considering the probability of extreme accidents, the scenario analysis method is used to address randomness, ensuring that the configuration results can be adapted to various scenarios. The proposed method can fully combine the time–space flexibility of MESS and the economic advantages of SESS, which can reduce the total cost and ensure the power system’s reliability. Finally, the effectiveness of the proposed method is verified by the improved IEEE33 system.

Wind power access site selection method based on scenario probability

The fluctuation of new energy output makes the power system operation more complex, and the traditional power system tide calculation is no longer fully applicable. Therefore, the determination of wind farm output and site selection is important and fundamental research at present. Based on this, a combination of wind farm output scenario and probability is proposed. The site selection model with the minimum network loss of the distribution network as the optimization objective is proposed. First, the wind farm output is clustered into several typical scenarios by K-Means, and the output time series model and the probability of each typical scenario are obtained. The probabilities of each scenario are multiplied by the network losses under that scenario. Then, the network losses obtained for all individual scenarios are summed up and used as the minimum objective function. The model is solved by a genetic algorithm with tidal current constraint and node voltage constraint to derive the optimal wind farm access point. With the IEEE33 node, simulations are performed to derive the minimum value of the daily average network loss, which verifies the rationality and feasibility of the optimized model.

ETXRE: Energy and delay efficient routing metric for RPL protocol and wireless sensor networks

AbstractInternet of Things is an emerging paradigm based on interconnecting physical and virtual objects with each other and to the Internet. Most connected things fall into the category of constrained devices, with restricted resources (processing power, memory, and energy). These low‐power and lossy networks (LLNs) are known for their instability, high loss rates and low data rates, which makes routing one of the most challenging problems in low‐cost communications. A routing protocol for low‐power and lossy networks (RPL) is a proactive dynamic routing protocol based on IPv6. This protocol defines an objective function (OF) that utilises a set of metrics to select the best possible path to the destination. Minimum rank hysteresis objective function (MRHOF) and objective function zero (OF0) are the most basic OFs, where the first one selects the path to the sink based on the expected transmission count (ETX) metric, and OF0 is based on the hop count (HC). These two metrics prioritise either brute performance (i.e. ETX) or simplicity (i.e. HC). Therefore, using a single metric with an OF can either limit the performance or have an inefficient impact on load management and energy consumption. To overcome these challenges, a routing metric based on MRHOF OF which takes into consideration the link‐based routing metric (i.e. ETX) and node‐based metric (i.e. remaining energy) for route selection is provided. Expected transmission count remaining energy (ETXRE) is evaluated through 36 scenarios with different parameters. Preliminary results show that ETXRE outperforms ETX and RE in terms of end‐to‐end delay by an average of at least 17%, packet delay by 13% and consumes 10% less energy.

CYP3A5*3 and CYP3A4*22 Cluster Polymorphism Effects on LCP-Tac Tacrolimus Exposure: Population Pharmacokinetic Approach.

The aim of the study is to develop a population pharmacokinetic (PopPK) model and to investigate the influence of CYP3A5/CYP3A4 and ABCB1 single nucleotide polymorphisms (SNPs) on the Tacrolimus PK parameters after LCP-Tac formulation in stable adult renal transplant patients. The model was developed, using NONMEM v7.5, from full PK profiles from a clinical study (n = 30) and trough concentrations (C0) from patient follow-up (n = 68). The PK profile of the LCP-Tac formulation was best described by a two-compartment model with linear elimination, parameterized in elimination (CL/F) and distributional (CLD/F) clearances and central compartment (Vc/F) and peripheral compartment (Vp/F) distribution volumes. A time-lagged first-order absorption process was characterized using transit compartment models. According to the structural part of the base model, the LCP-Tac showed an absorption profile characterized by two transit compartments and a mean transit time of 3.02 h. Inter-individual variability was associated with CL/F, Vc/F, and Vp/F. Adding inter-occasion variability (IOV) on CL/F caused a statistically significant reduction in the model minimum objective function MOFV (p < 0.001). Genetic polymorphism of CYP3A5 and a cluster of CYP3A4/A5 SNPs statistically significantly influenced Tac CL/F. In conclusion, a PopPK model was successfully developed for LCP-Tac formulation in stable renal transplant patients. CYP3A4/A5 SNPs as a combined cluster including three different phenotypes (high, intermediate, and poor metabolizers) was the most powerful covariate to describe part of the inter-individual variability associated with apparent elimination clearance. Considering this covariate in the initial dose estimation and during the therapeutic drug monitoring (TDM) would probably optimize Tac exposure attainments.

Optimization of Green Vehicle Paths Considering the Impact of Carbon Emissions: A Case Study of Municipal Solid Waste Collection and Transportation

In recent years, the waste produced as a result of the production and consumption activities of urban residents has led to significant environmental degradation and resource wastage. This paper focuses on the research object of municipal solid waste (MSW) collection and transportation based on the concept of “sustainable development and green economy”. Firstly, this study examines the current state of urban domestic garbage collection and transportation. It analyzes the following challenges and deficiencies of the existing collection and transportation system: (1) the operating efficiency of garbage collection vehicles is low, resulting in a significant accumulation of waste on the roadside and within the community; (2) the vehicle collection and transportation routes are fixed, and there are empty vehicles running; (3) the amount of garbage on a route exceeds the vehicle’s loading capacity, which requires the vehicle to perform a second round of collection and transportation. To enhance the efficiency of urban garbage collection and transportation and minimize the collection and transportation costs, we are investigating the problem of optimizing the path for green vehicles. To comprehensively optimize the fixed cost, variable cost, and carbon emission cost incurred during vehicle operation, a vehicle routing model with time windows is established, taking into account vehicle load constraints. Carbon emission coefficient and carbon tax parameters are introduced into the model and the “fuel-carbon emission” conversion method is used to measure the carbon cost of enterprises. An improved ant colony optimization (ACO) method is proposed: (1) the introduction of a vehicle load factor improves the ant state transfer method; (2) the updated pheromone method is improved, and additional pheromone is added to both the feasible path and the path with the minimum objective function; (3) the max–min ACO algorithm is introduced to address the issue of premature convergence of the algorithm; (4) the embedding of a 2-opt algorithm further prevents the ACO algorithm from falling into the local optimum. Finally, the calculation results based on the example data demonstrate that the algorithm has a significant advantage over the genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. The total transportation distance determined by this algorithm is shorter than that of the GA and PSO methods, and the total cost of the scheme is 1.66% and 1.89% lower than that determined by GA and PSO, respectively. Compared to the data from the actual case, the number of vehicles required in the operation of this algorithm and model is reduced by three. Additionally, the total cost, fixed cost, and carbon emission cost incurred by the vehicles during operation were reduced by 31.2%, 60%, and 25.3% respectively. The results of this study help the station to collect and distribute waste efficiently, while also achieving the goals of energy saving, consumption reduction, and emission reduction.

Evaluation of energy saving and emission reduction effect of distributed energy system

The conventional evaluation methods of energy conservation and emission reduction lack the discussion of quantification index of energy conservation and emission reduction potential, and the evaluation effect is poor. Therefore, an evaluation method for energy conservation and emission reduction of distributed energy systems is proposed, which considers system dynamics and demand response. According to the requirements of system dynamics analysis, the relational variables in the system dynamics model are determined. The input-output relationship of energy saving, and emission reduction effect evaluation is described by system dynamics equation, and the input-output relationship of energy saving, and emission reduction effect evaluation is determined. Based on the maximum profit objective function and the minimum cost objective function of the user, the continuum equation of the medium transmission process in the distributed energy system is obtained. The evaluation indexes of energy saving, and emission reduction effect are selected from the three aspects of power consumption side, power generation side and the system itself to realize the evaluation of energy saving and emission reduction effect. The experimental results show that the evaluation curve obtained by this method is basically consistent with the actual curve, and the evaluation accuracy is high.

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.