Calculation Of Objective Function Research Articles

Theoretical analysis and methods of rapid evaluation: Solving the blocking flowshop group scheduling problem with the total flow time and total tardiness time criteria

For the blocking flowshop group scheduling problem (BFGSP), this study addresses its high computational burden associated with insertion operations due to over-much objective function calculations as the number of groups and jobs increases. Unfortunately, the existing rapid evaluation methods exhibit limitations when handling group-based insertion, blocking constraint, total flow time, and total tardiness time criteria. We emphasize the need for improved rapid evaluation techniques tailored to these limitations and propose the theoretical analysis and methods of a critical machine-based rapid evaluation for total flow time and tardiness criteria of BFGSP. More specifically, first, under the two scenarios of the group and job scheduling, we propose the concept of the critical machines, three theorems, one corollary, and their corresponding proofs, respectively. Secondly, we present rapid evaluation methods for group insertion and job insertion, respectively, namely Rapid_group and Rapid_job based on the above theorems and corollary. We find that it is unnecessary to start the computation from the first machine when scheduling the changed groups or jobs, and it suffices to begin the computation from the critical machine, thus reducing the computational cost. Finally, we conduct five experiments on four well-known benchmarks (a total of 6000 instances). Through statistical analysis, it becomes evident that our computational efforts have decreased significantly in computing both the total flow time and the total tardiness time for group-based and jobs-based insertion operations. The development of rapid evaluation mechanisms is a promising approach to mitigate the time complexity by reducing the number of machines involved in the evaluation, and makes up for gaps in existing accelerated evaluation methods for BFGSP.

A novel low‐complexity model predictive control for Vienna rectifier

SummaryA Vienna rectifier is a kind of three‐phase converter with complex operation constraints. Traditional control methods suffer from poor dynamic responses and total harmonic distortion (THD), particularly when operating with adjustable wide‐range power. A novel low‐complexity model predictive control (LC‐MPC) algorithm is proposed based on the optimal switching vector sequence in this paper. First, a model predictive optimization control (MPOC) method is designed to search for the voltage vector sequence and its acting time. Second, the equivalent transformation and coordinate mapping of MPOC are efficiently achieved through the derived correlation factors and lookup table. Supported by the correlation factors, the redundant objective function calculation and repetitive online optimization are eliminated. Meanwhile, the simplified optimal over‐modulation strategy is implemented. Finally, the effectiveness and superiority of the algorithm are verified by comparative experiments. The results show that the proposed LC‐MPC is beneficial in terms of the computation time, dynamic response, over‐modulation, and harmonic content reduction.

Control algorithm for decision making in multi-criteria optimization problems

The main feature of the multi-criteria optimization of the design processes of complex electronic devices is that they are all interconnected, heterogeneous in nature and, as a rule, non-linear. That is, by changing some of them by varying the corresponding parameters, we inevitably change other parameters of the system, and not always in the right direction. The purpose of the work is to propose a way to organize the procedure for finding the optimal solution to multicriteria design problems. When developing and creating new schemes, structures and systems, the task of determining the optimal values of the parameters of the designed technical device or system is reduced to the task of finding the extremum of a certain function, called the quality function. Usually, it is a non-linear function of many independent variables, which, as a rule, cannot be investigated by analytical methods. In this situation, it is advisable to search for a solution to the problem using special algorithms. At the early stages of designing complex radio electronic devices, an algorithm for finding the optimal solution based on the application of search optimization theory methods is proposed. The paper describes the procedure for finding the optimal solution, the distinctive feature of which is that during the search for a solution, information is accumulated and a search direction vector is constructed. This vector offers options for changing weights for subsequent search procedures. The algorithm developed on its basis is used in the information system for the complex analysis of the designs of radio-electronic facilities. The use of random search provides the algorithm with global properties, reduces the number of objective function calculations by one step, which is especially noticeable with a large number of optimized parameters. Allows you to quite simply include any restrictions on the set of valid values of the vector of optimized parameters, which is not always possible when using regular search methods. The proposed algorithm is simply tuned to search for a global extremum by selecting the appropriate parameters. For each specific case, there are some optimal ratios of the values of these algorithm parameters, which, when searching for a solution, reduce the number of working steps. The developed algorithm is less critical to the optimal values of its own parameters, which makes it much easier to tune it when solving practical problems of optimizing design processes.

Uncertainty Inclusive Runway Balancing Using Convolutional Neural Network

This paper proposes a new optimization scheme using neural networks for runway balancing to minimize departure and arrival aircraft delay. The delay prediction for runway balancing optimization is obtained by a neural network, only without any additional simulations. Developing an accurate simulation model under an uncertain environment is difficult, but the proposed neural network model can estimate the average delay without modeling uncertainty explicitly. In this paper, the effectiveness of the proposed method is validated through numerical simulations. First, simulations are used to generate the data, which are then used to train the neural network. Next, the runway balancing problem is solved via simulated annealing using the delay predicted by the neural network. The simulation result shows that the proposed approach outperforms the simulation-based method under an uncertainty environment. Therefore, the neural network is shown to accurately estimate the delay under the uncertainty environment, which makes the proposed neural-network-based method applicable to objective function calculations for optimization.

Modularization with Rule Based Algorithm in Three-Dimensional Design of Engine Room Layout Harbour Tug Diesel – LNG Dual Fuel Engine 2 × 2500 HP

Implementation of the dual-fuel engine as ship main propulsion in Indonesia is low. There is a need for a study about the ship design process for dual fuel engine ship, especially for the engine room. Process and instrumentation diagram can’t give a whole picture of the real engine room, but three-dimensional can provide this. First, this study is to know about the process and instrumentation diagram on harbour tug diesel-LNG dual fuel engine 2 × 2500 HP. Second, this study is to know about the original, clustered, and reordered design structure matrix of all piping components. Third, this study is to know about three-dimensional design using modularization with rule-based algorithm. Components from the bilge & ballast system, oily water separator system, firefighting system, domestic supply and discharge system, marine diesel fuel oil system, LNG fuel oil system, lubricating oil system, cooling system, and compressed air system are inserted in original DSM. The rule-based algorithm is for clustering and reordering. At the end of the original, clustered, and reordered DSM there is a need for the objective function and sum value calculation. In this study, DSM modeler is used to do the clustering and reordering process included in one by clicked clustering algorithm feature. So, in this study is decided that reordering process is done manually using the workflow of the system to ensure that clustering algorithm feature can give clustered and reordered DSM, by compared the objective function and sum value from the original, clustered, and reordered DSM. The result of the objective function and sum value comparison always give less value than the original and clustered DSM. Clustered and reordered DSM had the same value. Sometimes the objective function and sum value of reordered DSM is greater than clustered DSM, which means there is human error when manually reordering the clustered DSM. Less value of the objective function and sum value DSM is used to create three-dimensional. Components that are included in one cluster need to be located nearly. Modularization with rule-based algorithm is applicable in three-dimensional design engine room layout.

New One-Dimensional Search Iteration Algorithm and Engineering Application

In structural optimization design, obtaining the optimal solution of the objective function is the key to optimal design, and one-dimensional search is one of the important methods for function optimization. The Golden Section method is the main method of one-dimensional search, which has better convergence and stability. Based on the solution of the Golden Section method, this paper proposes an efficient one-dimensional search algorithm, which has the advantages of fast convergence and good stability. An objective function calculation formula is introduced to compare and analyse this method with the Golden Section method, Newton method, and Fibonacci method. It is concluded that when the accuracy is set to 0.1, the new algorithm needs 3 iterations to obtain the target value. The Golden Section method takes 11 iterations, and the Fibonacci method requires 11 iterations. The Newton method cannot obtain the target value. When the accuracy is set to 0.01, the number of iterations of the new method is still the least. The optimized design of the T-section beam is introduced for engineering application research. When the accuracy is set to 0.1, the new method needs 3 iterations to obtain the target value and the Golden Section method requires 13 iterations. When the accuracy is set to 0.01, the new method requires 4 iterations and the Golden Section method requires 18 iterations. The new method has significant advantages in the one-dimensional search optimization problem.

Optimization of flexible fixture layout to improve form quality using parametric finite element model and mixed discrete-integer genetic algorithm

Dimensional and form accuracy of the workpiece can be improved by effective fixture layout design which shows minimum deformation of the workpiece during machining. Flexible fixtures are inevitable in industries owing to high product variety and shortened production time. Hence, an integrated approach is presented to select the optimum position of locating and clamping elements in a flexible fixture that provide good form accuracy. In this approach, a Parametric Finite Element Model (PFEM) is developed using the information about the workpiece, fixture plan and machining condition. PFEM is used to predict the elastic deformation of the workpiece for the fixture layouts generated using a discrete Genetic Algorithm (GA) with mixed integer-discrete variables. The objective is to minimize the maximum deformation of the workpiece by optimizing fixture layouts. The stability of the workpiece and fixture system is ensured by implementing non-negative reaction force constraints in GA. The proposed approach is applied for a prismatic workpiece to carry out pocket milling operation. The significance of this work is to express the flexibility and computational effectiveness of PFEM to accommodate variation in the workpiece, machining condition and fixture plan while designing flexible fixtures. Further, it highlights a significant reduction in search space due to the use of discrete GA and stability constraint as it takes less objective function calculations. An experimental analysis is performed to study the effectiveness of the proposed approach. Therefore, the proposed approach provides a viable solution to the optimization problem in flexible fixtures.

Controller design and multi-objective optimization of heavy goods vehicle suspension system by geometry-inspired GA

This paper presents the design of a suspension system for a Heavy Goods Vehicle (HGV). Four types of linear and non-linear, passive and semi-active suspension systems are modelled with Quarter Vehicle Model (QVM). A modified control law is proposed for the semi-active suspension system that uses a Proportional, Integral, Derivative (PID) controller. Suspension systems are designed by performing multi-objective optimization with road damage and goods damage as design criteria. In current optimization problems, objective function calculation is costly in terms of computational resources and time. Thus, it is necessary to reach actual optimal values in fewer generations with a small population. A fast-converging optimization algorithm is proposed to save computational cost and is used to design suspension systems. The results of the proposed algorithm are compared with the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The proposed algorithm saves a substantial amount of computational cost by fast convergence with a small population. Our results show that the semi-active suspension system with proposed control law performs better in terms of road-friendliness and goods safety.

Current status of the high-temperature kinetic models of silane: Part II. Oxidation

Abstract The present study is the second part of our work on the current status of high-temperature kinetic models of silane. Except Slakman’s model, all the models tested in the first part of the study, restricted to the pyrolysis dataset, are now compared against a large validation dataset (230 conditions) for silane oxidation. This large validation dataset is composed of both new and literature data, mainly representative of the highly-diluted and high-temperature oxidation of silane with different oxidizers ( O 2 , N 2 O , and NO) and diluents (Ar and N 2 ) over an extensive range of temperature ( T = [801– 2955 K]) and pressure ( P = [50 – 629 kPa]) conditions. The new experimental data are limited to SiH 4 - O 2 -Ar mixtures, obtained in a double-diaphragm shock tube equipped with an Atomic Resonance Absorption Spectroscopy (ARAS) detection technique. Experimental results present the temporal evolution of the total absorption signal, considering the absorption of O, Si, N 2 O , and SiH 4 . The performance of the models is assessed based on the same five validation criteria and objective function calculation, as presented in the first part of the study. The model of Chatelain and of Mevel present good performances with a global error of 2.4, i.e. meaning an average error of 2.4 fold above the experimental uncertainty, and high fraction (70 %) of criteria predicted within two times the experimental uncertainty. Although the reference reaction models performed better on the oxidation dataset compared to the pyrolysis dataset (part I), their global error is still 50 to 125 % higher than the two most accurate reaction models. Rate of production and sensitivity analyses revealed that the origin of the discrepancy of the least performing models can be attributed to the reaction pathways consuming/producing Si and O atoms and to some kinetic rates that must be updated.

Ellipsoid Method for Linear Regression Parameters Determination

Introduction. Linear regression parameters determination can be formulated as a non-smooth function minimization problem, which is Lp-norm of residual of the linear equations system. To solve it non-smooth function minimization methods can be used, e.g. subgradient methods. The article [7] considers ellipsoid method application for finding Lp-solution of redefined linear equations system with 1≤p≤2. The purpose of the paper is to extend the algorithm based on the ellipsoid method for a linear regression parameters determination problem with an arbitrary value of parameter p≥2 so that under big values of p the solution of the problem equals minimax method solution, which corresponds to p=∞ case. To describe the formulation of observation approximation problem with quadratic function as linear regression parameters determination problem. To analyze algorithm work results for great number of observations and outliers. To compare the minimax method and the ellipsoid method algorithm work results for linear regression parameters determination problem with big values of parameter p. Results. The way of calculation of objective function and its subgradient values with large values of parameter p was developed and verified on example of observation approximation containing outliers with linear function. Algorithm based on ellipsoid method changes linear function parameters monotonically using parameter p adjusting, thereby permits to reject or consider these or those observations. It is shown in [3] that Least Absolute Deviations method (LAD) is advised to be used as far as it ignores outliers and reconstructs linear function accurately. Experiment results with big number of observations and outliers using p=1 confirmed that conclusion: LAD ignores outlier groups and approximates observations with linear function adequately. Least Square Method (LSM) deviates from optimal linear function if a group of outliers is present in particular area. In case of using big values of parameter p problem solution converges to minimax method solution. Conclusions. Algorithm based on ellipsoid method permits to determine linear regression parameters with arbitrary value of parameter p≥1. So, three known methods can be used – LAD, LSM and minimax method – as its special cases. Moreover, directing p to 1, intensity of outliers ignoring can be regulated, that gives a possibility to use external sources of information (expert opinions, measuring devices readings, statistical forecasts, etc.) for more correct and adequate approximation function reconstruction. Keywords: ellipsoid method, linear regression, outliers.

Water management using genetic algorithm-based machine learning

Water scarcity is the major problem presently being faced globally; it is to be managed in an efficient manner. The water management procedure is one of the techniques to condense necessary water. The objective of water management system is that water supply agency to collect, distribute quality water without any delay and scarcity. An intelligent system is necessary for efficient production, collection and distribution. The proposed intelligent system consists of genetic operations with fitness value and neural network for training. The fitness function is used to make new intelligent members from existing population of water resources for water collection and distribution. The system is applicable for prediction about water consumption, distribution using decision-making algorithms to increase optimization performance by calculation of objective function of various population types. The regression performance of proposed intelligent system is calculated and compared with other algorithms.

Параллельный алгоритм для получения равномерного приближения решений множества задач глобальной оптимизации с нелинейными ограничениями

In this work building of a parallel version of a method simultaneously solving a set of constrained global optimization problems is considered. This method converges uniformly to solutions of all the problems. That allows the method to arrange computational resources in an optimal way, since uniform convergence guarantees approximately equal precision of numerical solutions at the whole set of problems at the each iteration of optimization. The algorithm assigns a priority to each problem, and then at the each iteration carries out calculation of objective functions and constraints in several problems in parallel. If the method stops at any arbitrary moment, in all the problems numerical sulutions with the similar accuracy will be obtained. Sets of similar global optimization problems appear for an instance after scalarization of multi-objective problems or when a global optimization problem has a discrete parameter which takes a finite number of possible values. The considered method uses Peano-type curves to transform multidimensional problems into univariate ones. Efficiency of the implemented parallel algorithm is evaluated on several sets of synthetically generated constrained global optimization problems and on a scalarized multi-objective problem. Also the uniform convergence was confirmed numerically by validation quality of intermediate solutions during the optimization process.

The Dependence of Actual Laser Cutting Speed on CNC Sheet Equipment on Number of NC Program Commands for Metal Grades 1.0114 and AWAIMg3

One of the complex optimization problems arising in technical applications is the cutting path problem for CNC sheet metal cutting machines. This problem is to optimize the tool path for the CNC technological equipment when cutting a fixed set of parts allocated on sheet metal. The time of cutting process is one of objective functions for the optimization problem. This objective function depends on six parameters of cutting process: 1) cutting speed; 2) lengths of the cutting tool path; 3) speed of idling motion of tool; 4) length of idling motion; 5) number of piercings; 6) time of one piercing. When programming NC program, speed of cutting is defined by the user of the CAM (Computer-Aided-Manufacturing) system and considered as a constant. However, this is actually not the case. Consequently, the problem of exact calculation of objective function is arisen. In order to solve this problem, the correction coefficients for the cutting speed value defined by the user must been calculated. Obviously, these coefficients will vary for different thicknesses and grades of metal. The paper presents the results of investigates, which made it possible to find the functional dependences of the cutting speed for the CNC laser cutting machine (CO2) on the number of NC program commands for the following metal grades: 1.0114 (thickness Δ = 1-10 mm) and AWAIMg3 (Δ = 1-5 mm).The statistical materials of experiments were processed by using software “Mathcad”. The received results show that the actual average value of cutting speed is monotonically decreasing function depended on number of NC program commands. In addition, the calculation of the actual cutting speed provides not only an accurate calculation of the value of the objective function, but also, as a result, the correct finding of the optimal tool path

A Multi-Objective Modeling Method of Multi-Satellite Imaging Task Planning for Large Regional Mapping

Regional remote sensing image products are playing an important role in an increasing number of application fields. Aiming at multi-satellite imaging task planning for large-area image acquisition, this paper proposes a multi-objective modeling method. First, we analyzed the core requirements of regional mapping for multi-satellite imaging mission planning: Full coverage of the target area and low consumption of satellite resources. Second, an optimization model with two objective functions, namely the maximum target area coverage and minimum satellite resource utilization, was established. Using the selection of imaging strips and their swing angles as two types of decision variables, the regional decomposition and satellite resource allocation were integrated into the planning model. Third, two efficient algorithms, Vatti and non-dominated sorting genetic algorithm (NSGA-II), were used for objective function calculation and model solving, respectively. Finally, the experiments used Hubei, Finland, and Congo as the target areas and GF1, GF6, ZY1-02C, and ZY3 as imaging satellites to verify the modeling method proposed in this paper. The experiments showed that the proposed multi-objective modeling method could complete the coverage of regional targets with fewer satellite resources and improve the satellite application efficiency significantly.

Multi-Topic Misinformation Blocking With Budget Constraint on Online Social Networks

Along with the development of Information Technology, Online Social Networks (OSN) are constantly developing and have become popular media in the world. Besides communication enhancement benefits, OSN have such limitations on rapid spread of false information as rumors, fake news, and contradictory news. False information spread is collectively referred to as misinformation which has significant on social communities. The more sources and topics of misinformation are, the greater the number of users are affected. Therefore, it is necessary to prevent the spread of misinformation with multiple topics within a given period of time. In this paper, we propose a Multiple Topics Linear Threshold model for misinformation diffusion, and define a misinformation blocking problem based on this model that takes account of multiple topics and budget constraint. The problem is to find a set of nodes that minimizes the impact of misinformation at an allowed cost when blocking them from the network. We prove that the problem is NP-hard and the time complexity of the objective function calculation is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\#P$ </tex-math></inline-formula> -hard. We also prove that the objective function is monotone and submodular. We propose an approximation algorithm with approximation ratio <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(1-1/\sqrt {e})$ </tex-math></inline-formula> based on these attributes. For large networks, we propose an extended algorithm by using a tree data structure for quickly updating and calculating the objective function. Experiments conducted on real-world datasets show efficiency and effectiveness of our proposed algorithms in comparison with other state-of-the-art algorithms.

Current-voltage analytical model and multiobjective optimization of design of a short channel gate-all-around-junctionless MOSFET

In this paper we investigate the optimized design of a short channel gate-all-around-junctionless (GAAJ) metal-oxidesemiconductor field-effect-transistor (MOSFET), including the source-drain extensions, by means of genetic algorithm solutions applied to a compact current-voltage analytical model. In fact, due to the complex device structure, it seems useful to exploit a metaheuristic-based approach to search the optimal combination of the fundamental geometrical and physical parameters that lead to an improved performance. Through this analysis, different parameter constraints are imposed for the calculation of specific objective functions. In particular, for a fixed gate-drain bias level, the task pursues the maximization of the drain current and cut-off frequency while limiting the short channel (SC) effects. The MOSFET series resistance is also evaluated in the transition region of the Id – Vgs characteristics which appear, however, strongly affected by SC effects. The accuracy of the model is verified by comparison with experimental data reported in literature.

Frequency optimisation of composite cylinder using an evolutionary algorithm and neural networks

The paper deals with the optimisation of dynamic properties of a composite cantilever cylinder. The optimised parameters are both the fundamental natural frequency f1 as well as the gap in frequency space around a selected external excitation force allowing to avoid the resonance phenomenon. The optimisation is performed using a novel approach combining particle swarm optimisation and artificial neural networks. The evolutionary algorithms are used to solve the optimisation problem with many local minima while neural networks are used to substitute time-consuming finite element calculations of the minimisation problem objective function.

NEW WAVEGUIDE METHOD FOR DIELECTRIC PARAMETER MEASUREMENT

Perfect knowledge of dielectric parameters is necessary for its application in various devices. In spite of the whole range of measurement techniques, their practical implementation in the microwave frequency band runs into some difficulties. This article describes a new method for nonmagnetic dielectrics permittivity and loss tangent measurement in the microwave frequency band. A dielectric specimen slab is placed in the short-circuited waveguide section normal to its axis and fills the whole cross-section of the waveguide at approximately quarter wavelength from its short-circuited endpoint. By means of the vector network analyzer the waveguide section reflection factor is measured. Objective function is de-termined as difference between calculated and measured module and phase of the reflection factor. Specific code for ob-jective function calculation and its minimization is worked out. Minimization of this function by varying dielectric parameters makes it possible to find real values of these parameters. The method needs no de-embedding and can be used with non-calibrated waveguide-to-coax transitions. Also it is less sensitive to the noise component of reflected signal. The testing results show that new method’s error does not exceed 0.2 % for relative permittivity and 1% for dielectric loss tangent.

Random restart local search optimization technique for sustainable energy-generating induction machine

The goal focused upon is efficiency optimization of an induction machine, using a Random Restart Local Search Optimization technique. Recently, many studies have been designed to boost the operation efficiency of induction machines using optimization techniques, but the existing techniques have failed in the efficiency enhancement of induction machine design. To resolve this efficiency problem, a Hill Climbing Based Local Search Optimization technique was designed. Initially, IM data are collected, and the random restart local search optimization is implemented to formulate four objective functions. After the objective function calculation, the value obtained is compared to a threshold value using the continuous hill climbing algorithm. Finally, the optimal induction machine data set with the highest efficiency is selected for designing the induction machine. The proposed method is compared to state-of-the-art methods.

Grid fins shape design of a launch vehicle based on sequential approximation optimization

This paper performed the optimization of grid fins shape of a launch vehicle based on Sequential Approximation Optimization (SAO) and Computational Fluid Dynamics (CFD) simulation coupling. An efficient and reliable method is proposed for determining the width of Gaussian functions based on a logical relationship between the width and local density. The performance of the proposed method is evaluated using five classical test functions. The proposed method for width determination generates almost no excessive calculation costs, and improves the accuracy, reliability, and stability of the Radial Basis Function (RBF) surrogate model notably. Based on the improved RBF surrogate model, a framework and detailed procedure for the SAO algorithm is presented, and the performance of the proposed SAO algorithm is tested, with obtained results showing that the proposed SAO algorithm reduces the calling times of the original model and improves the optimization efficiency remarkably. The objective function is strictly deduced and reflects the momentum loss caused by aerodynamic drag directly. Three constraints are imposed to ensure the static stability and controllability of the launch vehicle. Finally, grid fins shape optimization problem of the launch vehicle is solved, with the objective function and constraints calculation tasks accomplished automatically by batch mode CFD simulations. The global optimal solution is obtained after 54 calling times of the original model, and 92 h (3.84 days) of computation on a 96-core cluster. Once the baseline shape is replaced with the optimized shape, it is detected that (1) taking the minimum fuel as an objective function, the take-off mass is 2.07% lighter than the take-off mass of the baseline shape, (2) taking the maximum payload mass as an objective function, the payload mass is 14.3% heavier than the payload mass of the baseline shape.