Objective Function Research Articles

Optimization of Cold Chain Path forS company of C city based on Dijkstra's Algorithm

With regard to the existing transportation means and distribution routes of S company of C city, this paper analyzes them in terms of theoretical optimization and practical significance, aiming to reduce the cost of cold chain transportation. To this end, we determined the objective function of cold chain route optimization forS company of C city. Then, Dijkstra's algorithm is used to solve the cold chain routes. Combined with the example analysis results show that the optimization results based on Dijkstra's algorithm are reasonable and reliable. In this paper, based on the location information of S C city's stores and transit centers, as well as various data of distribution, respectively, the path optimization is carried out to ultimately achieve cost reduction and efficiency. Compared with the data of the original distribution method, both the use of transportation tools, distribution distance, and the problem of high empty rate have been improved.

Integrated Optimisation Model of Daily Freight Train Scheduling and Dynamic Railcar Routing Based on a Two-Layer Space-Time Network

This paper focuses on daily freight train scheduling and dynamic railcar routing problems for rail freight transportation at the operational level. Two mixed integer linear programming models that adopted different strategies were formulated based on a continuous two-layer time-space network. We simultaneously considered the benefits of railroad company and service quality when setting the objective function. By solving the models, we can distribute the dynamic railcar flows to the train paths in the basic train timetable to obtain the daily train operation plan over a short time horizon (e.g. a day), which will be helpful for dispatchers to make decisions such as the empty railcar distribution and car routing (trip planning). Finally, we compared two models on a part of the Chinese railroad network. The results show that the second model can effectively improve the efficiency of railroad freight transportation.

A hybrid ICEEMDAN and OMEDA-based vibrodiagnosis method for the bearing of rolling stock

Purpose. To develop a hybrid method based on ICEEMDAN and OMEDA for high-fidelity detection of the diagnostic features of the technical condition of roller bearing. Methodology. Due to digital signal processing the search was made of the informative components on the broadband spectra, envelope spectra, squared envelope spectra. The usage of the methods of mathematical statistics for the selection of informative IMFs as a result of iterative calculate procedures. The introduction of blind deconvolution method with a proper objective function for the enhancement of impulse fault features. Findings. The use of traditional spectral methods provided an incomplete list of diagnostic features of bearing roller damage. The empirical mode decomposition (EMD) method and its minor versions provide the series of intrinsic mode functions (IMFs). On the broadband vibration spectra of the selected low-frequency IMFs, diagnostic features were not detected in a sufficient number. Further research focused on the development of a hybrid method that takes into account the demodulation procedure of the high-frequency components of those IMFs that were selected according to the complex evaluation index. The Fast Kurtogram technique determined an informative frequency band of 7.2–7.5 kHz for demodulation and construction of the squared envelope spectra, where harmonics of the roller spin frequency and some side bands with a width equal to the separator rotation frequency appeared. The use of OMEDA caused the reduction of residual noise on the squared envelope spectra and bilateral sidebands to appear around all harmonics of the roller spin frequency. Originality. For the first time, the whole list of the diagnostic features of roller faults of the axle-box bearing was identified using the developed hybrid method, which involves steps of noise reduction for enhancing a physical meaning of a proper frequency components, associated with faults. The usage of the optimal minimum entropy deconvolution adjusted method helped to eliminate noise and provide all diagnostic features of the technical condition on the squared envelope spectrum. Practical value. The results of the study help to control the quality of repair of the axle-box rolling bearings on the test rig at the workshop of the freight railway car depot.

Towards Sustainable Production: An Adaptive Intelligent Optimization Genetic Algorithm for Solid Wood Panel Manufacturing

Optimizing production processes to conserve resources and reduce waste has become crucial in pursuing sustainable manufacturing practices. The solid wood panel industry, marked by substantial raw materials and energy consumption, stands at the forefront of addressing this challenge. This research delves into production scheduling and equipment utilization inefficiencies, offering innovative solutions for the solid wood panel processing line aimed at achieving environmental sustainability and operational efficiency. The study is articulated through two main segments: (1) an exhaustive analysis and the development of a simulation system for the solid wood panel processing line, delineating all production elements and operational logic, furnished with a user-friendly simulation interface, and (2) a comprehensive evaluation and enhancement of various scheduling algorithms specific to the Flexible Job-Shop Scheduling Problem (FJSP) encountered in solid wood panel workshops. A significant leap forward is made with the introduction of the Adaptive Intelligent Optimization Genetic Algorithm (AIOGA), an evolved version of the standard Genetic Algorithm (GA) engineered for optimal scheduling within the solid wood panel processing line. AIOGA incorporates advanced features such as encoding strategy, population initialization, objective function setting, selection strategy, crossover operation, and mutation operation, demonstrating the methodological depth of the study. We applied AIOGA in a designed FJSP, and AIOGA substantially reduced the maximum completion time to 90 min. It evidenced an improvement of 39.60% over the conventional GA, enhancing the equilibrium of the equipment workload across the system. This research presents a multifaceted strategy to address the scheduling complications inherent in solid wood panel production and highlights the extensive applicability of adaptive intelligent optimization in diverse industrial settings. This study establishes a new paradigm in manufacturing optimization, underlining the valuable integration of sustainability and efficiency in production methodologies.

Multi-strategy enhanced Marine Predators Algorithm with applications in engineering optimization and feature selection problems

This paper introduces a novel meta-heuristic optimization algorithm named Clustering Wavelet Opposition-based Marine Predators Algorithm (CWOMPA) to address some limitations present in the well-established Marine Predators Algorithm (MPA). CWOMPA incorporates three key strategies: a fuzzy clustering approach for escaping local optima, using wavelet basis function-based impact coefficient adjustment for elites to prevent premature convergence, and finally an adaptive opposition-based learning strategy for maintaining population diversity. Compared with some recent meta-heuristic algorithms, extensive evaluations conducted affirm that CWOMPA achieves the best Friedman rank, 4.30 and 1.95 respectively, on 23 benchmark functions and the CEC 2017 benchmark set. Not only does CWOMPA demonstrate significant effectiveness on six constrained problems from the CEC 2020 real-world benchmarks, but also when applied to 14 medical datasets, it gains superior Friedman ranks in terms of selected features, classification accuracy, F-Score, and objective function value, 2.5, 2.25, 2.96, 2.93 respectively, outperforming other common methods. Finally, CWOMPA exhibits the highest classification accuracy across all datasets and the best F-Score performance in nine datasets compared to traditional feature selection algorithms. The obtained results reveal that CWOMPA is a powerful and versatile optimization algorithm with significant potential in various real-world applications, including feature selection for medical datasets.

Maintenance and transformation method for a multi-AUV dense formation

Accurate formation maintenance and safe formation transformations are significant challenges for multiple autonomous underwater vehicle (multi-AUV) dense formations. To address these problems, an innovative control method for a multi-AUV dense formation is proposed. First, a model predictive controller (MPC) that considers AUV input constraints and external disturbances is designed such that a multi-AUV dense formation can accurately maintain a desired formation while tracking a reference trajectory. After that, at the kinematics level, an optimal path for a safe and efficient multi-AUV dense formation transformation is generated based on the Hungarian method. Furthermore, considering an underactuated and nonlinear AUV dynamics model at the dynamics level, a potential function based on collision avoidance is established. It is added to the MPC objective function to further guarantee the potential of the formation transformation. Finally, a multi-AUV dense formation maintenance simulation shows that the proposed method can guarantee higher trajectory tracking accuracy than other algorithms. A multi-AUV dense formation transformation simulation shows that the proposed method avoids the occurrence of cross paths and a safe distance between AUVs is always maintained. The above results demonstrate that multi-AUV dense formations can achieve accurate maintenance and safe transformations, and the proposed method is feasible and effective.

공액경사법을 이용한 LPG 운반선 화물창 내부구조물 중량최소화 설계

Since the cargo tank of LPG carriers is made of expensive low-temperature steel that can maintain its function even at -50oC, the reduction of cargo tank materials has been a major concern for shipyards to improve price competitiveness. The purpose of this study is to minimize the weight of the web frames and stringers that form the interior of the cargo tank of the LPG carriers. A total of 92 design variables including 6 shape-related design variables were selected for the minimum weight design. In order to reduce the time required for the optimization process, the conjugate gradient method, which is a gradient-based optimization technique, was adopted. In addition, for the structural analysis, the cargo tank located at the second position in the bow was selected as the structural analysis target, and in order to improve the reliability of the analysis, a boundary condition considering the deformation of the entire ship for each loading condition was applied to the partial model. As a result of the study, it was confirmed that the error rate did not exceed the maximum 3% by comparing the maximum stress value generated in all internal structures for the entire model structure analysis and the partial model one. A total of 92 dimensions with the minimum objective function were determined, and the weight was reduced by about 39 tons per cargo tank.

Marine shaft optimization using surrogate models and multi-objective optimization

This paper aims to obtain an application software using Ansys software in which a static, dynamic, and modal analysis for the power transmission of ships is presented. The objective functions of this research are maximum static stress, maximum dynamic stress, shaft mass, and modal shaft frequency analysis. A complete, comprehensive, and generalizable model for metal shaft types is presented. Then, using the kriging response surface and multi-objective genetic algorithm (NSGA II), these goals are optimized simultaneously. In this research, the optimization parameters are geometric parameters of the shaft design, including the position of the supports and the inner and outer diameters of the shaft. As a result of this optimization, the shaft's maximum static and dynamic stresses are reduced by 36% and 42%, respectively. The shaft's mass, which is one of the most critical factors during the shaft and its vibrations, is reduced by about 9%. In this regard, the first natural frequency of the optimized shaft increased by about 28.5% compared to the initial shaft.

Dual Response Surface Optimization based on Skill Scores

The popular formulations of dual-response optimization are constructed on minimizing a function of bias and system variability. This study provides an opportunity to evaluate the dual response surface (DRS) problem from a different perspective by adapting two new terms such that internal and external quality forecasts. The background of the proposed approach focuses on the relationship between internal and external quality forecasts and discusses the DRS problem in regards of skill scores by defining a model quality criterion. Skill is the relative accuracy of the forecast and defines a correspondence between forecast of interest and reference forecasts. The reference forecast does not require any knowledge or modelling; thus, it is an unskilled forecast. In this context, skill score is a measure of this relative improvement and widely used in evaluating the performance of operational and experimental forecasts. An alternative version of mean square error (MSE) which is reconstructed by skill scores and model quality criterion is proposed as an objective function for the DRS problem. Integrating the relationship between internal and external quality forecasts into such a response function can improve the effectiveness and cooperation of the applied technique. The proposed approach has a flexible structure and provides decision makers alternative solutions for different values of the model quality criterion. The proposed procedure is discussed by conducted a simulation study and demonstrated in an engineering process.

A Method for State of Charge and State of Health Estimation of LithiumBatteries Based on an Adaptive Weighting Unscented Kalman Filter

This paper considers the estimation of SOC and SOH for lithium batteries using multi-innovation Levenberg–Marquardt and adaptive weighting unscented Kalman filter algorithms. For parameter identification, the second-order derivative of the objective function to optimize the traditional gradient descent algorithm is used. For SOC estimation, an adaptive weighting unscented Kalman filter algorithm is proposed to deal with the nonlinear update problem of the mean and covariance, which can substantially improve the estimation accuracy of the internal state of the lithium battery. Compared with fixed weights in the traditional unscented Kalman filtering algorithm, this algorithm adaptively adjusts the weights according to the state and measured values to improve the state estimation update accuracy. Finally, according to simulations, the errors of this algorithm are all lower than 1.63 %, which confirms the effectiveness of this algorithm.

Multilingual Information Retrieval Using Graph Neural Networks: Practical Applications in English Translation

Multilingual information retrieval using graph neural networks offers practical applications in English translation by leveraging advanced computational models to enhance the efficiency and accuracy of cross-lingual search and translation tasks. By representing textual data as graphs and utilizing graph neural networks (GNNs), this approach captures intricate relationships between words and phrases across different languages, enabling more effective language understanding and translation. GNNs can learn complex linguistic structures and semantic similarities from multilingual corpora, facilitating the development of more robust translation systems that are capable of handling diverse language pairs and domains. The paper introduces a novel approach termed the Multilingual Ant Bee Optimization Graph Neural Network (MABO-GNN) for addressing optimization, classification, and multilingual translation tasks. MABO-GNN integrates ant bee optimization algorithms with graph neural networks to provide a versatile framework capable of optimizing objective functions, improving classification accuracy iteratively, and facilitating high-quality translations across multiple languages. Through comprehensive experimentation, the efficacy of MABO-GNN is demonstrated across various tasks, languages, and datasets. in optimization experiments, MABO-GNN achieves objective function values of 0.012, 0.015, 0.011, and 0.013 in Experiment 1, Experiment 2, Experiment 3, and Experiment 4, respectively, with convergence times ranging from 90 to 150 seconds. In classification tasks, the model exhibits notable performance improvements over iterations, with BLEU scores reaching 0.84 and METEOR scores reaching 0.78 in the fifth iteration. The translation results showcase BLEU scores of 0.85 for English, 0.82 for French, 0.79 for German, 0.81 for Spanish, and 0.75 for Chinese, indicating the model's proficiency in generating high-quality translations across diverse languages.

Maximisation the autonomous flight performance of unmanned helicopter using BSO algorithm

Abstract The usage areas of rotary or fixed wing unmanned aerial vehicles (UAV) have become very widespread with technological developments. For this reason, UAV designs differ in terms of aerodynamic design, flight performance and endurance depending on the intended use. In this study, maximising of the autonomous flight performance of the unmanned helicopter produced at Erciyes University using an optimisation algorithm is discussed. For this purpose, the input parameters of the dynamic model are chosen as blade length, blade mass density, blade chord width and blade twist angle of the unmanned helicopter and the proportional, integral, derivative gain coefficients of the lateral axis of the autopilot. The output parameters of the dynamic model are selected as settling time, rise time and maximum overshoot, which are autonomous performance parameters. The dynamic model consisting of helicopter and autopilot parameters is integrated into the back-tracking search optimisation (BSO) algorithm as an objective function. In the optimization process, where mean squared error (MSE) is used as the performance criterion, optimum input and output values were determined. Thus, helicopter and autopilot parameters, which are among the factors affecting autonomous performance, are taken into account with equal importance and simultaneously. Simulations show that the obtained values are satisfactory. With this approach based on the optimisation method, complex and time-consuming dynamic model calculations are reduced, time and cost are saved, and practicality is achieved in applications. Therefore, this approach can be an innovative and alternative method to improve UAV designs and increase flight performance compared to classical methods.

Improving performance in swarm robots using multi-objective optimization

This paper presents a localization task for a robot swarm guided by the RAOI behavioral rules (repulsion, attraction, orientation, and influence). Slight changes in these parameters can significantly affect the task’s performance. To address this challenge, we have developed a swarm simulator incorporating the robots’ dynamic model. The localization task is evaluated using objective functions, represented as metrics, which are minimized using multi-objective optimization techniques. Our results showcase the Pareto fronts, illustrating how the objective functions react to variations in the RAOI parameters, aiming to expedite target localization while maintaining the swarm’s integrity.

Optimization model for multibeam sounding line deployment based on genetic algorithm

Multibeam sounding technology is a cutting-edge method used for measuring underwater topography, widely applied across various fields. The actual seafloor terrain often exhibits significant fluctuations, leading to challenges such as insufficient coverage in shallow areas and excessive overlap in deep-water zones, resulting in inefficient operations. Rational selection of line spacing helps improve measurement efficiency and ensures data integrity. In this paper, taking the 2023 National College Student Mathematical Modeling Competition Problem B as a background, we conduct a thorough analysis of the variation patterns of the coverage width of multibeam sounding strips with respect to various parameters. We establish models for ocean depth and coverage width, determining how the strip coverage width changes with distance and the angle between survey lines in different scenarios. Finally, employing genetic algorithms and differential methods, we identify decision variables, objective functions, and constraints to formulate a nonlinear programming model. Through iterative searches, we obtain an optimal sounding line deployment plan that maximizes coverage of the target sea area while keeping the overlap rate below 20%. The calculated missed measurement error is approximately 32.774%, and the overlap rate is around 10.477%, indicating a high level of model accuracy.

Construction of a Cutting-Tool Wear Prediction Model through Ensemble Learning

This study begins by conducting side milling experiments on SKD11 using tungsten carbide TiAlN-coated end mills to compare the surface roughness performance between two combinations of milling process parameters (feed rate and radial depth of cut), along with three ultrasonic-assisted methods (rotary, dual-axis, and rotary combined with dual-axis). The results suggest that the rotary (z-axis oscillation) ultrasonic-assisted method may provide better performance. Subsequently, this superior ultrasonic-assisted method was applied both with and without laser locally preheating assistance, respectively. Using a Taguchi orthogonal array, milling process parameters (spindle speed, feed rate, and radial depth of cut) were planned for experiments with the same cutting tool and the workpiece just mentioned above. The surface roughness serves as the objective function while being constrained by cutting-tool life. The characteristics of the smaller-the-better in the Taguchi method were applied to determine the optimal combination of process parameters. Based on the optimal milling process parameters obtained and the superior hybrid-assisted method adopted, milling experiments were repeatedly performed to collect the data on cutting force and cutting-tool wear. Feature engineering was performed on the cutting force signals, and different domain characteristics from both the time and frequency domains were extracted. Hereafter, feature selection by random forest and data standardization were further applied to feature extractions, and the data processing was thus completed. For the processed data, a cutting-tool wear prediction model was constructed by ensemble learning. This method leverages various machine learning regression models, including decision tree, random forest, extremely randomized tree, light gradient boosting machine, extreme gradient boosting, AdaBoost, stochastic gradient descent, support vector regression, linear support vector regression, and multilayer perceptron. After hyper-parameter tuning, the ensemble voting regression prediction was performed based on these ten mentioned models. The experimental results demonstrate that the ensemble voting regression model surpasses the performance of each individual machine learning regression model. In addition, this regression model achieves a coefficient of determination (R2) of 0.94576, a root mean square error (RMSE) of 0.24348, a mean squared error (MSE) of 0.05928, and a mean absolute error (MAE) of 0.18182. Therefore, the ensemble learning approach has been proven to be a feasible and effective method for monitoring cutting-tool wear.

Feature Extraction and Classification of Power Quality Disturbances Using Optimized Tunable-Q Wavelet Transform and Incremental Support Vector Machine

The widespread integration of renewable energy sources (RESs) into power systems using power electronics-based interface devices has led to a substantial rise in power quality (PQ) issues. There is an immediate requirement for effective monitoring, detection, and classification of power quality disturbances (PQDs) that is needed to take remedial measures and design planning of the system architecture. This study presents a hybrid approach with an objective for the feature extraction and classification of PQDs. The proposed hybrid approach is comprised of an optimized tunable-Q wavelet transform (OTQWT) for the feature extraction and incremental support vector machine (ISVM). A four-stage approach is suggested for the PQ detection and classification in this study. In the first stage, the various data are retrieved both in the form of synthetic data by mathematical formulations and real-time data with prototype design setup. In the second stage, regardless of the specified wavelet function, the PQD signals are decomposed into low-pass and high-pass sub-bands using the tunable-Q wavelet transform (TQWT). However, the utilization of default decomposition parameters to address nonstationary PQ signals may lead to information loss and reduced performance of the system. To avoid this limitation, an OTQWT as an enhanced technique to TQWT based on an Adaptive Particle Swarm Optimization (APSO) is suggested. A modified objective function based on the mean square error (MSE) is used to improve the decomposition process. In the third stage, an efficient classifier is suggested based on the ISVM. Lastly, to test and evaluate the performance of the proposed approach, twelve types of PQDs including noise and multiple occurrences are considered. The comparative analysis with other popular methods reflects the better performance of the proposed approach and justifies its use for PQ detection and classification purposes in real-time​ conditions.

Control co-design optimization of floating offshore wind turbines with tuned liquid multi-column dampers

Abstract. The technical progress in the development and industrialization of floating offshore wind turbines (FOWTs) over the past decade has been significant. Yet, the higher levelized cost of energy (LCOE) of FOWTs compared to onshore wind turbines is still limiting the market share. One of the reasons for this is the larger motions and loads caused by the rough environmental excitations. Many prototype projects tend to employ more conservative substructure designs to meet the requirements for motion dynamics and structural safety. Another challenge lies in the multidisciplinary nature of a FOWT system, which consists of several strongly coupled subsystems. If these subsystems cannot work in synergy, the overall system performance may not be optimized. Previous research has shown that a well-designed blade pitch controller is able to reduce the motions and structural loads of FOWTs. Nevertheless, due to the negative aerodynamic damping effect, improvement in the performance by tuning the controller is limited. One of the solutions is adding tuned liquid multi-column dampers (TLMCDs), meaning that there is a structural solution to mitigate this limiting factor for the controller performance. It has been found that the additional damping, provided by TLMCDs, is able to improve the platform pitch stability, which allows a larger blade pitch controller bandwidth and thus a better dynamic response. However, if a TLMCD is not designed with the whole FOWT system dynamics taken into account, it may even deteriorate the overall performance. Essentially, an integrated optimization of these subsystems is needed. For this paper, we develop a control co-design optimization framework for FOWTs installed with TLMCDs. Using the multi-objective optimizer non-dominated sorting genetic algorithm II (NSGA-II), the objective is to optimize the platform, the blade pitch controller, and the TLMCD simultaneously. Five free variables characterizing these subsystems are selected, and the objective function includes the FOWT's volume of displaced water (displacement) and several motion and load indicators. Instead of searching for a unique optimal design, an optimal Pareto surface of the defined objectives is determined. It has been found that the optimization is able to improve the dynamic performance of the FOWT, which is quantified by motions and loads, when the displacement remains similar. On the other hand, if motions and loads are constant, the displacement of the FOWT can be reduced, which is an important indication of lower manufacturing, transportation, and installation costs. In conclusion, this work demonstrates the potential of advanced technologies such as TLMCDs to advance FOWTs for commercial competitiveness.

Automatic generation method for long-focal-length unobscured freeform optical systems with small volume

The existing design methods for long-focal-length unobscured freeform systems rarely consider the imaging quality requirements and volume constraints simultaneously, causing most of the final designs to not fulfill the requirement of light weight. This study proposes a method to automatically design a long-focal-length unobscured reflective system that satisfies volume constraints while maintaining high imaging quality. First, a method to adaptively set the structural parameter range is proposed, and multiple parameters for different systemic specifications can be effectively calculated within it. Subsequently, the systemic volume and area functions are constructed using the ray tracing method, where the tilt angles, distances between mirrors, and radii of curvature of the mirrors are chosen as the optimization parameters. Third, a comprehensive objective function is jointly established combining ray obscuration and convergence as performance evaluation factors. Then, the structural parameters of a long-focal-length unobscured system with small volume are easily obtained via the simulated annealing method. Finally, the improved W-W method is used to further enhance the imaging quality of the system, and an unobscured freeform reflective optical system with three mirrors is automatically generated. Experimental results demonstrate that our method can automatically calculate the parameter ranges to facilitate the search for structural parameters, and effectively design the long-focal-length unobscured freeform systems with small volume and high imaging quality.

A globally convergent SQP-type method with least constraint violation for nonlinear semidefinite programming

A globally convergent SQP-type method with least constraint violation for nonlinear semidefinite programming

Using Genetic Algorithms and Core Values of Cooperative Games to Solve Fuzzy Multiobjective Optimization Problems

A new methodology for solving the fuzzy multiobjective optimization problems is proposed in this paper by considering the fusion of cooperative game theory and genetic algorithm. The original fuzzy multiobjective optimization problem needs to be transformed into a scalar optimization problem, which is a conventional optimization problem. Usually, the assignments of suitable coefficients to the corresponding scalar optimization problem are subjectively determined by the decision makers. However, these assignments may cause some biases by their subjectivity. Therefore, this paper proposes a mechanical procedure to avoid this subjective biases. We are going to formulate a cooperative game using the α-level functions of the multiple fuzzy objective functions. Under this setting, the suitable coefficients can be determined mechanically by involving the core values of the cooperative game, which is formulated using the multiple fuzzy objective functions. We shall prove that the optimal solutions of the transformed scalar optimization problem are indeed the nondominated solutions of fuzzy multiobjective optimization problem. Since the core-nondominated solutions will depend on the coefficients that are determined by the core values of cooperative game, there will be a lot of core-nondominated solutions that will also depend on the corresponding coefficients. In order to obtain the best core-nondominated solution, we shall invoke the genetic algorithms by evolving the coefficients.