Single-objective Optimization Algorithms Research Articles

Advancements in Optimization: Critical Analysis of Evolutionary, Swarm, and Behavior-Based Algorithms

The research work on optimization has witnessed significant growth in the past few years, particularly within multi- and single-objective optimization algorithm areas. This study provides a comprehensive overview and critical evaluation of a wide range of optimization algorithms from conventional methods to innovative metaheuristic techniques. The methods used for analysis include bibliometric analysis, keyword analysis, and content analysis, focusing on studies from the period 2000–2023. Databases such as IEEE Xplore, SpringerLink, and ScienceDirect were extensively utilized. Our analysis reveals that while traditional algorithms like evolutionary optimization (EO) and particle swarm optimization (PSO) remain popular, newer methods like the fitness-dependent optimizer (FDO) and learner performance-based behavior (LPBB) are gaining attraction due to their adaptability and efficiency. The main conclusion emphasizes the importance of algorithmic diversity, benchmarking standards, and performance evaluation metrics, highlighting future research paths including the exploration of hybrid algorithms, use of domain-specific knowledge, and addressing scalability issues in multi-objective optimization.

Filter Cake Neural-Objective Data Modeling and Image Optimization

Designing drilling mud rheology is a complex task, particularly when it comes to preventing filter cakes from obstructing formation pores and making sure they can be easily decomposed using breakers. Incorporating both multiphysics and data-driven numerical simulations into the design of mud rheology experiments creates an additional challenge due to their symmetrical integration. In this computational intelligence study, we introduced numerical validation techniques using 498 available datasets from mud rheology and images from filter cakes. The goal was to symmetrically predict flow, maximize filtration volume, monitor void spaces, and evaluate formation damage occurrences. A neural-objective and image optimization approach to drilling mud rheology automation was employed using an artificial neural network feedforward (ANN-FF) function, a non-ANN-FF function, an image processing tool, and an objective optimization tool. These methods utilized the Google TensorFlow Sequential API-DNN architecture, MATLAB-nftool, the MATLAB-image processing tool, and a single-objective optimization algorithm. However, the analysis emanating from the ANN-FF and non-ANN-FF (with neurons of 10, 12, and 18) indicated that, unlike non-ANN-FF, ANN-FF obtained the highest correlation coefficient of 0.96–0.99. Also, the analysis of SBM and OBM image processing revealed a total void area of 1790 M µm2 and 1739 M µm2, respectively. Both SBM and OBM exhibited notable porosity and permeability that contributed to the enhancement of the flow index. Nonetheless, this study did reveal that the experimental-informed single objective analysis impeded the filtration volume; hence, it demonstrated potential formation damage. It is, therefore, consistent to note that automating flow predictions from mud rheology and filter cakes present an alternative intelligence method for non-programmers to optimize drilling productive time.

Surge arrester optimal placement in distribution networks: A decision theory-based approach

The study introduces a novel method for optimizing surge arrester placement in the distribution line to mitigate lightning-induced overvoltages, employing a single-objective optimization algorithm. The study assesses the effectiveness of two types of surge arresters concerning discharge energy in reducing lightning overvoltage. Moreover, the comparative analysis takes into account the transfer of overvoltage performance from protected to unprotected towers, highlighting its significance in estimating flashover rates under different protection alternatives. Decision theory analysis is employed in the present study to identify optimal arrester locations. The study aims to minimize the expected flashover rate and identify the most effective protection strategy by considering futures/scenarios associated with different values of peak current and lightning locations. The results of numerical applications also showed the substantial impact of lightning surge transfer within the network, emphasizing the imperative to incorporate this phenomenon into lightning protection modelling.

Non-dominated sorting artificial rabbit multi-objective sizing optimization for a conceptual powertrain of a 6 × 4 battery electric tractor truck

In order to tackle the increasingly severe energy crisis, improving the efficiency of the powertrain system in battery electric vehicles has become an effective approach. Based on a 6 × 4 battery electric tractor truck (BETT), the paper focuses on enhancing the dynamic and economic performance of vehicles through advancements in configuration, control strategies, and parameter design. Firstly, a novel multi-motor torque coupling powertrain system based on the parallel-axle transmission is proposed and modeled. Then, an instantaneous minimum energy consumption control strategy for the economic performance simulation and an instantaneous maximum acceleration control strategy for the dynamic performance simulation are designed. Furthermore, a conventional heuristic single-objective optimization algorithm, artificial rabbit optimization (ARO), is improved into a multi-objectives version, non-dominated sorting artificial rabbit multi-objective optimization (NSARMO), by combining the fast non-dominated sorting (FNS) and modifying the calculation method of the energy factor. Finally, an optimization framework consisting of a control layer, model layer, and optimization layer is established and applied to the parameter optimization of the proposed powertrain system. Simulation results demonstrate that the optimization results of the proposed method are superior to those optimized by commonly used non-dominated sorting genetic algorithm-II (NSGA-II) and NSARMO without the modified energy factor, achieving a better balance between dynamic performance and economic performance. Moreover, the proposed method exhibits demonstrates 40.67% and 24.67% improvement in its ability to search for optimal Pareto solutions compared to NSARMO (-)(- means the calculation method of energy factor is not modified) and NSGA-II. At last, a hardware-in-the-loop (HIL) experiment bench is established, and the experiment results indicate that a scheme optimized by the proposed NSARMO exhibits only an approximate performance in energy consumption in the HIL environment compared to the simulation environment, which signifies the effectiveness of control strategy equipped with the optimization results optimized by the proposed method.

A Multi-Objective Pigeon-Inspired Optimization Algorithm for Community Detection in Complex Networks

Community structure is a very interesting attribute and feature in complex networks, which has attracted scholars’ attention and research on community detection. Many single-objective optimization algorithms have been migrated and modified to serve community detection problems. Due to the limitation of resolution, the final algorithm implementation effect is not ideal. In this paper, a multi-objective community detection method based on a pigeon-inspired optimization algorithm, MOPIO-Net, is proposed. Firstly, the PIO algorithm is discretized in terms of the solution space representation, position, and velocity-updating strategies to adapt to discrete community detection scenarios. Secondly, by minimizing the two objective functions of community score and community fitness at the same time, the community structure with a tight interior and sparse exterior is obtained. Finally, for the misclassification caused by boundary nodes, a mutation strategy is added to improve the accuracy of the final community recognition. Experiments on synthetic and real networks verify that the proposed algorithm is more accurate in community recognition compared to 11 benchmark algorithms, confirming the effectiveness of the proposed method.

A Bi-level optimization dispatch for hybrid shipboard microgrid considering electricity-gas-heat coupling

With the increasingly severe problem of air pollution and energy crisis, new energy power generation technology in ship has quickly become the focus of attention. Compared with traditional ships, hybrid shipboard microgrid systems can achieve pollution-free, renewable and high use value. However, the integration of electricity-gas-heat in hybrid energy shipboard microgrid system also poses challenges to current optimization methods. Therefore, this paper develops a bi-level optimization dispatch model for hybrid shipboard microgrid system based on multi-objective particle swarm optimization algorithm. Taking the diesel generators, photovoltaic generation system, energy storage system (ESS) and thermal energy storage equipment into account, a hybrid shipboard microgrid system model considering electricity-gas-heat coupling is constructed. Based on this, a bi-level optimization dispatch model is established to reduce total cost, GHG (GHG) emissions and lifespan loss of ESS. The upper-level model achieves the optimization dispatch of power generation equipment and loads; a lower-level optimization model with the goal of reducing the lifespan loss of ESS is constructed. The improved multi-objective and single-objective particle swarm optimization algorithms are introduced to find the optimal dispatch solutions for bi-level optimization dispatch model. Finally, simulation results show that the proposed optimization method can not only reduce the cost and GHG emissions by 8.7% and 10.9%, but also improve the cycle life of ESS by 9.2%.

An adaptative differential evolution with enhanced diversity and restart mechanism

Differential Evolution (DE) stands out as an exceptional intelligent evolutionary algorithm, acclaimed for its simplicity in implementation and the ability to optimize without necessitating differentiable conditions. However, a significant pitfall of DE lies in its susceptibility to getting trapped in local minima, leading to algorithmic stagnation and substantial performance impairments. To counteract the shortcoming, the Adaptative Differential Evolution with Diversity Maintenance and Restart Mechanism (ADE-DMRM) is proposed. This approach integrates three primary innovations. Firstly, the algorithm controls the number of generations that individuals stay in the external archive based on the successful evolution rate, thereby optimizing the mutation strategy to effectively maintain population diversity. Secondly, ADE-DMRM proposes a novel restart mechanism in which the current stagnant individuals are identified by combining a stagnation tracker and a diversity assessment indicator and then regenerated using a dimension-learning-based approach. Thirdly, wavelet basis functions and Cauchy distributions are employed for scaling factor implementation across different stages, while the dimension change information of successfully evolved individuals is harnessed to refine the adaptive parameter control scheme. Finally, comprehensive experiments were undertaken on the CEC2013, CEC2014, and CEC2017 test sets, assessing accuracy, convergence speed, the efficacy of each module, and time complexity. The results confirm that ADE-DMRM is an efficient single-objective optimization algorithm that outperforms current advanced variants.

Large-scale evolutionary optimization: A review and comparative study

Large-scale global optimization (LSGO) problems have widely appeared in various real-world applications. However, their inherent complexity, coupled with the curse of dimensionality, makes them challenging to solve. Continuous efforts have been devoted to designing computational intelligence-based approaches to solve them. This paper offers a comprehensive review of the latest developments in the field, focusing on the advances in both single-objective and multi-objective large-scale evolutionary optimization algorithms over the past five years. We systematically categorize these algorithms, discuss their distinct features, and highlight benchmark test suites essential for performance evaluation. After that, comparative studies are conducted using numerical solutions to evaluate the performance of state-of-the-art LSGO for both single-objective and multi-objective problems. Finally, we discuss the real-world applications of LSGO, some challenges, and possible future research directions.

Research on vegetable sales decision-making based on single-objective nonlinear optimization and genetic algorithm

Research on vegetable sales decision-making based on single-objective nonlinear optimization and genetic algorithm

Coarse and Fine Two-Stage Calibration Method for Enhancing the Accuracy of Inverse Finite Element Method.

The inverse finite element method (iFEM) is a novel method for reconstructing the full-field displacement of structures by discrete measurement strain. In practical engineering applications, the accuracy of iFEM is reduced due to the positional offset of strain sensors during installation and errors in structural installation. Therefore, a coarse and fine two-stage calibration (CFTSC) method is proposed to enhance the accuracy of the reconstruction of structures. Firstly, the coarse calibration is based on a single-objective particle swarm optimization algorithm (SOPSO) to optimize the displacement-strain transformation matrix related to the sensor position. Secondly, as selecting different training data can affect the training effect of self-constructed fuzzy networks (SCFN), this paper proposes to screen the appropriate training data based on residual analysis. Finally, the experiments of the wing-integrated antenna structure verify the efficiency of the method on the reconstruction accuracy of the structural body displacement field.

Application research of combined model based on VMD and MOHHO in precipitable water vapor Prediction

The change characteristics of precipitable water vapor (PWV) are closely related to the timing of artificial rainfall enhancement operations, and accurate prediction of PWV changes is of great practical significance. The instability and nonlinearity of PWV are the difficulties in its accurate prediction. However, most of the current PWV prediction models are individual models and simple hybrid models, without considering the limitations of a individual prediction model, efficient data preprocessing strategies, and weight optimization. At the same time, the research on the application of PWV prediction in artificial rainfall enhancement operations also needs to be strengthened., therefore, this paper proposes a new combination forecasting system, which is effectively applied to solve the problem of PWV forecasting, and analyzes the job timing with the forecasted value. The system consists of variational mode decomposition (VMD), multi-objective Harris hawks optimization (MOHHO) and six different types of individual prediction algorithms. Among them, VMD can accurately separate the noise sequence and the main feature sequence of the original PWV sequence. MOHHO overcomes the shortcoming that the single-objective optimization algorithm can only achieve one criterion, and it can optimize the accuracy and stability at the same time. Autoregressive integrated moving average (Arima) and Exponential smoothing (ES), as representatives of statistical models, are responsible for predicting the linear trend of PWV, while Back Propagation neural network (BP), Radial Basis Function neural network(RBF), Long Short Term Memory(LSTM) and Temporal Convolutional Network(TCN), as representatives of neural networks, are responsible for capturing the nonlinear characteristics of PWV. Through experiments and analysis, compared with the individual model such as Arima, BP and LSTM, the prediction accuracy of the proposed combined model is improved significantly in all prediction steps. The PWV threshold and the PWV hourly slope threshold can be used as indicators for the timing selection of artificial rainfall enhancement operations. Using the proposed combined model to predict PWV in precipitation events can accurately obtain the timing of the reflection index, which can provide technical reference for artificial rainfall enhancement operations.

Multi-objective particle swarm optimization for multimode surface wave analysis

Obtaining S-wave velocity profiles by inverting Rayleigh wave dispersion curves is crucial for the Rayleigh wave exploration method. Rayleigh wave inversion is a highly nonlinear and multi-extremum problem; therefore, global optimization algorithms are superior to local optimization methods for this inversion problem. Higher modes of dispersion curves have deeper penetration, which can improve the inversion quality. This study utilizes the multi-objective particle swarm optimization (MOPSO) algorithm, rather than a traditional single-objective optimization algorithm, to obtain S-velocity profiles from Rayleigh wave multimode phase velocity dispersion curves. The uncertainty of the inversion parameters is evaluated through the morphology of the Pareto front and the standard deviation of the Pareto optimal solution set. This is the first application of MOPSO in solving the multimode Rayleigh wave phase velocity dispersion curves joint inversion problem. It inverts three synthetic datasets, compares the inversion results with the synthetic data, and then conducts a comparative analysis with the particle swarm optimization (PSO) algorithm and the multi-objective grey wolf optimization (MOGWO) algorithm in one of these synthetic models to evaluate the accuracy and stability of MOPSO to the joint inversion. In addition, this research inverts observed data from an expressway roadbed in Henan, China, to examine the applicability of MOPSO for the joint inversion of multimode dispersion curves. The MOPSO inversion closely yields S-wave velocity profiles that match the borehole data. The synthetic and observed data inversion results indicated that the MOPSO algorithm accurately inverts multimode dispersion curves.

Evaluation on Software Performance Optimization Based on Multi-objective Optimization Algorithms

The tasks undertaken by software in various tasks include precise positioning of computational targets, utilization of hardware resources, and so on. Therefore, updating software performance is an essential and important step. However, currently, software iteration in computers is not smooth sailing. Therefore, this article aimed to study the problem of software performance optimization through the direction of objective optimization algorithms. This article used the method of evaluating parameter optimization results to conclude that multi-objective optimization algorithms have stronger computational power in models in other fields. The optimization results of the target software are statistically analyzed through web log mining, and the Chebyshev method is also used to decompose one of the classic multi-objective algorithms, MOEA/D. Finally, the optimization approach was divided into two types: multi-objective optimization algorithm and single objective optimization algorithm. Two other computers with identical configurations were selected to use these two algorithms for experiments. The multi-objective optimization algorithm was set as the experimental group, while the single objective optimization algorithm was set as the control group. After performing several software optimization operations, the results showed that the software performance optimization operation based on the multi-objective optimization algorithm improved the software running speed much higher than the control group executing the single objective optimization algorithm. The final conclusion is that in the research of software performance optimization, MOEA/D in multi-objective optimization algorithms not only defeats single objective optimization algorithms, but also is a highly efficient means in itself.

A multitask optimization algorithm based on elite individual transfer.

Evolutionary multitasking algorithms aim to solve several optimization tasks simultaneously, and they can improve the efficiency of various tasks evolution through the knowledge transfer between different optimization tasks. Evolutionary multitasking algorithms have been applied to various applications and achieved certain results. However, how to transfer knowledge between tasks is still a problem worthy of research. Aiming to improve the positive transfer between tasks and reduce the negative transfer, we propose a single-objective multitask optimization algorithm based on elite individual transfer, namely MSOET. In this paper, whether to execute knowledge transfer between tasks depends on a certain probability. Meanwhile, in order to enhance the effectiveness and the global search ability of the algorithm, the current population and the elite individual in the transfer population are further utilized as the learning sources to construct a Gaussian distribution model, and the offspring is generated by the Gaussian distribution model to achieve knowledge transfer between tasks. We compared the proposed MSOET with ten multitask optimization algorithms, and the experimental results verify the algorithm's excellent performance and strong robustness.

An Environmentally Sustainable Software-Defined Networking Data Dissemination Method for Mixed Traffic Flows in RSU Clouds with Energy Restriction.

The connected multi road side unit (RSU) environment can be envisioned as the RSU cloud. In this paper, the Software-Defined Networking (SDN) framework is utilized to dynamically reconfigure the RSU clouds for the mixed traffic flows with energy restrictions, which are composed of five categories of vehicles with distinctive communication demands. An environmentally sustainable SDN data dissemination method for safer and greener transportation solutions is thus proposed, aiming to achieve the lowest overall SDN cloud delay with the least working hosts and minimum energy consumption, which is a mixed integer linear programming problem (MILP). To solve the problem, Joint optimization algorithms with Finite resources (JF) in three hyperparameters versions, JF (DW = 0.3, HW = 0.7), JF (DW = 0.5, HW = 0.5) and JF (DW = 0.7, HW = 0.3), were proposed, which are in contrast with single-objective optimization algorithms, the Host Optimization (H) algorithm, and the Delay optimization (D) algorithm. Results show that JF (DW = 0.3, HW = 0.7) and JF (DW = 0.5, HW = 0.5), when compared with the D algorithm, usually had slightly larger cloud delays, but fewer working hosts and energy consumptions, which has vital significance for enhancing energy efficiency and environmental protection, and shows the superiority of JFs over the D algorithm. Meanwhile, the H algorithm had the least working hosts and fewest energy consumptions under the same conditions, but completely ignored the explosive surge of delay, which is not desirable for most cases of the SDN RSU cloud. Further analysis showed that the larger the network topology of the SDN cloud, the harder it was to find a feasible network configuration. Therefore, when designing an environmentally sustainable SDN RSU cloud for the greener future mobility of intelligent transportation systems, its size should be limited or partitioned into a relatively small topology.

Volatility index prediction based on a hybrid deep learning system with multi-objective optimization and mode decomposition

Advances in volatility index prediction based on computational intelligence have brought wide-ranging benefits to financial risk management. However, current studies in the field remain limited and need further improvement due to these research gaps: (1) ignoring the important role of probabilistic prediction in characterizing uncertainty risks; (2) relying on single-objective optimization algorithm to optimize prediction model, thereby ignoring the advantages of multi-objective optimization; (3) emphasizing nonlinear modeling, not considering both nonlinear and linear modeling simultaneously. Aiming to address these gaps, a novel multi-objective hybrid deep learning system, composed of a modified multi-objective optimizer, a clockwork recurrent neural network, and an improved mode decomposition method, is newly proposed to perform deterministic and probabilistic volatility index prediction. Concretely, the volatility index is decomposed into some modes using an advanced data decomposition method; further, the clockwork recurrent neural network is considered a prediction engine to model these modes, which has an excellent ability to model the long-term dependency for linear and nonlinear time series depending on its mechanism of temporal granularity, as compared to traditional recurrent neural networks; finally, the prediction results can be obtained by integrating the predictions from these modes, using the mode weights calculated by an improved multi-objective optimizer with the objectives of prediction accuracy and stability. To validate the performance of the proposed hybrid deep learning system, case studies and corresponding sensitivity and convergence analyses are carried out. From the perspective of the indicator mean absolute percentage error, the maximum improvements of our proposed system reach 67.50%, 75.82%, and 75.42% in Case I, Case II, and Case III, respectively, thus indicating its superiority and practical feasibility.

Multisite calibration of a semi-distributed hydrologic and thermal model in a large Canadian watershed

ABSTRACT This study compares single-site and multisite calibration methods with upscaled parameters for thermal modelling. Multisite calibration and parameter upscaling are novel for calibrating a hydrological–thermal model. To this end, model calibration and simulations are carried out using a semi-distributed hydrological–thermal model (CEQUEAU). First, a hydrological calibration is carried out. The same calibrated hydrological model outputs are used for all thermal calibrations. The covariance matrix adaptation evolution strategy (CMA-ES) single-objective optimization algorithm is applied to calibrate the thermal module using observed water temperatures at seven monitoring sites within the Nechako Watershed in British Columbia, Canada. Single-site calibration provided the best performance for individual sites, but these sets of parameters performed poorly when applied to the other sites. The multisite calibration and the upscaled methods perform adequately for all sites with overall Root Mean Square Error (RMSE)<2°C as an acceptable threshold. However, the multisite method resulted in the best performance metrics and shortest computing time.

Optimal Design of the Gating and Riser System for Complex Casting Using an Evolutionary Algorithm.

The gating and riser system design is essential for both quality and cost in large-scale casting and is expected to reach several objectives simultaneously. However, even with the help of commercial simulation software, the design of gating and riser systems is still the result of a long-term trial-and-error optimal process owing to the conflict between the objectives. Several evolutionary algorithms (EAs) have been reported to be helpful in the selection of the geometrical dimensions of gating and riser systems. In this study, a route with sequential use of a multi-objective EA and single-objective optimization algorithm was developed to help design gating and riser systems, respectively. This route was applied in an actual case and verified using commercial simulation software. The results showed a dramatic decrease in the time cost in design and acceptable casting quality. Thus, the proposed design method is time-saving.

Evolutionary based Pareto optimization algorithms for bi-objective PV array reconfiguration under partial shading conditions

During the daily operation of photovoltaic array, it easily faces the partial shading conditions resulted from the cloud shadow, dropping dust, etc. It will directly cause a lifetime reduction and a generation efficiency decrement for the photovoltaic array. To weaken the negative influence of partial shading condition, one of the most favoured ways is the photovoltaic array reconfiguration. However, the conventional photovoltaic array reconfiguration only aims to maximize the power output, which did not consider the lifetime and control complexity of switching devices. To fill up this gap, this paper constructs a new bi-objective optimization of photovoltaic array reconfiguration, which attempts to simultaneously maximize the output power and minimize the switching number. Consequently, it can dramatically reduce the switching control complexity while improving the generation efficiency, while the operation life of the switching devices can be lengthened. In order to find a high-quality Pareto optimal reconfiguration schemes, six frequently-used evolutionary multi-objective optimization algorithms are employed to solve this bi-objective optimization. The effectiveness of bi-objective optimization of photovoltaic array reconfiguration is tested on three scales of total-cross-tied photovoltaic arrays under four partial shading patterns. The simulation results show that the maximum power increment by the proposed technique is up to 26.6% against to that without optimization, while the average switch number decrement is up to 31.1% compared with the single-objective optimization algorithms.

Design and optimization of two-degree-of-freedom parallel four pure-slide- and four parallel quadrilateral-pair precision positioning platform.

Aiming at the complex structure, small output displacement, and low positioning accuracy of the two-degree-of-freedom (2-DOF) precision positioning platform, theoretical analyses and experimental tests are carried out so that the platform has the characteristics of compact structure, large output stroke, and high positioning accuracy. First, to optimize the structural parameters of the positioning platform, a modeling method to improve the modeling accuracy of the compliant mechanism of the positioning platform is proposed. A static model of the positioning platform based on Euler-Bernoulli beam theory and the sixth-order compliance matrix method is established, and the accuracy of the model is verified by simulation. In addition, the single-objective genetic optimization algorithm is used to optimize the structural size parameters of the positioning platform, and the optimal solution set of the structural size parameters of the positioning platform is obtained by taking the displacement amplification rate of the positioning platform as the optimization target. Finally, according to theoretical and simulation analysis and optimization results, an experimental prototype was fabricated, and a series of experimental tests were carried out on the working stroke, displacement magnification, and output stiffness. The experimental results show that the displacement magnification of the positioning platform reaches 3.39, the positioning stroke is 89.2 × 85.9 µm2, and the displacement resolutions of the x-axis and y-axis are 35 and 31nm, respectively. The positioning platform designed in this paper meets the requirements of large output stroke and high positioning accuracy.