Premature Convergence Research Articles

An adaptive pyramid PSO for high-dimensional feature selection

Feature selection (FS) is an important data pre-processing method in machine learning tasks. However, FS becomes an NP-hard combinatorial optimization problem due to the huge search space of high-dimensional datasets and the complex interaction among features. As a simple implementation algorithm, particle swarm optimization (PSO) has been employed for dealing with FS problems. At the same time, it still suffers from issues such as the premature convergence and falling into local optimum. In this paper, an adaptive pyramid PSO (APPSO) is proposed for FS on dataset classification problems. In APPSO, a weighted initialization strategy based on correlation and the cubic chaotic map is employed to generate particles in the initial stage, aiming to improve the diversity of a population. Then, an adaptive constrained updating strategy, based on the pyramid structure, is proposed to enhance the exploration ability of the population. Moreover, a new dynamical flip strategy (DFS), which combines feature correlation and occurrence frequencies of features, is proposed to improve the exploitation ability of the population. The proposed APPSO is compared with 8 representative wrapper-based FS methods. Experimental results show that APPSO significantly outperforms these competitors on all 18 datasets.

Hybrid optimization algorithm based on chaos game and differential evolution for constrained optimization of structures

ABSTRACT A novel hybrid optimization algorithm, chaos game optimization–differential evolution (CGO-DE), is developed in this study for the size optimization of structures. The key contribution lies in the synergistic combination of chaos game optimization (CGO) and differential evolution (DE), using their respective strengths in exploration and exploitation to effectively identify global optima. The innovative approach independently applies CGO and DE to subpopulations, preventing premature convergence and enhancing overall performance while ensuring accuracy, accounting for design factors and respecting constraints. Comprehensive numerical evaluations on established structural benchmarks (three-bar truss, welded beam and cantilever beam) and large-scale structures (272-bar and 942-bar truss tower) demonstrate the versatility and efficiency of CGO-DE in solving complex optimization problems across various engineering applications. The results underscore the ability of the algorithm to achieve optimal solutions and improve designs compared to other optimization techniques, highlighting its potential as a powerful tool for engineering optimization.

Balancing individual and collective strategies: A new approach in metaheuristic optimization

Metaheuristic approaches commonly disregard the individual strategies of each agent within a population, focusing primarily on the collective best solution discovered so far. While this methodology can yield promising results, it also has several significant drawbacks, such as premature convergence. This study introduces a new metaheuristic approach that emphasizes the balance between individual and social learning in agents. In this approach, each agent employs two strategies: an individual search technique performed by the agent and a social or collective strategy involving the best-known solution. The search strategy is considered a learning problem, and agents must adjust the use of both individual and social strategies accordingly. The equilibrium of this adjustment is determined by a counter randomly set for each agent, which determines the frequency of use invested in each strategy. This mechanism promotes diverse search patterns and fosters a dynamic and adaptive process, potentially improving problem-solving efficiency in intricate spaces. The proposed method was assessed by comparing it with several well-established metaheuristic algorithms using 21 test functions. The results demonstrate that the new method surpasses popular metaheuristic algorithms by offering superior solutions and attaining quicker convergence.

Financial distress prediction using an improved particle swarm optimization wrapper feature selection method and tree boosting ensemble

Financial distress prediction (FDP) is a complex task involving both feature selection and model construction. While many studies have addressed these challenges individually, there is a lack of FDP models that integrate feature selection into the overall model building process. To address the issues of fast convergence and local optimization in particle swarm optimization (PSO), this study proposes a modified PSO algorithm with three improvement strategies. This improved PSO, known as IPSO, is embedded within state-of-the-art tree boosting ensemble models for feature selection. IPSO continuously evolves toward the optimal feature subset, preventing premature convergence and avoiding local optima. To construct the FDP model, four state-of-the-art tree boosting models are combined using an improved majority voting ensemble strategy. The integration of IPSO enhances the prediction performance of the model. Comparative experiments are conducted on samples of Chinese listed companies under short-term and long-term prediction scenarios to evaluate the proposed model. The results demonstrate that IPSO significantly improves the prediction performance, and the ensemble strategy enhances the robustness of the predictions.

An adaptive suspended-dome structure: Static control methods based on minimum strain energy

The suspended-dome structure is a rigid-flexible and pre-stressed space structure composed of grid shells, cable and struts. It is widely used in large-span space structures for its efficient mechanical properties. The emergence of adaptive structure enables the structure to change its shape and stiffness according to the change of external environment, realizing light weight, high efficiency and intelligence of the structure. The concept of adaptivity is introduced into the traditional suspended-dome structure, presenting an Adaptive Suspended-Dome Structure (ASDS) where actuators replace the struts. A static control method utilizing a multi-population gradient genetic algorithm based on a strain energy optimization control model is proposed and developed in terms of control model research, control algorithm theory, and control effects. Specifically, an ASDS control optimization model is established with the adjustment values of the actuators as control variables and the strain energy of the upper grid shell as the objective function. The multi-population gradient genetic algorithm is improved to overcome the premature convergence problem of traditional genetic algorithms, further enhancing the search speed. A numerical simulation of a suspended-dome structure model with a span of 12 m, an aspect ratio of 10, and equipped with 16 actuator struts is featured. The overall strain energy of the controlled structure is reduced by about 40 % at maximum and the sum of squared displacements is reduced by nearly 41 % at maximum, which verifies the adaptability of ASDS to loads and the effectiveness of the control method. The suspended-dome structure of Jinan Olympic Sports Center Gymnasium is selected for data simulation to verify the effectiveness and application value of ASDS in engineering. The research methodology and conclusions provide valuable references for the design and control of adaptive structures.

Virtual Position Guided Strategy for Particle Swarm Optimization Algorithms on Multimodal Problems.

Premature convergence is a thorny problem for particle swarm optimization (PSO) algorithms, especially on multimodal problems, where maintaining swarm diversity is crucial. However, most enhancement strategies for PSO, including the existing diversity-guided strategies, have not fully addressed this issue. This paper proposes the virtual position guided (VPG) strategy for PSO algorithms. The VPG strategy calculates diversity values for two different populations and establishes a diversity baseline. It then dynamically guides the algorithm to conduct different search behaviors, through three phases - divergence, normal, and acceleration - in each iteration, based on the relationships among these diversity values and the baseline. Collectively, these phases orchestrate different schemes to balance exploration and exploitation, collaboratively steering the algorithm away from local optima and towards enhanced solution quality. The introduction of 'virtual position' caters to the strategy's adaptability across various PSO algorithms, ensuring the generality and effectiveness of the proposed VPG strategy. With a single hyperparameter and a recommended usual setup, VPG is easy to implement. The experimental results demonstrate that the VPG strategy is superior to several canonical and the state-of-the-art strategies for diversity guidance, and is effective in improving the search performance of most PSO algorithms on multimodal problems of various dimensionalities.

Photovoltaic model parameters identification using diversity improvement-oriented differential evolution

Fast and accurate parameter identification of the photovoltaic (PV) model is crucial for calculating, controlling, and managing PV generation systems. Numerous meta-heuristic algorithms have been applied to identify unknown parameters due to the multimodal and nonlinear characteristics of the parameter identification problems. Although many of them can obtain satisfactory results, problems such as premature convergence and population stagnation still exist, influencing the optimization performance. A novel variant of Differential Evolution, namely, Diversity Improvement-Oriented Differential Evolution (DIODE), is proposed to mitigate these deficiencies and obtain reliable parameters for PV models. In DIODE, an adaptive perturbation strategy is employed to perturb current individuals to mitigate premature convergence by enhancing population diversity. Secondly, a diversity improvement mechanism is proposed, where information on the covariance matrix and fitness improvement of individuals is used as a diversity indicator to detect stagnant individuals, which are then updated by the intervention strategy. Lastly, a novel parameter adaptation strategy is employed to maintain a sound balance between exploration and exploitation. The proposed DIODE algorithm is applied to parameter identification problems of six PV models, including single, double, and triple diode and three PV module models. In addition, a large test bed containing 72 benchmark functions from CEC2014, CEC2017, and CEC2022 test suites is employed to verify DIODE’s overall performance in terms of optimization accuracy. Experiment results demonstrate that DIODE can secure accurate parameters of PV models and achieve highly competitive performance on benchmark functions.

A Fractional Order-Kepler Optimization Algorithm (FO-KOA) for single and double-diode parameters PV cell extraction

The primary objective of this study is to investigate the effects of the Fractional Order Kepler Optimization Algorithm (FO-KOA) on photovoltaic (PV) module feature identification in solar systems. Leveraging the strengths of the original KOA, FO-KOA introduces fractional order elements and a Local Escaping Approach (LEA) to enhance search efficiency and prevent premature convergence. The FO element provides effective information and past expertise sharing amongst the participants to avoid premature converging. Additionally, LEA is incorporated to boost the search procedure by evading local optimization. The single-diode-model (SDM) and Double-diode-model (DDM) are two different equivalent circuits that are used for obtaining the unidentified parameters of the PV. Applied to KC-200, Ultra-Power-85, and SP-70 PV modules, FO-KOA is compared to the original KOA technique and contemporary algorithms. Simulation results demonstrate FO-KOA's remarkable average improvement rates, showcasing its significant advantages and robustness over earlier reported methods. The proposed FO-KOA demonstrates exceptional performance, outperforming existing algorithms by 94.42 %–99.73 % in optimizing PV cell parameter extraction, particularly for the KC200GT module, showcasing consistent superiority and robustness. Also, the proposed FO-KOA is validated of on SDM and DDM for the well-known RTC France PV cell.

Fuzzy PID control based on genetic algorithm optimization inverted pendulum system

Abstract For the first-order inverted pendulum control system, a fuzzy PID control system based on the optimization of the genetic algorithm is proposed. The traditional genetic algorithm has the problem that the difference in the fuzzy subset parameter leads to a decrease in the interpretative ability of the fuzzy system. The main problem of the current genetic algorithm is the complexity of the computation and the low efficiency. Based on this problem, this paper proposes an improved genetic algorithm, i.e., it adopts the variance operator and adaptive change of the variance index and elite retention strategy, which solves the premature and local convergence problems of the standard genetic algorithm, in order to optimize the fuzzy system. The experimental results show that the optimized genetic algorithm gives full play to the advantages of fuzzy control in terms of interpretability and robustness, and at the same time guarantees the prediction accuracy, which provides a new research idea in the field of artificial intelligence control.

Solving Multiobjective Feature Selection Problems in Classification via Problem Reformulation and Duplication Handling

Reducing the number of selected features and improving the classification performance are two major objectives in feature selection, which can be viewed as a multi-objective optimization problem. Multi-objective feature selection in classification has its unique characteristics, such as it has a strong preference for the classification performance over the number of selected features. Besides, solution duplication often appears in both the search and the objective spaces, which degenerates the diversity and results in the premature convergence of the population. To deal with the above issues, in this paper, during the evolutionary training process, a multi-objective feature selection problem is reformulated and solved as a constrained multi-objective optimization problem, which adds a constraint on the classification performance for each solution (e.g., feature subset) according to the distribution of nondominated solutions, with the aim of selecting promising feature subsets that contain more informative and strongly relevant features, which are beneficial to improve the classification performance. Furthermore, based on the distribution of feature subsets in the objective space and their similarity in the search space, a duplication analysis and handling method is proposed to enhance the diversity of the population. Experimental results demonstrate that the proposed method outperforms six state-of-the-art algorithms and is computationally efficient on 18 classification datasets.

An improved grey wolf optimization algorithm based on scale-free network topology

The grey wolf optimizer is a novel intelligent optimization algorithm that has become popular due to its low number of parameters, fast convergence speed, and simplicity. However, the classical algorithm, with its update strategy allowing wolves to learn only from the alpha wolves, often leads to premature convergence and lower convergence accuracy. Therefore, in this paper, an improved grey wolf optimization algorithm based on scale-free network topology (SFGWO) is proposed to address these issues. The improved algorithm first employs a strategy for formulating a population based on a scale-free network topology, where interaction between wolves is limited to topological neighbors, which helps enhance the exploration capabilities of the algorithm. Second, a neighbor learning strategy is introduced to capture individual diversity, facilitating the solution space exploration. Finally, an adaptive individual regeneration strategy is adopted to balance the exploration and exploitation processes and reduce the risk of falling into local optima. The proposed algorithm is evaluated through simulation experiments using 23 classical and the CEC2019 benchmark functions. The experimental results demonstrate that the SFGWO algorithm excels in terms of solution accuracy and exploration capabilities. The applicability and effectiveness of the SFGWO algorithm are further validated through testing on three practical engineering problems.

Capacity optimization configuration of multi-source independent microgrids based on TLC-GOLD-GWO algorithm

Abstract To guarantee the economic efficiency and reliability of standalone microgrids, this paper introduces an enhanced Grey Wolf optimization algorithm (GWO) [1] that leverages chaos mapping techniques, nonlinear convergence factor, and golden operator for solving multi-source capacity allocation problems. Taking the reliability of the power supply as a significant constraint, an optimization model is constructed with the minimization of the annual total economic cost as the objective function. Given the issues of local convergence and premature convergence encountered during the solution process of the fundamental Grey Wolf optimization algorithm, we employ chaotic mapping technology to address the challenge of unequal initial population distribution. Subsequently, a nonlinear convergence factor is introduced to expedite the convergence rate, enhancing the algorithm’s performance. Lastly, to update the grey wolf’s position, the golden sine operator is used, thereby refining the solution space and enhancing the effectiveness of the optimization process. The simulation outcomes reveal that the enhanced Grey Wolf optimization algorithm notably enhances the precision of the objective function, delivering superior performance. Compared to the Grey Wolf optimization algorithm and Whale optimization algorithm (WOA) [2], the enhanced algorithm demonstrates superiority in terms of reducing economic costs, enhancing the capability for global optimal search, and accelerating the optimization process.

A FDA-based multi-robot cooperation algorithm for multi-target searching in unknown environments

Target search using a swarm of robots is a classic research topic that poses challenges, particularly in conducting multi-target searching in unknown environments. Key challenges include high communication cost among robots, unknown positions of obstacles, and the presence of multiple targets. To address these challenges, we propose a novel Robotic Flow Direction Algorithm (RFDA), building upon the modified Flow Direction Algorithm (FDA) to suit the characteristics of the robot’s motion. RFDA efficiently reduces the communication cost and navigates around unknown obstacles. The algorithm also accounts for scenarios involving isolated robots. The pipeline of the proposed RFDA method is outlined as follows: (1). Learning strategy: a neighborhood information based learning strategy is adopted to enhance the FDA’s position update formula. This allows swarm robots to systematically locate the target (the lowest height) in a stepwise manner. (2). Adaptive inertia weighting: An adaptive inertia weighting mechanism is employed to maintain diversity among robots during the search and avoid premature convergence. (3). Sink-filling process: The algorithm simulates the sink-filling process and moving to the aspect slope to escape from local optima. (4). Isolated robot scenario: The case of an isolated robot (a robot without neighbors) is considered. Global optimal information is only required when the robot is isolated or undergoing the sink-filling process, thereby reducing communication costs. We not only demonstrate the probabilistic completeness of RFDA but also validate its effectiveness by comparing it with six other competing algorithms in a simulated environment. Experiments cover various aspects such as target number, population size, and environment size. Our findings indicate that RFDA outperforms other methods in terms of the number of required iterations and the full success rate. The Friedman and Wilcoxon tests further demonstrate the superiority of RFDA.

Synergistic Application of Particle Swarm Optimization and Gravitational Search Algorithm for Solar PV Performance Improvement

This study aims to optimize photovoltaic systems by developing a novel hybrid metaheuristic approach for maximum power point tracking (MPPT). The proposed method eclectically combines particle swarm optimization (PSO) and gravitational search algorithm (GSA) to overcome individual limitations and leverage complementary strengths. PSO, while surpassing in exploration, may suffer from premature convergence. GSA demonstrates strong exploitation capabilities but can struggle with slow convergence. A simulation model is developed to evaluate the hybrid algorithm’s performance in optimizing PV systems’ duty cycle. The approach utilizes the exploitation capabilities of PSO and GSA to navigate the search space effectively. Results demonstrate that the hybrid algorithm outperforms traditional techniques and standalone metaheuristics, achieving improved convergence time, faster settling time, and enhanced MPPT tracking efficiency. Under varying irradiance conditions, the proposed method consistently delivers higher power generation and improved overall PV system efficiency, offering a promising solution for optimizing PV systems and maximizing energy generation.

Feature selection on real-time application using hybrid of flamingo search algorithm and improved non-dominated sorting genetic algorithm III

ABSTRACT Feature selection plays an essential role in enhancing the efficiency and effectiveness of machine learning models, particularly in the context of large-scale datasets where the dimensionality of features presents significant challenges. This research presents a novel approach to feature selection, a critical aspect of enhancing machine learning model efficiency, particularly in the context of large-scale datasets. By integrating the Flamingo Search Algorithm (FSA), Non-dominated Sorting Genetic Algorithm III (NSGA-III), and Regularised Extreme Learning Machine (RELM), the proposed method addresses limitations in existing feature selection and multi-objective optimisation algorithms. Leveraging FSA’s emulation of flamingo behaviours, the approach achieves a balance between global exploration and local exploitation, mitigating issues like premature convergence and local optima. Integration with NSGA-III enhances multi-objective optimisation capabilities, maintaining a delicate equilibrium between convergence and diversity. FSA-RELM is employed for accurate feature assessment, given its rapid learning and suitability for large datasets with multiple labels. Experimental evaluations demonstrate the proposed method’s superiority in feature selection accuracy, classification performance, and computational efficiency compared to existing approaches. This research contributes to advancing feature selection methodologies, offering a comprehensive solution for high-dimensional datasets in machine learning and data mining applications.

Multi-Objective Optimization of Short-Inverted Transport Scheduling Strategy Based on Road–Railway Intermodal Transport

This study focuses on the ‘short-inverted transportation’ scenario of intermodal transport. It proposes a vehicle unloading reservation mechanism to optimize the point-of-demand scheduling system for the inefficiency of transport due to the complexity and uncertainty of the scheduling strategy. This paper establishes a scheduling strategy optimization model to minimize the cost of short backhaul and obtain the shortest delivery time window and designs a hybrid NSGWO algorithm suitable for multi-objective optimization to solve the problem. The algorithm incorporates the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm based on the Grey Wolf Optimizer (GWO) algorithm, compensating for a single algorithm’s premature convergence. The experiment selects a logistics carrier’s actual road–rail intermodal short-inverted data and compares and verifies the above data. The results show that the scheduling scheme obtained by this algorithm can save 41.01% of the transport cost and shorten the total delivery time by 46.94% compared with the original scheme, which can effectively protect the enterprise’s economic benefits while achieving timely delivery. At the same time, the optimized scheduling plan resulted in a lower number of transport vehicles, which positively impacted the sustainability of green logistics.

A dual-population Constrained Many-Objective Evolutionary Algorithm based on reference point and angle easing strategy.

Constrained many-objective optimization problems (CMaOPs) have gradually emerged in various areas and are significant for this field. These problems often involve intricate Pareto frontiers (PFs) that are both refined and uneven, thereby making their resolution difficult and challenging. Traditional algorithms tend to over prioritize convergence, leading to premature convergence of the decision variables, which greatly reduces the possibility of finding the constrained Pareto frontiers (CPFs). This results in poor overall performance. To tackle this challenge, our solution involves a novel dual-population constrained many-objective evolutionary algorithm based on reference point and angle easing strategy (dCMaOEA-RAE). It relies on a relaxed selection strategy utilizing reference points and angles to facilitate cooperation between dual populations by retaining solutions that may currently perform poorly but contribute positively to the overall optimization process. We are able to guide the population to move to the optimal feasible solution region in a timely manner in order to obtain a series of superior solutions can be obtained. Our proposed algorithm's competitiveness across all three evaluation indicators was demonstrated through experimental results conducted on 77 test problems. Comparisons with ten other cutting-edge algorithms further validated its efficacy.

A robust multi-objective optimization algorithm for accurate parameter estimation for solar cell models

The accuracy of solar cell models is crucial for enhancing the performance of solar photovoltaic (PV) systems. However, existing solar cell models lack precise parameters, and the manufacturer's datasheet does not provide the required information for reliable modeling. Consequently, accurate parameter estimation becomes necessary. This paper presents a simple multi-objective optimization algorithm (Hybrid Particle Swarm Optimization and Rat Search Algorithm (PSORSA)) designed to estimate cell parameters based on this observation. Unlike other optimization algorithms addressing this issue, the proposed algorithm aims to overcome challenges related to local minima and premature convergence, which often lead to suboptimal results. The paper focuses on assessing the reliability of the proposed algorithm by comparing its performance with other well-known optimization algorithms. The proposed optimizing algorithm is tested on the CEC 2019 benchmark function. Experimental results (RMSE), including statistical analysis, validate the algorithm's effectiveness by comparing them with other algorithms. At the end, non-parametric test is performed to justify the outcomes, vouching for the better performance of the proposed algorithm. The findings demonstrate that the proposed algorithms are particularly well-suited for estimating solar PV models. With its simple structure and high accuracy, the proposed algorithm exhibits great potential for various applications in the field of solar energy. Moreover, its computational efficiency and ease of implementation further contribute to its practicality.

Multi-Point Seawall Settlement Prediction with Limited Data Volume Using an Improved Fractional-Order Grey Model

Settlement prediction based on monitoring data holds significant importance for engineering maintenance of seawalls. In practical engineering, the volume of the collected monitoring data is often limited due to the restrictions of devices and engineering budgets. Previous studies have applied the fractional-order grey model to time series prediction under the situation of limited data volume. However, the performance of the fractional-order grey model is easily affected by the inappropriate settings of fractional order. Also, the model cannot make dynamic predictions due to the characteristic of fixed step size. To solve the above problems, in this paper, the genetic algorithm with enhanced search capabilities was employed to solve the premature convergence problem. Additionally, to solve the problem of the fractional-order grey model associated with fixed step size, the real-time tracing algorithm was introduced to conduct equal-dimensionally recursive calculation. The proposed model was validated using monitoring data of four monitoring points at Haiyan seawall in Zhejiang province, China. The prediction performance of the proposed model was then compared with those of the fractional-order GM(1,1), integer-order GM(1,1), and fractal theory model. Results indicate that the proposed model significantly improves the prediction performance compared to other models.

Application of the artificial neural network and enhanced particle swarm optimization to model updating of structures

AbstractAn efficient and accurate two-stage approach, based on the artificial neural network (ANN) and an enhanced particle swarm optimization (EPSO) approach for model updating of structures using incomplete measurements, is proposed in this study. The first stage, preliminary model updating, employs the ANN to quickly learn the mapping relationship between the natural frequencies and stiffness of the structure using a few training, validation, and testing instances. The inputs and outputs of the ANN are the natural frequencies and stiffness of the structure, respectively. The ANN’s training, validation, and testing instances are extracted through Latin hypercube sampling. The ANN-predicted stiffness provides an excellent basis for determining and reducing the search space of the optimal stiffness in the second stage. The second stage, detailed model updating, searches for the optimal stiffness of the structure by using the EPSO approach. The EPSO approach improves particle swarm optimization (PSO) by employing an elite crossover strategy to avoid trapping in the local optimum and premature convergence. The feasibility and effectiveness of the proposed two-stage approach for stiffness updating of shear building structures using incomplete measurements are demonstrated by numerical and experimental examples. The results present that the proposed two-stage approach improves the computational efficiency and solution quality of the GA (Genetic Algorithm) and PSO for stiffness updating of shear building structures.