Meta-heuristic Optimization Method Research Articles

Optimization of plasma parameters for effective attenuation of microwaves in specified frequency range

AbstractIn this article, a plasma‐metal model is studied as an electromagnetic absorber for stealth application. Epstain distribution is considered for plasma and the electromagnetic reflection of the structure is analyzed by the Green's function volume integral equation method. The attenuation of microwaves in plasma depends on microwave frequency, plasma electron density, spatial distribution of plasma, collision frequency, and plasma thickness. Using a metaheuristic optimization method, it is possible to change the parameters simultaneously in the specified domains to obtain conditions for which microwaves can be absorbed effectively in the specified frequency. In this paper, optimized plasma parameters related to ideal attenuation in desired frequency band are determined by this method. The advantage of this method is that the intervals related to the plasma parameters are selecting according to the practical conditions and in many cases prevent the production of high volume with high density plasma to achieve effective attenuation. The proposed method can be useful for designing adjustable devices in stealth applications. Proper management of power consumption in these devices is one of the results of adjustment.

High-Performance Technique for Estimating the Unknown Parameters of Photovoltaic Cells and Modules Based on Improved Spider Wasp Optimizer

To better estimate the unknown parameters of the double-diode model, a new optimization technique based on the newly proposed spider wasp optimizer (SWO) is introduced in this study. The performance of SWO was further enhanced by integrating it with a local search strategy to propose a new improved variant called ISWO. This improved variant has a high ability to extensively exploit the solutions surrounding the best-so-far solution in an effort to speed up convergence and produce better results in fewer function evaluations. Using the RTC France solar cell and three PV modules (STM6-40/36, STP6-120/36, and Kyocera KC200GT), ISWO and SWO are evaluated and compared to four well-known metaheuristic optimization methods. The objective values acquired by those algorithms in thirty separate runs are examined using the Wilcoxon rank sum test and a number of performance measures. The experimental findings demonstrate ISWO's exceptional performance for every PV module under consideration.

Optimization Techniques for Human Multi-Biometric Recognition System

Researchers are increasingly using multimodal biometrics to strengthen the security of biometric applications. In this study, a strong multimodal human identification model was developed to address the growing problem of spoofing attacks in biometric security systems. Through the use of metaheuristic optimization methods, such as the Genetic Algorithm(GA), Ant Colony Optimization(ACO), and Particle Swarm Optimization (PSO) for feature selection, this unique model incorporates three biometric modalities: face, iris, and fingerprint. Image pre-processing, feature extraction, critical image feature selection, and multibiometric recognition are the four main steps in the workflow of the system. To determine its performance, the model was evaluated on the SDUMLA-HMT dataset, which contains a variety of biometric features from various individuals. The system outperformed existing techniques in the literature with an excellent recognition accuracy of 99.4%. Although this result is encouraging, further research on larger and more varied datasets is necessary to confirm its applicability across many circumstances. This study highlights how multimodal biometrics strengthened by metaheuristic algorithms can considerably increase biometric security against spoofing assaults, thereby opening a promising new direction for future development in the field.

Maximizing energy storage in Microgrids with an amended multi-verse optimizer

Microgrids have emerged as a possible alternative to overcome the difficulties of the combined cooling, heating, and power (CCHP) system in power networks. Energy storage devices are vital for the stable and effective functioning of Microgrids. In this paper, a new modified metaheuristic technique, called the Amended Multiverse Optimizer algorithm (AMVOA) is used to suggest a new method of Microgrid design with energy storage. The Multiverse theory notion served as the inspiration for the metaheuristic optimization method known as the AMVOA. The suggested strategy takes into account the load demand, energy storage technologies, and architecture of a Microgrid with renewable energy sources. The goal is to keep the Microgrid's overall cost as low as possible while preserving its dependability and sustainability. To validate the efficiency of the proposed method, two HRES scenarios are put out, the first of which relies on PV, wind, diesel, and battery power, and the second of which uses PV, diesel, and battery power. To validate the superiority of the proposed method, the method has been compared with five state-of-the-art algorithms, including the Evolutionary Algorithm (EA), Modified Grasshopper Optimization Algorithm (MGOA), Improved Gray Wolf Optimization Algorithm (IGWOA), Improved Arithmetic Optimization Algorithm (IAOA), and the original MVOA. The study compares two scenarios: one with wind, PV, diesel, and battery power and the other with only PV, diesel, and battery power. In scenario 1 (Wind/PV/DG/BESS), the AMVOA algorithm achieves optimal results, resulting in a Net Present Cost (NPC) of $299,010 and an energy cost of $0.2309 per kilowatt-hour. The proposed technique successfully integrates 84.86 % renewable energy sources while meeting defined limitations. The optimal sizing for scenario 2 (PV/DG/BESS) is $333,800 with an energy cost of $0.3451 per kilowatt-hour. The AMVOA algorithm outperforms other algorithms in convergence and provides efficient power management. However, further analysis and evaluation are necessary to assess the robustness, practicality, and reliability of the proposed Microgrid configurations. The outcomes show how the suggested AMVO-based strategy may be used to create the best Microgrid architecture with energy storage. The recommended method may be applied as a decision-making tool for Microgrid planning and design, especially for the integration of renewable energy.

Face Image Segmentation Using Boosted Grey Wolf Optimizer.

Image segmentation methods have received widespread attention in face image recognition, which can divide each pixel in the image into different regions and effectively distinguish the face region from the background for further recognition. Threshold segmentation, a common image segmentation method, suffers from the problem that the computational complexity shows exponential growth with the increase in the segmentation threshold level. Therefore, in order to improve the segmentation quality and obtain the segmentation thresholds more efficiently, a multi-threshold image segmentation framework based on a meta-heuristic optimization technique combined with Kapur's entropy is proposed in this study. A meta-heuristic optimization method based on an improved grey wolf optimizer variant is proposed to optimize the 2D Kapur's entropy of the greyscale and nonlocal mean 2D histograms generated by image computation. In order to verify the advancement of the method, experiments compared with the state-of-the-art method on IEEE CEC2020 and face image segmentation public dataset were conducted in this paper. The proposed method has achieved better results than other methods in various tests at 18 thresholds with an average feature similarity of 0.8792, an average structural similarity of 0.8532, and an average peak signal-to-noise ratio of 24.9 dB. It can be used as an effective tool for face segmentation.

A modified fractional‑order-based future search algorithm for performance enhancement of a PEMFC-based CCHP

ABSTRACT Load control and cost optimization are considered to be crucial in tri-generation or combined cooling, heating, and power (CCHP) systems. In this study, an inventive CCHP system employs an FC system as its first mover and includes a heat exchanger, a heat recovery, as well as an auxiliary boiler, an electric chiller, and an absorption chiller. The electrical grid is linked to this system. The idea here is to maximize the system’s performance from a financial perspective and to make the annual expenditure of the system minimum over a 20–year period that is considered as the cycle life-span. It is a multi-objective optimization problem which is optimized using a newly introduced metaheuristic optimization method and a Fractional-order future search optimizer. The findings of this study are used to divine an ideal configuration of the CCHP. Finally, to demonstrate the higher efficiency of the suggested method, a comparison should be conducted among the optimization results of the fractional-order-based future search algorithm, the results of Non-dominated Sorting Genetic Algorithm II (NSGA-II), and standard future search algorithms in previous studies. Based on the results presented, the proposed Fractional-order Future Search Algorithm (FOFSA) was able to optimize the performance of a PEMFC-based CCHP system more effectively than conventional methods. The system’s exergy efficiency was found to decrease from 52% at 793 mA/cm2 current density to 36% at 1000 mA/cm2 current density. However, with the application of FOFSA, the suggested optimal system had a higher exergy efficiency of 41.6% and a yearly cost of $2765, resulting in the maximum annual greenhouse gas (GHG) reduction of 4.48E6 g. Therefore, in summary, the proposed FOFSA yielded an optimized CCHP system configuration that had higher energy efficiency, lower annual cost, and reduced GHG emissions. These findings highlight the effectiveness of the FOFSA method in optimizing the performance of PEMFC-based CCHP systems.

Optimizing PID Gains of a Vehicle using the state-of-the-art Metaheuristic Methods

PID controllers are important control methods that are widely used in industrial processes. Proper tuning of PID gains is critical for achieving the state-of-the-art system performance. Therefore, optimizing PID gains is an important research topic in the field of control engineering. In this study, PID controller gains are automatically tuned using metaheuristic optimization methods. These methods use an iterative approach to calculate optimal values of PID controller gains based on different optimization techniques. The interaction between artificial intelligence and control systems requires a multidimensional approach across different disciplines. In the study, we perform Particle Swarm Optimization, Gray Wolf Optimization, Whale Optimization Algorithm, Firefly Algorithm, Harris Hawks Optimization, Artificial Hummingbird Algorithm and African Vulture Optimization Algorithm to determine PID gains. In the simulation, step input is applied to the dynamic equation of the unmanned free-swimming submersible vehicle. The fitness function is determined with respect to controller integral square error, settling time value, and maximum percent overshoot value. We also evaluate the optimization time of the selected algorithms based on the fitness function. Experimental results present that Artificial Hummingbird Algorithm, Gray Wolf Optimization and Particle Swarm Optimization achieve significant performance. This underlines that using metaheuristic methods in PID gain optimization increase overall system performance.

Electrical power output prediction of combined cycle power plants using a recurrent neural network optimized by waterwheel plant algorithm

It is difficult to analyze and anticipate the power output of Combined Cycle Power Plants (CCPPs) when considering operational thermal variables such as ambient pressure, vacuum, relative humidity, and temperature. Our data visualization study shows strong non-linearity in the experimental data. We observe that CCPP energy production increases linearly with temperature but not pressure. We offer the Waterwheel Plant Algorithm (WWPA), a unique metaheuristic optimization method, to fine-tune Recurrent Neural Network hyperparameters to improve prediction accuracy. A robust mathematical model for energy production prediction is built and validated using anticipated and experimental data residuals. The residuals’ uniformity above and below the regression line suggests acceptable prediction errors. Our mathematical model has an R-squared value of 0.935 and 0.999 during training and testing, demonstrating its outstanding predictive accuracy. This research provides an accurate way to forecast CCPP energy output, which could improve operational efficiency and resource utilization in these power plants.

A Novel Black Widow Optimized Controller Approach for Automatic Generation Control in Modern Hybrid Power Systems

This research paper demonstrates an application of the Black Widow Optimization (BWO) approach to address the issue of load-frequency control (LFC) in networked power systems. BWO is an innovative metaheuristic method that quickly suggests technique is initially evaluated on a non-reheat thermal-thermal (NRTT) power system spanning two areas of interconnection, and then it is applied to two different actual power systems: (a) a two-area thermal-thermal considering Generation Rate Constraint (GRC); and (b) a two-area having thermal, hydro, wind, solar, and gas systems. The BWO method uses two fitness functions based on integral time multiplied absolute error (ITAE) and integral square error (ISE) to optimize controller gains. The suggested BWO algorithm's performance has been compared to that of existing meta-heuristic optimization methods, such as grey wolf optimization (GWO), comprehensive learning particle swarm optimization (CLPSO), and an ensemble of parameters in differential evolution (EPSDE). The simulation results show that BWO's tuning skills are better than other population-based planning methods like CLPSO, EPSDE, and GWO. The ITAE value is enhanced by 33.28% (GWO), 40.28% (EPSDE), and 43.27% (CLPSO) when the BWO algorithm is used in conjunction with the PID Controller for thermal system.

A Meta-Heuristic Algorithm-Based Feature Selection Approach to Improve Prediction Success for Salmonella Occurrence in Agricultural Waters

The presence of Salmonella in agricultural waters may be a source of produce contamination. Recently, the performance of various algorithms has been tested for the prediction of indicator bacteria population and pathogen occurrence in agricultural water sources. The purpose of this study was to evaluate the effect of meta-heuristic optimization algorithms for feature selection to increase the Salmonella occurrence prediction performance of commonly used algorithms in agricultural waters. Previously collected dataset from six agricultural ponds in Central Florida included the population of indicator microorganisms, physicochemical water attributes, and weather station measurements. Salmonella presence was also reported with PCR-confirmed method in data set. Features were selected by binary meta-heuristic optimization methods including differential evolution optimization (DEO), grey wolf optimization (GWO), Harris hawks optimization (HHO) and particle swarm optimization (PSO). Each meta-heuristic method was run for 100 times for the extraction of features before classification analysis. Selected features after optimization were used in the K-nearest neighbor algorithm (kNN), support vector machine (SVM) and decision tree (DT) classification methods. Microbiological indicators were ranked as the first or second features by all optimization algorithms. Generic Escherichia coli was selected as the first feature 81 and 91 times out of 100 by GWO and DEO, respectively. The meta-heuristic optimization algorithms for the feature selection process followed by machine learning classification methods yielded the prediction accuracy between 93.57 and 95.55%. Meta-heuristic optimization algorithms had a positive effect to improve Salmonella prediction success in agricultural waters despite spatio-temporal variations in agricultural water quality.

Optimization of a hybrid solar/wind/storage system with bio-generator for a household by emerging metaheuristic optimization algorithm

The ever-increasing need for electricity in off-grid areas requires a safe and effective energy supply system. Considering the development of a sustainable energy system and the reduction of environmental pollution and energy cost per unit, this study focuses on the techno-economic study and optimal sizing of the solar, wind, bio-diesel generator, and energy storage structure. The emerging metaheuristic optimization method is used to estimate the techno-economic benefits of the suggested structure to provide the required electricity for a residential household. The optimal design is done with the harmony search (HS) method to validate the results obtained with the suggested algorithm. Minimizing the total annual cost (TAC) is a main objective for the design optimization of the system while satisfying the reliability and techno-enviro-economic constraints. The impact of the investment cost of biodiesel, biofuel cost, and reliability is investigated on the system sizing. The results show that the proposed algorithm has low simulation time (by 4.1 %) and the operating cost of the proposed algorithm is 1.12 % less than the existing HS algorithm based on the best TAC value. The TAC is received as $24,259 with the suggested method, which is the best optimal result compared to the result given by the HS algorithm. The proposed off-grid renewable energy system based on a bio-diesel generator is a viable and scalable solution to provide the required electricity for a residential household in all periods. The sensitivity analysis show that if the biofuel cost is reduced by 50.8 %, TAC will decrease by about 36.6 %. On the other hand, if the bio-diesel generator cost is reduced by 17 %, TAC will be decreased by 2.7 %. Finally, if the limit value of reliability is reduced from 2 to 0 %, TAC will increase by 13.2 %.

A Comparative Assessment of Five Different Distributions Based on Five Different Optimization Methods for Modeling Wind Speed Distribution

Determining wind regime distribution patterns is essential for many reasons; modelling wind power potential is one of the most crucial. In that regard, Weibull, Gamma, and Rayleigh functions are the most widely used distributions for describing wind speed distribution. However, they could not be the best for describing all wind systems. Also, estimation methods play a significant role in deciding which distribution can achieve the best matching. Consequently, alternative distributions and estimation methods are required to be studied. An extensive analysis of five different distributions to describe the wind speeds distribution, namely Rayleigh, Weibull, Inverse Gaussian, Burr Type XII, and Generalized Pareto, are introduced in this study. Further, five metaheuristic optimization methods, Grasshopper Optimization Algorithm, Grey Wolf Optimization, Moth-Flame Optimization, Salp Swarm Algorithm, and Whale Optimization Algorithm, are employed to specify the optimum parameters per distribution. Five error criteria and seven statistical descriptors are utilized to compare the good-of-fitness of the introduced distributions. Therefore, this paper provides different important methods to estimate the wind potential at any site.

Optimization of system of Oscillating Water Columns to mitigate pitch response of FPSO platforms submitted to head waves

This work presents a novel method for reducing the pitch response of FPSO (Floating, Production, Storage and Offloading) platforms submitted to head waves. The method is based on installing a couple of moonpools, modeled as opened Oscillating Water Columns (OWC), on the vessel. According to detailed literature review, the effects of the vortex shedding can be represented through a nonlinear damping factor, which is proportional to the relative motion between the vessel and the water column within the moonpool.Optimization solvers are adopted to design the moonpools, using potential theory to calculate the vessel response with an iterative procedure to properly account for the nonlinear viscous damping factor related to the vortex shedding.The use of metaheuristic optimization method is discussed, with the choice of Particle Swarm Optimization. Different mono-objective functions are explored by weighing the minimization of the peak response and the area underneath the response curve. The importance of imposing restrictions on the modified vessels to avoid increasing heave motion is presented, using the penalty function also by weighing the peak response and the area. Results show the effectiveness of the procedures proposed in the study and indicate the possibility of expanding to implement it in other applications.

Superposition of populations in multi-objective evolutionary optimization of car suspensions

The design of the suspension model of road cars is extremely important for both driver comfort and safety. Road traffic injuries are currently the eighth leading cause of death worldwide and are predicted to become the seventh leading cause of death by 2030, according to the World Health Organization (WHO). Among other factors, road infrastructure is one of the most important factors to consider when designing the suspension model, especially as autonomous driving becomes more popular. In addition, there is a growing need to test and study the impact of road roughness and pavement type on autonomous vehicles (AVs). This work provides the following contributions: a platform for suspension system optimization–flexible, highly parameterizable and rich in applications. Our solution implements, tests and optimises the 2, 3 and 4 degrees of freedom (DOF) quarter-car models (QCM) with linear seat suspension and the 5 DOF half-car model (HCM), respectively, based on random road profiles generated according to ISO 8608 standards. In addition, many multi-objective optimization (MOO) algorithms have been implemented and applied in isolation to see their comparative performance (in terms of Pareto fronts, hypervolume, coverage, spread, and epsilon), but most importantly we have also introduced a meta-optimization technique by super-positioning Non-dominated Sorting Genetic Algorithm II and Strength Pareto Evolutionary Algorithm 2, where each of the algorithms, running concurrently, produces a percentage of the total number of individuals in a generation, percentage that is calculated according to the solution quality of the individuals in the previous generation. The experimental results were obtained by simulating the optimal configurations generated by the MOO heuristic algorithms on different categories of cars (small/medium). Finally, the Taguchi method and regression analysis were used to evaluate the effects of specific parameters on system responses such as sprung mass acceleration and displacement. The Taguchi simulation was performed to experimentally validate the results obtained by metaheuristic optimization methods.

Жадная эвристика размещения ортогональных многогранников для оптимизированного решения задач компоновки объектов нерегулярной формы

The article deals with the cutting and packing problems of irregular shape objects, which consist in finding the most compact way to place a given set of objects of arbitrary geometry inside a certain limited space. These problems belong to the class of ­NP-hard discrete optimization problems for which there are no methods of polynomial complexity to obtain exact solutions, so in practice they are most often solved approximately using heuristic and metaheuristic optimization methods. When placing objects of irregular shape, it is additionally necessary to take into account the geometry of objects to determine the correctness of their placement relative to each other. Existing methods of analyzing the geometry of objects and the formed placement scheme, based on the use of phi-functions and the construction of a hodograph of a vector function of dense placement, theoretically provide the possibility of obtaining an accurate solution, but require the use of time-consuming methods of nonlinear optimization. Therefore, in order to increase the speed of packing a large number of irregular-shaped objects, their shape is transformed by voxelization, followed by combining the resulting set of voxels into orthogonal polyhedra. To improve the quality of the solutions obtained, the paper proposes a greedy heuristic for the placement of orthogonal polyhedra, which implements the choice of the best orientation option for the object being placed, in which the formed packing will be the densest in comparison with other available orientation options for this object. The analysis of the effectiveness of this greedy heuristic on the problems of irregular cutting and packing of three-dimensional objects is carried out. Computational experiments have shown that the proposed greedy heuristic provides very fast high-quality solutions. Additionally, the results of testing the greedy placement heuristics using a genetic algorithm to optimize solutions to the packing problem are presented.

Adaptive penalty method with adam optimizer for enhanced convergence in optical waveguide mode solvers.

We propose a cutting-edge penalty method for optical waveguide mode solvers, integrating the Adam optimizer into pseudospectral frequency-domain (PSFD) frameworks. This strategy enables adaptable boundary fluctuations at material interfaces, significantly enhancing numerical convergence and stability. The Adam optimizer, an adaptive algorithm, is deployed to determine the penalty coefficient, greatly improving convergence rates and robustness while effectively incorporating boundary conditions into the interfaces of subdomains. Our solver evaluates the numerical performance of optical waveguides by calculating effective indices of standard benchmark waveguides with high accuracy. This method diminishes numerical boundary errors and provides a marked increase in convergence speed and superior accuracy when compared to conventional methods and even metaheuristic optimization methods, all while maintaining the inherent global spectral accuracy of the PSFD.

OPTIMIZATION OF STIFFENED COMPOSITE PLATE USING BALANCING COMPOSITE MOTION OPTIMIZATION

Recently, metaheuristic optimization algorithms have been studied and applied in many fields of engineering, especially in solving structural optimization problems. For structures with complex behaviors, the selection of a suitable optimization algorithm significantly increases the computational efficiency and the accuracy of the solution. In this paper, we investigate the optimization problem of stiffened composite plates using Balancing Composite Motion Optimization. The core idea of the Balancing Composite Motion Optimization algorithm is that the searching movements of candidate solutions are compositely equalized in both global and local ones in the solution space of solving the fiber optimization problem of stiffened composite plates. A candidate solution can move closer to better ones to exploit the local regions and move further to explore the search space also. The method does not require algorithm parameters. The calculation results are compared with many other metaheuristic optimization methods to prove the accuracy and efficiency of the method.

Advanced Optimization of Surface Characteristics and Material Removal Rate for Biocompatible Ti6Al4V Using WEDM Process with BBD and NSGA II.

Machining titanium alloy (Ti6Al4V) used in orthopedic implants via conventional metal cutting processes is challenging due to excessive cutting forces, low surface integrity, and tool wear. To overcome these difficulties and ensure high-quality products, various industries employ wire electrical discharge machining (WEDM) for precise machining of intricate shapes in titanium alloy. The objective is to make WEDM machining parameters as efficient as possible for machining the biocompatible alloy Ti6Al4Vusing Box-Behnken design (BBD) and nondominated sorting genetic algorithm II (NSGA II). A quadratic mathematical model is created to represent the productivity and the quality factor (MRR and surface roughness) in terms of varying input parameters, such as pulse active (Ton) time, pulse inactive (Toff) time, peak amplitude (A) current, and applied servo (V) voltage. The established regression models and related prediction plots provide a reliable approach for predicting how the process variables affect the two responses, namely, MRR and SR. The effects of four process variables on both the responses were examined, and the findings revealed that the pulse duration and voltage have a major influence on the rate at which material is removed (MRR), whereas the pulse duration influences quality (SR). The tradeoff between MRR and SR, when significant process factors are included, emphasizes the need for a reliable multi-objective optimization method. The intelligent metaheuristic optimization method named nondominated sorting genetic algorithm II (NSGA II) was utilized to provide pareto optimum solutions in order to achieve high material removal rate (MRR) and low surface roughness (SR).

Optimization of urban water pipe network design using fast-messy genetic algorithms (fmGA)

Abstract To have an efficient water distribution network, optimal design alternatives need to be identified and analysed using combined hydraulic modelling and optimization. This paper reports on the application of the fast-messy genetic algorithm (fmGA) coupled with hydraulic modelling tool EPANET to assess and select an optimum design and operational alternative for a water distribution pipe network. The sole objective of the optimization modelling was to minimize network costs subject to hydraulic and design constraints. The fmGA was first tested using the benchmark case study of the Hanoi network and then applied to the real network of Maun, Botswana which is considered as the case study. We have compared our results of the fmGA model application with other optimization techniques applied to the Hanoi network. The findings of the test revealed that the fmGA is superior to other popular metaheuristic optimization methods in terms of processing speed with comparable accuracy and pressure constraints fulfilled for all nodes. It also provides the best solution. For the water distribution network of Maun, the best pipeline configuration and route were determined, in which Configuration B is found to be the best and least cost solution to improve the water supply situation in Maun.

Opposition‐based ideal gas molecular movement algorithm with Cauchy mutation, velocity clamping, and mirror operator

AbstractThe ideal gas molecular movement (IGMM) as a metaheuristic optimization method is a prominent option for solving optimization problems. However, in some complex cases, IGMM may possess premature convergence or get trapped in local optima. Therefore, to tackle these issues, this paper indicates a new modified IGMM algorithm named opposition‐based IGMM, which has been incorporated with opposition based learning (OBL), Cauchy mutation (CM), velocity clamping (VC), and mirror operator (MO) to enhance its performance. OBL, VC, and MO improve the convergence of IGMM, whereas CM assists IGMM to escape local optima. The effect of each strategy, OBL, CM, VC, and MO, on IGMM, is confirmed through 30 low and high‐dimensional benchmarks, including 23 well‐known mathematical problems and CEC2017 as complex test functions and three engineering problems. Analysis results represent that integration IGMM with OBL, CM, VC, and MO has the best performance among other IGMM variants and eventually improved IGMM in exploration, exploitation, accelerating convergence, and local optima avoidance.