Bee Colony Optimization Research Articles

Lateral Control Calibration and Testing in a Co-Simulation Framework for Automated Vehicles

Lateral vehicle control is of high importance in automated vehicles as it directly influences the vehicle’s performance and safety during operation. The linear quadratic regulator (LQR) controller stands out due to its high-performance characteristics and is used in the open source for self-driving functions. However, a notable limitation of the current approach is the manual calibration of LQR controllers based on the experience and intuition of the designers, leading to empirical uncertainties. To address this issue and enhance the lateral control performance, this paper concentrates on refining the LQR by employing three optimization algorithms: artificial bee colony optimization (ABC), genetic algorithm (GA), and particle swarm optimization (PSO). These algorithms aim to overcome the reliance on empirical methods and enable a data-driven approach to LQR calibration. By comparing the outcomes of these optimization algorithms to the manual LQR controller within an offline multibody simulation as a testing platform, this study highlights the superiority of the best-performing optimization approach. Following this, the optimal algorithm is implemented on a real-time system for the full vehicle level, revealing the model-in-the-loop and the hardware-in-the-loop gap up to 78.89% with lateral velocity when we use the relative error criterion (REC) method to validate and 2.35 m with lateral displacement when considering the maximum absolute value method.

Optimisation of Product Recovery Options in End-of-Life Product Disassembly by Robots

In a circular economy, strategies for product recovery, such as reuse, recycling, and remanufacturing, play an important role at the end of a product’s life. A sustainability model was developed to solve the problem of sequence-dependent robotic disassembly line balancing. This research aimed to assess the viability of the model, which was optimised using the Multi-Objective Bees Algorithm in a robotic disassembly setting. Two industrial gear pumps were used as case studies. Four objectives (maximising profit, energy savings, emissions reductions and minimising line imbalance) were set. Several product recovery scenarios were developed to find the best recovery plans for each component. An efficient metaheuristic, the Bees Algorithm, was used to find the best solution. The robotic disassembly plans were generated and assigned to robotic workstations simultaneously. Using the proposed sustainability model on end-of-life industrial gear pumps shows the applicability of the model to real-world problems. The Multi-Objective Bees Algorithm was able to find the best scenario for product recovery by assigning each component to recycling, reuse, remanufacturing, or disposal. The performance of the algorithm is consistent, producing a similar performance for all sustainable strategies. This study addresses issues that arise with product recovery options for end-of-life products and provides optimal solutions through case studies.

An atom search optimization approach for IIR system identification

ABSTRACT Filtering, or digital signal processing, is a significant and fundamental requirement in fields such as signal systems and computers. The process of designing optimal digital filters is difficult, which has led researchers to design filters using emerging evolutionary computations. Metaheuristics have emerged as the most promising tool for solving optimization problems, with excellent development and improvement. However, it has not been clear how to select the best performing metaheuristic to design an optimal digital filter. In this paper, a digital infinite impulse response (IIR) filter is constructed using the atom search optimization (ASO) algorithm impressed by the physical motion of atoms in nature based on molecular dynamics. The simulation results obtained are extensively compared with the results of other optimization algorithms such as moth flame optimization, gravitational search algorithm and artificial bee colony optimization. ASO was found to have the highest percentage of improvement. Furthermore, eight cases are analyzed across four numerical filter instances with the same degree and four with reduced degree, and the results are validated by outperforming several different algorithm-based approaches in the literature. The stability analysis on the basis of pole zero diagrams further cements the efficacy of the ASO for IIR system identification problem.

Optimal sizing of battery energy storage systems and reliability analysis under diverse regulatory frameworks in microgrids

The integration of battery energy storage systems (BESS) with microgrids (MG) is crucial to improve the reliability and flexibility of renewable energy sources (RES) integration. However, the reliability and regulatory policies are critical factors that affect the optimal operation of MGs in the market. This study aims to enhance the reliability of MGs integrated with RES and BESS by evaluating their performance under different regulatory frameworks, namely feed-in tariff (FiT), net metering (NM), and energy storage incentive (ESI). Also, a dynamic FiT (D-FiT) framework is utilized to improve the reliability of the MG. An artificial bee colony optimization algorithm is utilized to optimize the size of BESS for each regulatory policy to minimize the total cost of the MG. Each policy is formulated based on its specific constraints in the problem. Subsequently, the reliability indices of Loss of Load Expectation (LOLE) and Expected Energy not Supplied (EENS) are calculated for each optimized solution. Moreover, we have integrated the dynamic thermal rating (DTR) system into our proposed model, focusing on the safe augmentation of system component ratings. The study finds that the D-FiT and standard FiT frameworks provide the best reliability level, whereas the reliability improvement under the ESI policy is not significant, as most of the MG's demand is supplied by the main grid. Furthermore, the study shows that the improvements in EENS are higher than LOLE, indicating that installing BESS reduces the loss of energy rather than the number of interruption hours. D-FiT framework has a significant positive impact on both reliability indices, unlike the other frameworks that have a greater effect on EENS. Furthermore, we have noticed a substantial improvement in reliability indices when the DTR system is taken into account, as compared to the static thermal rating (STR) system.

Composing Multiple Online Exams: The Bees Algorithm Solution

Online education has gained increasing importance in recent years due to its flexibility and ability to cater to a diverse range of learners. The COVID-19 pandemic has further emphasized the significance of online education as a means to ensure continuous learning during crisis situations. With the disruption of traditional in-person exams, online examinations have become the new norm for universities worldwide. Among the popular formats for online tests are multiple-choice questions, which are drawn from a large question bank. However, creating online tests often involves meeting specific requirements, such as minimizing the overlap between exams, grouping related questions, and determining the desired difficulty level. The manual selection of questions from a sizable question bank while adhering to numerous constraints can be a laborious task. Additionally, traditional search methods that evaluate all possible solutions are impractical and time-consuming for such a complex problem. Consequently, approximate methods like metaheuristics are commonly employed to achieve satisfactory solutions within a reasonable timeframe. This research proposes the application of the Bees Algorithm (BA), a popular metaheuristic algorithm, to address the problem of generating online exams. The proposed solution entails creating multiple exam forms that align with the desired difficulty level specified by the educator, while considering other identified constraints. Through extensive testing and comparison with four rival methods, the BA demonstrates superior performance in achieving the primary objective of matching the desired difficulty level in most test cases, as required by the educator. Furthermore, the algorithm exhibits robustness, indicated by minimal standard deviation across all experiments, which suggests its ability to generalize, adapt, and be practically applicable in real-world scenarios. However, the algorithm does have limitations related to the number of successful solutions and the achieved overlap percentage. These limitations have also been thoroughly discussed and highlighted in this research.

Formulation of the airport collaborative gate allocation problem and the Bee Colony Optimization solution approach

This article formulates the Collaborative Gate Allocation (CGA) problem as a novel concept to reduce aircraft gate-waiting time and to increase aircraft gate utilization. The proposed CGA concept assumes voluntary collaboration and negotiation among airlines and airport operators, enabling them to share real-time information on gate-utilization and gate-sharing. The proposed policy is especially applicable to U.S. airports, as an alternative to exclusive or preferential gate-sharing practices, at terminal buildings that accommodate a large number of smaller airlines during periods of high congestion and delays caused by high traffic demands, bad weather conditions, or any ad hoc situations. The CGA problem belongs to the class of complex combinatorial optimization problems, whose optimal solution is difficult to discover. This article develops a Swarm Intelligence-based model for the CGA problem. Our approach to solving the CGA problem is based on the Bee Colony Optimization (BCO) metaheuristic. The BCO algorithm belongs to the class of population-based algorithms. This technique uses a similarity between the way in which bees in nature look for nectar, and the way in which optimization algorithms search for an optimum solution to a combinatorial optimization problem. Numerical experiments are performed using Denver International Airport as a real-world case study. We show that the proposed CGA problem can be efficiently solved by our BCO algorithm, and that applications of the CGA concept can significantly reduce gate delays.

Joint energy and spectral optimization in Heterogeneous Vehicular Network

With the latest developments in both the automotive and communications industries, especially concerning the emerging 5G networks, IoV, and the adoption of Vehicle-to-Everything (V2X) connectivity, there has been a shift towards the establishment of Heterogeneous Vehicular Networks (HetVNets) environments. The rapid growth of data traffic and the drastic expansion of heterogeneous network infrastructure have resulted in a significant increase in energy consumption within wireless communication systems. Balancing energy efficiency and spectral efficiency has become a major challenge in Heterogeneous Vehicular networks, particularly concerning energy optimization, making the design of network systems considerably more challenging. Therefore, this paper attempts to optimize the energy utilized for each packet transmission, considering its stochastic nature and the optimized control parameters of two meta-heuristic algorithms-Particle Swarm Optimization and Artificial Bee Colony Optimization. The optimization process is executed using the Particle Bee Colony Swarm algorithm. Subsequently, a comparison is made with other proposed algorithms, namely LDOD, FO, RO, and MATO, in terms of energy efficiency and spectral efficiency. The performance analysis reveals that the numerical results outperform existing algorithms, demonstrating a 30.32% increase in spectral efficiency and 73.25% increase in energy efficiency.

A user-friendly Bees Algorithm for continuous and combinatorial optimisation

A user-friendly Bees Algorithm for continuous and combinatorial optimisation

Forensic detection of heterogeneous activity in data using deep learning methods

The abundance of digital images has been facilitated by smartphones and inexpensive storage. Digital forensic investigation requires the processing of tons of digital images collected on devices to either identify or validate the device's user or to ascertain whether the operator has any connections to the case that would be of interest. Examining and evaluating heterogeneous activity presents several difficulties, including variability, complex interaction across information, and volume. Digital forensics processes are said to need the inspection and analysis stages. This research presents a hybrid optimization of the Grey Wolf and artificial bee colony (GW-ABC) optimization with deep learning model Convolutional Neural Network (CNN) i.e., GW-ABC-CNN, and the developed framework is integrated as a module for Autopsy software. The main objective of this research is to detect the heterogeneous activity of humans from the Heterogeneous Human Activity Recognition (HHAR) database. The developed model is integrated into the data-source ingest module; in this module, pre-processing, feature extraction, and detection process is performed. Moreover, in the pre-processing stage, the Min-Max normalization method is used and the required frequency and time features are extracted using the GW-ABC method. In addition, CNN is used to detect heterogeneous activity; this detection process is performed by four layers. Finally, the effectiveness of the developed model is assessed, and the outcomes of using the GW-ABC-CNN paradigm were compared to those of other strategies to evaluate the model's effectiveness.

A novel power conversion structure for grid-connected photovoltaic applications based on MLI and LeBlanc transformer using IRSA technique

This article proposes a new energy conversion structure by employing a hybrid approach for grid-tied photovoltaic (PV) applications. This structure depends on the LeBlanc transformer and multilevel inverter (MLI). The proposed hybrid system combines the honey badger algorithm (HBA) and the reptile search algorithm (RSA). Crocodiles hunting behavior is enhanced by the HBA technique, also known as the IRSA technique. Voltage source inverters (VSI) are used in the proposed multilevel power converter. The MLI output is attached to the LeBlanc transformer. Multi-string technology is essential to the PV system's configuration. This innovative power converter's structural layout allows for an output voltage at the MLI's output. The proposed IRSA approach is utilized to regulate this power converter. This control system permits a fast and robust response from the MLI. This is also ensured by using the IRSA technique. The performance of the proposed hybrid method is run in MATLAB, and the performance is compared with various existing methods. From the simulation, the proposed approach-based efficiency is higher than the existing one. The proposed method shows a high efficiency of 99% compared with other existing methods, such as the salp swarm algorithm (SSA), bee colony optimization (BCO), and grasshopper optimization algorithm (GOA).

An Accurate Metaheuristic Mountain Gazelle Optimizer for Parameter Estimation of Single- and Double-Diode Photovoltaic Cell Models

Accurate parameter estimation is crucial and challenging for the design and modeling of PV cells/modules. However, the high degree of non-linearity of the typical I–V characteristic further complicates this task. Consequently, significant research interest has been generated in recent years. Currently, this trend has been marked by a noteworthy acceleration, mainly due to the rise of swarm intelligence and the rapid progress of computer technology. This paper proposes a developed Mountain Gazelle Optimizer (MGO) to generate the best values of the unknown parameters of PV generation units. The MGO mimics the social life and hierarchy of mountain gazelles in the wild. The MGO was compared with well-recognized recent algorithms, which were the Grey Wolf Optimizer (GWO), the Squirrel Search Algorithm (SSA), the Differential Evolution (DE) algorithm, the Bat–Artificial Bee Colony Optimizer (BABCO), the Bat Algorithm (BA), Multiswarm Spiral Leader Particle Swarm Optimization (M-SLPSO), the Guaranteed Convergence Particle Swarm Optimization algorithm (GCPSO), Triple-Phase Teaching–Learning-Based Optimization (TPTLBO), the Criss-Cross-based Nelder–Mead simplex Gradient-Based Optimizer (CCNMGBO), the quasi-Opposition-Based Learning Whale Optimization Algorithm (OBLWOA), and the Fractional Chaotic Ensemble Particle Swarm Optimizer (FC-EPSO). The experimental findings and statistical studies proved that the MGO outperformed the competing techniques in identifying the parameters of the Single-Diode Model (SDM) and the Double-Diode Model (DDM) PV models of Photowatt-PWP201 (polycrystalline) and STM6-40/36 (monocrystalline). The RMSEs of the MGO on the SDM and the DDM of Photowatt-PWP201 and STM6-40/36 were 2.042717 ×10−3, 1.387641 ×10−3, 1.719946 ×10−3, and 1.686104 ×10−3, respectively. Overall, the identified results highlighted that the MGO-based approach featured a fast processing time and steady convergence while retaining a high level of accuracy in the achieved solution.

An power and bound-aware optimised scheduler for virtualized cloud computing

Cloud computing has become a crucial paradigm for large-scale data-intensive applications, but it also brings challenges like energy consumption, execution time, heat, and operational costs. Improving workflow scheduling in cloud environments can address these issues and optimize resource utilization, leading to significant ecological and financial benefits. As data centres and networks continue to expand globally, efficient scheduling becomes even more critical for achieving better performance and sustainability in cloud computing. Schedulers mindful of energy and deadlines will assign resources to jobs in a way that consumes the least energy while upholding the task’s quality standards. Because this scheduling involves a Non-deterministic Polynomial (NP)-hard problem, the schedulers are able to minimize complexity by utilizing metaheuristic techniques. This work has developed methods like Artificial Bee Colony (ABC), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) for optimizing the scheduler. Local search and exploration are respectably supported by heuristic algorithms. The algorithm’s exploration and exploitation features must also be balanced. The primary objective is to optimize computation-intensive workflows in a way that minimizes both energy consumption and execution time while maximizing throughput. This optimization should be achieved without compromising the Quality of Service (QoS) guarantee provided to users. The focus is on striking a balance between energy efficiency and performance to enhance the overall efficiency and cost-effectiveness of cloud computing environments. According to the simulation findings, the suggested ABC has a higher guarantee ratio for 5000 jobs when compared to the GA, PSO, GA with the longest processing time, and GA with the lowest processing time, by 7.14 percent, 4.7 percent, 3.5 percent, and 2.3 percent, respectively. It is observed that the proposed ABC possesses qualities like high flexibility, great robustness, and quick convergence leading to good performance.

Real Coded Binary Artificial Bee Colony (RC-BABC) Based Feature Selection and Relieff Based Feature Extraction Techniques for Heart Disease Prediction

Diagnosing heart disease is really a challenging task for which several intelligent diagnostic systems were developed for enhancing the performance of diagnosing heart disease. However, in these systems, low accuracy of predicting heart disease is still a challenging task. To provide better accuracy in predicting heart risks, a novel feature selection approach is proposed which employs Real Coded Binary Artificial Bee Colony (RC-BABC) optimization algorithm with adaptive size for feature elimination. This method has the advantages of reducing algorithmic computational time, improving prediction accuracy, enhanced data quality, and saves resources in successive data collection phases. Once the features are selected, the important feature extraction phase uses ReliefF based feature extraction method to extract the features from the heart disease data set. The scores of features are computed by estimating a comparison of feature values and class values neighbor samples. The proposed Real Coded Binary Artificial Bee Colony (RC-BABC) optimization algorithm is compared with three well known methods namely an artificial neural network (ANN), K-means clustering approach and Classification and Regression Algorithm (C&RT) with measures like accuracy, precision, recall and F1-score. The proposed method achieved 96.77% of accuracy,98.8% of recall, 97.8% of precision and 98.34% of F1-score.

Energy Efficient CH Selection Scheme Based on ABC and Q-Learning Approaches for IoUT Applications

Nowadays, the Internet of Underwater Things (IoUT) provides many marine 5G applications. However, it has some issues with energy efficiency and network lifetime. The network clustering approach is efficient for optimizing energy consumption, especially for underwater acoustic communications. Recently, many algorithms have been developed related to clustering-based underwater communications for energy efficiency. However, these algorithms have drawbacks when considered for heterogeneous IoUT applications. Clustering efficiency in heterogeneous IoUT is influenced by the uniform distribution of cluster heads (CHs). As a result, conventional schemes are inefficient when CHs are arranged in large and dense nodes since they are unable to optimize the right number of CHs. Consequently, the clustering approach cannot improve the IoUT network, and many underwater nodes will rapidly consume their energies and be exhausted because of the large number of clusters. In this paper, we developed an efficient clustering scheme to effectively select the best CHs based on artificial bee colony (ABC) and Q-learning optimization approaches. The proposed scheme enables an effective selection of the CHs based on four factors, the residual energy level, the depth and the distance from the base station, and the signal quality. We first evaluate the most suitable swarm algorithms and their impact on improving the CH selection mechanism. The evaluated algorithms are generic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO), and ABC. Then, the ABC algorithm process is improved by using the Q-learning approach to improve the process of ABC and its fitness function to optimize the CH selection. We observed from the simulation performance result that an improved ABC-QL scheme enables efficient selection of the best CHs to increase the network lifetime and reduce average energy consumption by 40% compared to the conventional ABC.

A NOVEL AND HYBRID WHALE OPTIMIZATION WITH RESTRICTED CROSSOVER AND MUTATION BASED FEATURE SELECTION METHOD FOR ANXIETY AND DEPRESSION.

Anxiety and depression are two leading human psychological disorders. In this work, several swarm intelligence-based metaheuristic techniques have been employed to find an optimal feature set for the diagnosis of these two human psychological disorders. To diagnose depression and anxiety among people, a random dataset comprising 1128 instances and 46 attributes has been considered and examined. The dataset was collected and compiled manually by visiting the number of clinics situated in different cities of Haryana (one of the states of India). Afterwards, nine emerging meta-heuristic techniques (Genetic algorithm, binary Grey Wolf Optimizer, Ant Colony Optimization, Particle Swarm Optimization, Artificial Bee Colony, Firefly Algorithm, Dragonfly Algorithm, Bat Algorithm and Whale Optimization Algorithm) have been employed to find the optimal feature set used to diagnose depression and anxiety among humans. To avoid local optima and to maintain the balance between exploration and exploitation, a new hybrid feature selection technique called Restricted Crossover Mutation based Whale Optimization Algorithm (RCM-WOA) has been designed. The swarm intelligence-based meta-heuristic algorithms have been applied to the datasets. The performance of these algorithms has been evaluated using different performance metrics such as accuracy, sensitivity, specificity, precision, recall, f-measure, error rate, execution time and convergence curve. The rate of accuracy reached utilizing the proposed method RCM-WOA is 91.4%. Depression and Anxiety are two critical psychological disorders that may lead to other chronic and life-threatening human disorders. The proposed algorithm (RCM-WOA) was found to be more suitable compared to the other state of art methods.

Actuator fault estimation using optimization-based learning techniques for linear parameter varying systems with unreliable scheduling parameters

A novel fault diagnosis procedure is proposed in this paper to estimate faults using a linear parameter varying (LPV) model whose scheduling parameters depend on the fault. A wrong determination of the operating conditions could lead the system to an undesired performance or even to an unstable situation, when classical fault diagnosis approaches are applied. This paper addresses this issue by formulating fault diagnosis as a dynamic optimization problem, solved by using a novel hybrid technique that combines a Luenberger-based observer with artificial intelligent (AI) optimization-based algorithms. The observer supervises the health of the system, while AI-based algorithms are able to reconstruct the faulty signal in real-time when the observer determines that the system is under a fault. The efficiency of the proposed fault diagnosis scheme, the three AI-based algorithms based on artificial bee colony and particle swarm optimization, and the gradient-based algorithm developed in this paper, are assessed using a numerical example.

Efficient reinforcement learning-based method for plagiarism detection boosted by a population-based algorithm for pretraining weights

Plagiarism detection (PD) in natural language processing involves locating similar words in two distinct sources. The paper introduces a new approach to plagiarism detection utilizing bidirectional encoder representations from transformers (BERT)-generated embedding, an enhanced artificial bee colony (ABC) optimization algorithm for pre-training, and a training process based on reinforcement learning (RL). The BERT model can be incorporated into a subsequent task and meticulously refined to function as a model, enabling it to apprehend a variety of linguistic characteristics. Imbalanced classification is one of the fundamental obstacles to PD. To handle this predicament, we present a novel methodology utilizing RL, in which the problem is framed as a series of sequential decisions in which an agent receives a reward at each level for classifying a received instance. To address the disparity between classes, it is determined that the majority class will receive a lower reward than the minority class. We also focus on the training stage, which often utilizes gradient-based learning techniques like backpropagation (BP), leading to certain drawbacks such as sensitivity to initialization. In our proposed model, we utilize a mutual learning-based ABC (ML-ABC) approach that adjusts the food source with the most beneficial results for the candidate by considering a mutual learning factor that incorporates the initial weight. We evaluated the efficacy of our novel approach by contrasting its results with those of population-based techniques using three standard datasets, namely Stanford Natural Language Inference (SNLI), Microsoft Research Paraphrase Corpus (MSRP), and Semantic Evaluation Database (SemEval2014). Our model attained excellent results that outperformed state-of-the-art models. Optimal values for important parameters, including reward function are identified for the model based on experiments on the study dataset. Ablation studies that exclude the proposed ML-ABC and reinforcement learning from the model confirm the independent positive incremental impact of these components on model performance.

Voice pathology detection using optimized convolutional neural networks and explainable artificial intelligence-based analysis

This article proposes a noninvasive computer-aided assessment approach based on optimized convolutional neural network for healthy and pathological voice detection. Firstly, the input voice samples are first transformed into mel-spectrogram time-frequency visual representations and fed for training the CNN model. The time-frequency image captures inherent speech variations beneficial for healthy and pathological voice sample detection. The weights and biases of trained CNN network are further optimized using artificial bee colony (ABC) optimization algorithm resulting in optimum CNN network employed for testing unseen data. The proposed approach is evaluated using three popular and publicly available datasets: SVD, AVPD and VOICED. Experimental results emphasize that proposed ABC optimized CNN model shows improved accuracy performance by 1.02% compared to conventional CNN network illustrating data-independent discriminative representation ability. Finally, gradient-weighted class activation mapping (Grad-CAM) explainable artificial intelligence (XAI) is utilized to make the decision understandable.

Performance evaluation of evolutionary algorithms for analog integrated circuit design optimisation

An automated sizing approach for analog circuits using evolutionary algorithms is presented in this paper. A targeted search of the search space has been implemented using a particle generation function and a repair-bounds function that has resulted in faster convergence to the optimal solution. The algorithms are tuned and modified to converge to a better optimal solution with less standard deviation for multiple runs compared to standard versions. Modified versions of the artificial bee colony optimisation algorithm, genetic algorithm, grey wolf optimisation algorithm, and particle swarm optimisation algorithm are tested and compared for the optimal sizing of two operational amplifier topologies. An extensive performance evaluation of all the modified algorithms showed that the modifications have resulted in consistent performance with improved convergence for all the algorithms. The implementation of parallel computation in the algorithms has reduced run time. Among the considered algorithms, the modified artificial bee colony optimisation algorithm gave the most optimal solution with consistent results across multiple runs.

Dynamic Optimal Power Flow for Grid-Connected Multi-Microgrid System considering Outage of Energy Sources

Recently multi-microgrid (MMG) system has attained additional attention because of significant assimilation of renewable energy sources, enhanced efficacy, reliability and stability through harmonization as well as cooperation of power swap amongst the microgrids (MGs). In this manuscript, dynamic optimal power flow (DOPF) for grid-connected MMG integrated demand response program (DRP) with and without energy source’s outage is presented. Total cost over the entire time-period considering instinctive characteristics of different phases is minimized. Power swap between grid and each MG is bidirectional. Each MG comprises small hydro power plants (SHPPs), solar PV plants (SPVPs), wind turbine generators (WTGs), bioenergy power plants (BPPs) and plug-in electric vehicles (PEVs). MMG used here comprises MG 1 including IEEE 33-bus system, MG 2 including 15-bus system and MG 3 including IEEE 69-bus system. This DOPF problem is solved by using quasi-oppositional fast convergence real coded genetic algorithm (QOFCRCGA), self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients (HPSO-TVAC), differential evolution (DE), artificial bee colony (ABC) optimization, fast convergence real coded genetic algorithm (FCRCGA) and real coded genetic algorithm (RCGA).