Moth Flame Optimization Research Articles

Weighted sum method based multi-objective optimal power flow considering various objectives: an application of whale optimization algorithm

Nowadays, multi-objective optimization plays a vital role in solving optimal power flow problems. Multi-objective optimal power flow (MOOPF) is a nonlinear optimization problem aimed at optimizing control variables while balancing multiple objective functions and satisfying both equality and inequality constraints and addresses this by integrating two more objectives into a single objective using a weighting factor. In this paper this weighted sum type multi-objective technique has been used to formulate the objective function. The whale optimization algorithm (WOA) has been used to reduce the cost, emission, losses, and voltage stability by considering various multi objectives like fuel cost along with emission, fuel cost with losses, fuel cost with voltage stability, fuel cost with voltage deviation and finally fuel cost with emission, losses, voltage deviation. In this paper, the IEEE 30 bus structure has been used to analyze the effect of WOA on the improvement of system performance. Obtained results with WOA have been compared with other optimization techniques like ensemble constraint handling technique with differential evolution (ECHT-DE), the superiority of feasible differential evolution (SF-DE), moth swarm algorithm (MSA), and moth-flame optimization (MFO), available in the literature.

COMPARISON OF CHOSEN METAHEURISTIC ALGORITHMS FOR THE OPTIMIZATION OF THE ABRASIVE WATER JET TREATMENT PROCESS

Abrasive waterjet machining (AWJ) is characterized by significantly better efficiency and better precision for difficult-to-machine materials than conventional machining technologies. However, the larger number of control parameters characterizing this process needs optimization. The study compares the performance of three nature-inspired metaheuristic algorithms, ALO, GWO, and MFO for optimizing the abrasive water jet (AWJ) treatment. The Response Surface Methodology was used to determine the cost function. The study evaluates the convergence and computational cost of the algorithms to aid future developments in this field. The study aims to maximize the cutting thickness by predicting the optimal water-abrasive cutting parameters (nozzle diameter, abrasive concentration, feed speed). For all three algorithms, the maximum cutting depth was determined to be 87.47 mm, which differs only less than 3% from the actual value. The results highlight the potential of ant-lion optimization (ALO), grey wolf optimizer (GWO), and (MFO) moth-flame optimization algorithms for resolving optimization issues in AWJ machining.

Prediction and reliability analysis of ultimate axial strength for outer circular CFRP-strengthened CFST columns with CTGAN and hybrid MFO-ET model

This study develops a novel hybrid machine learning model to estimate the ultimate axial strength and conduct a reliability analysis for outer circular carbon fiber-reinforced polymer (CFRP)-strengthened concrete-filled steel tube (CFST) columns. The experimental datasets are collected and enriched using the conditional tabular generative adversarial network (CTGAN). The column length, the steel properties (cross-section diameter, thickness, and yield strength), the CFRP properties (thickness, tensile strength, and elastic modulus), and concrete strength are selected as input variables to develop the Extra Trees (ET) model hybridized with Moth-Flame Optimization (MFO) algorithm for the ultimate axial strength estimation. The results reveal that the CTGAN can efficiently capture the actual data distribution of CFRP-strengthened CFST columns and the developed hybrid MFO-ET model can accurately predict the ultimate axial strength with a high accuracy (R2 of 0.985, A10 of 0.867, RMSE of 182.810 kN, and MAE of 124.534 kN) based on the synthetic database. In addition, compared with the best empirical model, the MFO-ET model increases the R2 by (6.78% and 13.48%) and A10 by (108.19% and 122.88%) and reduces the RMSE by (68.19% and 66.24%) and MAE by (71.33% and 68.48%) based on real and synthetic databases, respectively. Notably, a reliability analysis is performed to evaluate the safety of the developed MFO-ET model using Monte Carlo Simulation (MCS). Finally, a web application tool is created to make the developed MFO-ET model easier for users to design practical applications.

AI-optimization operation of biomass-based distributed generator for efficient radial distribution system

This research aims to optimize the size and location of biomass-based distributed generator (BMDG) units to enhance the voltage profile, reduce electrical losses, maximize cost savings, and decrease emissions from power distribution systems. Biomass-based distributed generator (BMDG) systems offer numerous advantages to enhance the efficiency of power distribution systems. However, achieving these benefits relies on determining the optimal size and position of the BMDGs. To achieve these objectives, the metaheuristic technique called particle swarm optimization (PSO) is employed to find the optimal placement and size of BMDGs. The proposed model was validated on MATLAB's IEEE-33 bus radial distribution system (RDS), confirming the aforementioned benefits. Comparative analysis between the PSO-based technique and other algorithms from previous research revealed better results with the proposed method. The results indicate that optimal placement and sizing of BMDG units have led to a reduction of more than 67.68% in active power losses and 65.90% in reactive power losses compared to the base case. Additionally, the reduction in active power loss was 40.44%, 11.39%, 42.85%, 1.81%, 0.85%, 29.83%, 5.82% and 28.38% more than artificial bee colony, backtracking search optimization algorithm, moth-flame optimization, Coordinate control, artificial Hummingbird algorithm, variable constants PSO (VCPSO), artificial gorilla troops optimizer (AGTO), and a jellyfish search optimizer respectively. Furthermore, the reactive power losses were reduced by 38.33% and 15.68% compared to VCPSO and AGTO respectively. Furthermore, this study revealed a cost reduction of 6.38% when compared to the AGTO and 1.30% when compared to the AHA. Moreover, the voltage profile of the power distribution system was improved by 7.28%. The presented methodology has demonstrated promising results for BMDGs in RDS across various applications.

Proxy model of constant-rate mercury intrusion experiment for low-permeability reservoir based on meta-learning

Pore structure parameters are used to characterize the reservoir pore structure and are crucial for evaluating and developing reservoirs for low-permeability reservoirs. However, traditional experiments to obtain pore structure parameters such as constant-rate mercury injection (CMI) can be time-consuming and expensive. To reduce the cost of obtaining these parameters, this study proposes using meta-learning as a proxy model for CMI experiments. We developed six meta-learning models: gray wolf optimizer extreme learning machine, whale optimization algorithm extreme learning machine (WOA-ELM), moth-flame optimization extreme learning machine, gray wolf optimizer support vector regression, whale optimization algorithm support vector regression, and moth-flame optimization support vector regression. These models were used as proxies for CMI and trained with conventional and experimental rock data to predict porous structure parameters such as average throat radius (ATR), maximum throat radius, variance, relative sorting coefficient (RSC), and uniformity coefficient. We compared our models with ten conventional proxy models. The results indicate that the WOA-ELM achieved the best performance, with an R2 (R-squared) of 90.1%, a mean absolute error of 0.4522, and a root mean square error of 0.3852. Compared to conventional models, this represents an improvement in R2 of 14.66%–30.46%. The meta-learning models also achieved the highest prediction accuracy in average throat radius (with R2 up to 96.58%) and showed an improvement (with R2 up to 91.21%) in relative sorting coefficient and uniformity coefficient, indicating the advantages of the meta-learning model in the prediction of pore homogeneity.

Address wind farm layout problems by an adaptive moth-flame optimization algorithm

As a clean renewable energy source, wind energy has been widely used to generate electricity in wind farms. Plenty of turbines work together to form a wind farm to increase electricity output. However, this produces an inevitable wake effect, which affects the efficiency of turbines in capturing wind energy, further leading to a decrease in the power generated by wind farms. To minimize the wake effect, optimizing the turbines layout in wind farms is necessary. Therefore, an adaptive Moth-Flame Optimization algorithm with enhanced Exploration and Exploitation capabilities (MFOEE) is proposed. The refinements of the algorithm include: i) defining a selection probability to utilize diverse information of moths; ii) an enhanced exploitation strategy by pushing moths towards the best flame; iii) developing an enhanced exploration strategy, in which three moths exchange information and two inferior moths fly to the superior moth. To validate the performance of MFOEE, four scenarios are set up using grid-based simulations of actual wind farm conditions. The experimental findings demonstrate that MFOEE can offer the most optimal scheme among the four scenarios, which indicates that MFOEE proves highly effective in addressing wind farm layout optimization challenges.

Machine learning based system for early heart disease detection and classification using audio signal processing approach

Cardiovascular diseases (CVDs) remain a leading cause of mortality globally, accounting for approximately 17.9 million deaths annually. Traditional diagnostic methods, though useful, have limitations such as invasiveness, high cost, and delays in detecting early-stage heart conditions. This study presents a novel machine learning-based system for early heart disease detection using audio signal processing, specifically leveraging phonocardiogram (PCG) data. Features were extracted using Mel-Frequency Cepstral Coefficients (MFCCs), Delta MFCCs, and Delta-Delta MFCCs, followed by dimensionality reduction via Principal Component Analysis (PCA). Support Vector Machine (SVM) and XGBoost classifiers were used to analyze the extracted features, and their performance was optimized through an ensemble model using the Moth Flame Optimization (MFO) algorithm. The model was rigorously evaluated using accuracy, precision, recall, and F1-score metrics. The ensemble model achieved an accuracy of 99.13%, precision of 98.94%, recall of 95.05%, and an F1-score of 97.46%. The application of SMOTE for data augmentation significantly improved classification performance, highlighting its effectiveness in addressing class imbalance. The proposed system provides a non-invasive, cost-effective solution for heart disease detection and holds potential for improving diagnostic access, particularly in resource-limited settings.

Optimizing the Bidding Data for power industry with elastic demand using hybrid Water Cycle Moth Flame Optimization Algorithm

Strategic Optimal Bidding of the data is a compulsory duty for Independent System Operator (ISO) which is the most complicated task that maximizes the profit of the supplier by handling bidding coefficient strategically. This paper endorses a strategy of optimal bidding coefficient data to improve the profit value by latest optimizing technique named hybrid Water Cycle Moth Flame Optimization Algorithm, which achieves a heuristic search thereby obtaining a global search of a stream using Levy flight movement. This method is applied and tested on an Indian-75 Bus system to test and investigate the new strategy whether receiving best solution of profit in comparison with other conventional techniques explained widely. On adding it evaluates the efficacy of the proposed method on the mentioned system through assessing total profit obtained, revenue, power generation, Market Clearing Price and cost of the individual GENCO. In order to show the Statistical Analysis the Box-plot is done to perform the visual data representation of the proposed and conventional methods.

Energy management and demand side management framework for nano-grid under various utility strategies and consumer’s preference

This research proposes a day-ahead scheduling utilizing both demand side management (DSM), and Energy Management (EM) in a grid-tied nanogrid comprises of photovoltaic, battery, and diesel generator for optimizing the generation cost and the energy not supplied (at grid-outage). Wider terminology is introduced to combine both load controllability (considered in traditional DSM), and interval capability to accommodate additional loads defined as flexible, non-flexible, and semi-flexible intervals. Moreover, the user selection for EM or combined operation of EM with DSM at different degrees of interval flexibility is defined as user preference. In addition, three utility’s operations are considered denoted as fixed rate pricing (FRP), time-of-use (ToU) pricing, and FRP with grid-outage. Hence, the suggested framework utilizes the opportunities of generation diversity, the electricity pricing strategy, and the load flexibility. The obtained result show that, DSM with flexible intervals reduces the cost by 21.02%, 25.23%, and 18.15% for FRP, ToU, and FRP with grid-outage scenarios respectively. And cost reduction by 20.41%, 22.42%, and 17.81% for DSM with semi-flexible intervals and 16.24%, 21.15%, and 13.8% for DSM with non-flexible intervals. This cost reduction is associated with full utilization of renewable energy generation and reduction of the energy from/to battery which enhances its lifetime or reduces the required battery size during design stage for cost and provisions saving in flexible and semi-flexible intervals. A hybrid optimization technique of Moth-flame optimization algorithm, and Lagrange’s multiplier is proposed and confirms its effectiveness with detailed comparison with other techniques.

Economic Load Dispatch Problem Analysis Based on Modified Moth Flame Optimizer (MMFO) Considering Emission and Wind Power

In electrical power system engineering, the economic load dispatch (ELD) problem is a critical issue for fuel cost minimization. This ELD problem is often characterized by non-convexity and subject to multiple constraints. These constraints include valve-point loading effects (VPLEs), generator limits, emissions, and wind power integration. In this study, both emission constraints and wind power are incorporated into the ELD problem formulation, with the influence of wind power quantified using the incomplete gamma function (IGF). This study proposes a novel metaheuristic algorithm, the modified moth flame optimization (MMFO), which improves the traditional moth flame optimization (MFO) algorithm through an innovative flame selection process and adaptive adjustment of the spiral length. MMFO is a population-based technique that leverages the intelligent behavior of flames to effectively search for the global optimum, making it particularly suited for solving the ELD problem. To demonstrate the efficacy of MMFO in addressing the ELD problem, the algorithm is applied to four well-known test systems. Results show that MMFO outperforms other methods in terms of solution quality, speed, minimum fuel cost, and convergence rate. Furthermore, statistical analysis validates the reliability, robustness, and consistency of the proposed optimizer, as evidenced by the consistently low fitness values across iterations.

An Innovative Enhanced JAYA Algorithm for the Optimization of Continuous and Discrete Problems

Metaheuristic algorithms have gained popularity in the past decade due to their remarkable ability to address various optimization challenges. Among these, the JAYA algorithm has emerged as a recent contender that demonstrates strong performance across different optimization problems, largely attributed to its simplicity. However, real-world problems have become increasingly complex in today’s era, creating a demand for more robust and effective solutions to tackle these intricate challenges and achieve outstanding results. This article proposes an enhanced JAYA (EJAYA) method that addresses its inherent shortcomings, resulting in improved convergence and search capabilities when dealing with diverse problems. The current study evaluates the performance of the proposed optimization methods on both continuous and discontinuous problems. Initially, EJAYA is applied to solve 20 prominent test functions and is validated by comparison with other contemporary algorithms in the literature, including moth–flame optimization, particle swarm optimization, the dragonfly algorithm, and the sine–cosine algorithm. The effectiveness of the proposed approach in discrete scenarios is tested using feature selection and compared to existing optimization strategies. Evaluations across various scenarios demonstrate that the proposed enhancements significantly improve the JAYA algorithm’s performance, facilitating escape from local minima, achieving faster convergence, and expanding the search capabilities.

High-Efficiency Finite Element Model Updating of Bridge Structure Using a Novel Physics-Guided Neural Network

An accurate finite element model (FEM) plays a critical role in the structural damage identification. However, due to the existence of the uncertainties, such as material properties and modeling errors, it always exists some gaps between the analytical FEM and experimental structure. While an artificial neural network (ANN)-based model updating methods have been widely adopted to narrow the gap and obtain a baseline FEM, it still faces inaccurate results and fails to meet the physical law. In this regard, the study proposes a novel physics-based loss function inspired by modal sensitivity analysis and incorporates it into the residual neural network, thereby forming a novel physics-guided neural network (PGNN) method. The mapping relationship between the input of structural responses and output of model updating variables is constrained to retain its physical meaning by guiding the training process instead of pure data association, which aims to improve the accuracy of the ANN-based method and achieve accurate and high-efficiency model updating. An experimental example of a continuous rigid frame bridge is adopted to verify the feasibility of the proposed method. Additionally, other common model updating methods, including moth-flame optimization and regularization method, are used to make a comparison. The noise-robustness of the proposed method is investigated as well. Compared to the existing method, the results illustrate that the proposed PGNN method can achieve better model updating and good noise-robustness under high uncertainties, which means the introduction of the physics-based loss function significantly enhances the parameters updating ability of the neural network. The proposed method exhibits high efficiency and promising potential for large-scale bridge structure model updating.

Solving Optimal Power Flow Using New Efficient Hybrid Jellyfish Search and Moth Flame Optimization Algorithms

This paper presents a new optimization technique based on the hybridization of two meta-heuristic methods, Jellyfish Search (JS) and Moth Flame Optimizer (MFO), to solve the Optimal Power Flow (OPF) problem. The JS algorithm offers good exploration capacity but lacks performance in its exploitation mechanism. To improve its efficiency, we combined it with the Moth Flame Optimizer, which has proven its ability to exploit good solutions in the search area. This hybrid algorithm combines the advantages of both algorithms. The performance and precision of the hybrid optimization approach (JS-MFO) were investigated by minimizing well-known mathematical benchmark functions and by solving the complex OPF problem. The OPF problem was solved by optimizing non-convex objective functions such as total fuel cost, total active transmission losses, total gas emission, total voltage deviation, and the voltage stability index. Two test systems, the IEEE 30-bus network and the Mauritanian RIM 27-bus transmission network, were considered for implementing the JS-MFO approach. Experimental tests of the JS, MFO, and JS-MFO algorithms on eight well-known benchmark functions, the IEEE 30-bus, and the Mauritanian RIM 27-bus system were conducted. For the IEEE 30-bus test system, the proposed hybrid approach provides a percent cost saving of 11.4028%, a percent gas emission reduction of 14.38%, and a percent loss saving of 50.60% with respect to the base case. For the RIM 27-bus system, JS-MFO achieved a loss percent saving of 50.67% and percent voltage reduction of 62.44% with reference to the base case. The simulation results using JS-MFO and obtained with the MATLAB 2009b software were compared with those of JS, MFO, and other well-known meta-heuristics cited in the literature. The comparison report proves the superiority of the JS-MFO method over JS, MFO, and other competing meta-heuristics in solving difficult OPF problems.

Synergetic UPQC Application for Power Quality Enhancement in Microgrid Distribution System: SCSO Approach

Nowadays, Hybrid renewable energy systems (HRES) are increasingly being integrated into grid-connected load systems to lower losses and boost dependability. When the HRES system is connected to the grid system to satisfy needed load demand, power quality issues arise because of imbalanced load circumstances, non-linear load, and critical load. So this manuscript proposed a synergetic Unified Power Quality Conditioner (UPQC) application for power quality enhancement in microgrid distribution systems. The Sand Cat Swarm Optimization (SCSO) technique is based on the proposed sand cat swarm optimization method. The proposed strategy's primary goal is to regulate power flow, minimize harmonic distortion in both voltage and current waveforms, and maximize UPQC. By then, the proposed method's performance has been implemented into practice on the MATLAB platform and contrasted with several currently used techniques. The proposed technique displays the low Total Harmonic Distortion (THD) and operation time in all existing approaches like Moth Flame Optimization (MFO), Genetic Algorithm (GA), Salp Swarm Algorithm (SSA), Ant Lion Optimizer (ALO), Improved Bat Search Algorithm (IBSA), Lion Algorithm (LA), Artificial Bee Colony (ABC), Atom Search Optimization (ASO) and Crow Search Algorithm (CSA). The proposed method attains THD as before UPQC is 31%, after UPQC is 3%, load current is 1.42%, and load voltage is 2%. It also achieves a low operation time of 506ms and a low settling time of 0.15s compared to the existing methods. The significant improvement in power quality metrics demonstrates the effectiveness of the proposed SCSO technique.

The superiority of feasible solutions-moth flame optimizer using valve point loading

The optimal power flow (OPF) problem deals with large-scale, nonlinear, and non-convex optimization challenges, often accompanied by stringent constraints. Apart from the primary operational objectives of an energy system, ensuring load bus voltages remain within acceptable ranges is essential for providing high-quality consumer services. The Moth-Flame Optimizer (MFO) method is inspired by the unique night flight characteristics of moths. Moths, much like butterflies, undergo two distinct life stages: larval and mature. They have evolved the ability to navigate at night using a technique called transverse orientation. This article presents a methodology for determining the optimal energy transmission system configuration by integrating power producers. The MFO, Grey Wolf Optimizer (GWO), Success-history-based Parameter Adaptation Technique of Differential Evolution - Superiority of Feasible Solutions (SHADE-SF), and Superiority of Feasible Solutions-Moth Flame Optimizer (SF-MFO) algorithms are applied to address the OPF problem with two objective functions: (1) reducing energy production costs and (2) minimizing power losses. The efficiency of MFO, SF-MFO, SHADE-SF, and GWO for the OPF challenge is evaluated using IEEE 30-feeder and IEEE 57-feeder systems. Based on the collected data, SF-MFO demonstrated the best performance across all simulated instances. For instance, the electricity production costs generated by SF-MFO are $845.521/hr and $25,908.325/hr for the IEEE 30-feeder and IEEE 57-feeder systems, respectively. This represents a cost savings of 0.37 % and 0.36 % per hour, respectively, compared to the lowest values obtained by other comparative methods.

Maximum power point tracking controller for photovoltaic system based on chaos quantum particle swarm optimization – moth-flame optimization hybrid model

To convert photovoltaic arrays to solar energy in a more efficient way, this paper has proposed a maximum power point tracking controller model based on the chaotic quantum particle swarm-mothballing hybrid algorithm. First, the optimization of the particle swarm algorithm is designed to solve defects, such as premature maturity by using the quantum and chaotic strategies. The mothballing algorithm is introduced to help the model find global optimization-seeking more quickly. After that, further optimization was made to operate the tracking model in both offline and real-time parameters. The conductivity increment method and the perturbation observation method were adopted to effectively track the model under different temperatures and light intensities. Finally, the simulation and analysis experiments were carried out on the Simulink platform. The study’s proposed maximum power point tracking controller achieved a steady-state accuracy η2 of 99.84%. In summary, the study has proposed a hybrid intelligent algorithm with extraction of internal parameters. The maximum power point tracker based on the proposed method is proved to be both effective and accurate.

Optimal sizing of islanded microgrid using pelican optimization algorithm for Kutubdia Island of Bangladesh

This study proposes an optimal design approach, based on the Pelican Optimization Algorithm (POA), to configure the optimal sizing of design variables on an islanded microgrid: photovoltaic (PV) modules, wind turbines (WT), diesel generators (DG), and batteries in Kutubdia, Bangladesh based on optimal life cycle cost (LCC) and cost of energy (COE). Additionally, the economic analysis of three independent battery technologies, notably lead acid, lithium-ion, and nickel-iron are carried out to find the economically feasible technology, to ensure uninterrupted power supply. Moreover, reliability and sensitivity analyses of the optimized microgrid using POA were conducted for various reliability indices and variable interest rates. Results show that proposed POA method provides the optimal island microgrid configuration with lead acid (LA) batteries (PV/WT/LA/DG) based on a minimum LCC of $8334901, COE of 0.1080$/KWh and greenhouse gas emission amount of 19664 kgs/year. Furthermore, the outcomes generated by the POA are compared with genetic algorithm, particle swarm optimization, moth flame optimization algorithm, whale optimization algorithm and grey wolf optimization. It is found that POA method achieves more competitive results compared to other optimization techniques due to its ability to adjust parameters, fast convergence speed, and straightforward computations.

Effect of multi-unit and multi-type DG installation using integrated optimization technique in distribution power system planning

With the rise in load demand, improving the voltage profile and reducing line loss is vital to ensure reliable power delivery to the customer. However, increasing power plant generation capacity is limited by environmental and economic factors, requiring a careful assessment of locally optimal options. Distributed Generation (DG) installation into the electricity grid is one of the reliable remedial actions to ensure a smooth power delivery. Installation of DG requires an optimization process to identify the appropriate placement and sizing. Inaccurate sizing and placement of the DG installation may result to over-compensation or under-compensation phenomena. This paper proposes a novel approach termed the Integrated Immune Moth Flame Evolutionary Programming technique (IIMFEP) for optimizing the installation of DG sources in distribution systems. It handles various scenarios, including multi-DG single-type and multi-DG multi-type installations, with the main objective of minimizing power loss in the system. This technique employs a hybrid approach that combines elements of immune algorithms, moth flame optimization, and evolutionary programming to achieve more accurate and efficient results. Two cases were considered in this study termed Case 1 and Case 2. Results in Case 1 discovered that the optimal sizing and placement of four Type III DGs exhibit the lowest power loss worth 2.74 kW (98.78 % reduction) for the 69-Bus RDS, while for the 118-Bus RDS the power loss is 319.89 kW (75.36 % reduction). In Case Study 2, the combination of DG Types I and III provided the highest power loss reduction. With one DG Type I and two DG Type III units installed, power loss was reduced by 97.15 % to 6.41 kW for the 69-Bus RDS and by 62.01 % to 493.21 kW for the 118-Bus RDS. The proposed IIMFEP managed to alleviate the setback experienced in the traditional EP, AIS and MFO which found to be stuck at local optimum. The IIMFEP method is compared to Moth Flame Optimization, Artificial Immune System and Evolutionary Programming and validated using the IEEE 69-Bus and 118-Bus Radial Distribution Systems, resulting in outstanding performance.

An enhanced Moth-Flame optimizer with quality enhancement and directional crossover: optimizing classic engineering problems

As a popular meta-heuristic algorithm, the Moth-Flame Optimization (MFO) algorithm has garnered significant interest owing to its high flexibility and straightforward implementation. However, when addressing engineering constraint problems with specific parameters, MFO also exhibits limitations such as fast convergence and a tendency to converge to local optima. In order to address these challenges, this paper introduces an enhanced version of the MFO, EQDXMFO. EQDXMFO integrates a Quality Enhancement (EQ) strategy and a Directional Crossover (DX) mechanism, fortifying the algorithm’s search dynamics. Specifically, the DX mechanism is designed to augment the population’s diversity, enhancing the algorithm’s exploratory potential. Concurrently, the EQ strategy is employed to elevate the solution quality, which in turn refines the convergence precision of the algorithm. To verify the effectiveness of EQDXMFO, experiments are carried out on the test set of the IEEE CEC2017. A total of 5 classical algorithms, five excellent MFO variants, and seven state-of-the-art algorithms are selected for comparison, which confirm the significant advantages of EQDXMFO. Next, EQDXMFO is applied to five complex engineering constraint problems, demonstrating that EQDXMFO can optimize realistic problems. The comprehensive analysis shows that EQDXMFO has strong optimization capabilities and provides methods for research on other complex real-world problems.

Deep contextual reinforcement learning algorithm for scalable power scheduling

This article introduces a deep contextual reinforcement learning (DCRL) optimization algorithm to tackle the NP-hard power scheduling problem. The algorithm is based on a multi-agent simulation environment that decomposes the power scheduling problem into sequential Markov decision processes (MDPs). The simulation environment inherently corrects incorrect decisions and adjusts supply capacities so that the MDPs adhere to the optimization constraints. A deep reinforcement learning (DRL) model is trained on these MDPs to provide optimal solutions. Demonstrating its applicability and effectiveness, the proposed method is evaluated on various test systems with different unit numbers, constraints, and production cost functions. The experimental results show that the proposed method has better performance relative to alternative methods, such as binary alternative moth-flame optimization (BAMFO), binary particle swarm optimization (BPSO), teaching learning-based optimization (TLBO), new binary particle swarm optimization (NBPSO), binary learning particle swarm optimization (BLPSO), quasi-oppositional teaching learning-based algorithm (QOTLBO), binary-real-coded genetic algorithm (BRCGA), hybrid genetic-imperialist competitive algorithm (HGICA), three-stage priority list (TSPL), and hybridized evolutionary algorithm and sequential quadratic programming (HEPSQP). The novelties of the proposed method lie in its adaptability to longer planning horizons and linear dimensionality complexity, rendering it suitable for large-scale power systems.