Emission Dispatch Problem Research Articles

An integrated binary metaheuristic approach in dynamic unit commitment and economic emission dispatch for hybrid energy systems

The current generation portfolio is obligated to incorporate zero-emissions energy sources, predominantly wind and solar, due to the depletion of fossil fuels and the alarming rate of global warming. In the current scenario, power engineers must devise a compromised solution that not only advocates for the adoption of renewable energy sources (RES) but also efficiently schedules all conventional power generation units to balance the increasing load demand while simultaneously minimizing fuel costs and harmful emissions that are currently addressed by Unit Commitment (UC) and Combined Economic Emission Dispatch (CEED) problem solutions. However, the integration of renewable energy resources (RES) further complicates the UC-CEED problem due to their intermittent nature. Recently, metaheuristic algorithms are acquiring momentum in resolving constrained UC-CEED problems due to their improved global solution ability, adaptability, and derivative-free construction. In this research, a computationally efficient binary hybrid version of crow search algorithm and improvised grey wolf optimization is proposed, namely Crow Search Improved Binary Grey Wolf Optimization Algorithm (CS-BIGWO) by inclusion of nonlinear control parameter, weight-based position updating, and mutation approach. Statistical results on standard mathematical functions prove the supremacy of the proposed algorithm over conventional algorithms. Further, a novel optimization strategy is devised by integrating enhanced lambda iteration with the CS-BIGWO algorithm (CS-BIGWO-λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}) to solve a day-ahead UC-CEED problem of the hybrid energy system incorporating cost functions of RES. For the model, a day-ahead forecast of wind power and solar photovoltaic power is obtained by using the Levy-Flight Chaotic Whale Optimization Algorithm optimized Extreme Learning Machines(LCWOA-ELM). The proposed algorithm is tested for the UC-CEED solution of an IEEE-39 bus system with two distinct cases: (1) without RES integration and (2) with RES integration. Several independent trial runs are executed, and the performance of the algorithms is assessed based on optimal UC schedules, fuel cost, emission quantization, convergence curve, and computational time. For case 1, the proposed algorithm resulted in a percentage reduction of 0.1021% in fuel cost and 0.7995% in emission. In contrast, for test case 2, it resulted in a percentage reduction of 0.12896% in fuel cost and 0.772% in emission with the proposed algorithm. The results validate the dominance of the proposed methodology over existing methods in terms of lower fuel costs and emissions.

An Improved Non-dominated Sorting Genetic Algorithm for the Optimal Economic Emission Dispatch Problem with Wind Power Sources

An Improved Non-dominated Sorting Genetic Algorithm for the Optimal Economic Emission Dispatch Problem with Wind Power Sources

A multi-objective robust dispatch strategy for renewable energy microgrids considering multiple uncertainties

The demand for low-carbon transformations and the uncertainty of renewable energy sources and loads present significant challenges for the optimal dispatch of microgrid. This study proposed a multi-objective robust dispatch strategy to reduce the risks associated with the uncertainty of renewable energy source output and loads while promoting low-carbon and economical microgrid operation. The economic emission dispatch problem for a microgrid was formulated as a multi-objective robust dual-layer optimization model. Consequently, a high-dimensional adjustable linear polyhedral uncertainty set was proposed to describe the uncertainty of renewable energy sources and loads. This study transformed the original model into an easy-to-solve single-layer second-order cone programming optimal power flow optimization model by employing second-order cone relaxation and duality transformation. Thereafter, a synthetic membership function was proposed to determine the optimal compromise solution. To determine the charging and discharging statuses of the battery storage system and the electricity traded between the microgrid and the external power grid, a battery storage system control strategy based on time-of-use electricity prices and real-time power flow calculations was proposed. Simulations conducted on a modified IEEE-30 bus system demonstrated that the proposed strategy effectively reduced the economic costs and carbon emissions of the microgrid by 8.23 % and 2.43 %, respectively.

Solving power system economic emission dispatch problem under complex constraints via dimension differential learn butterfly optimization algorithm with FDC-based

The economic emission dispatch (EED) aims to minimize the fuel and pollutant emission costs of generator units under various complex constraints. Optimizing the EED problem is of crucial importance for alleviating the current energy and environmental pressures. In this work, nearly all known complex constraints in the EED problem, including the valve-point effect, transmission line power loss, prohibited operating zones, and ramp-rate limits, are taken into account, and an enhanced version of butterfly optimization algorithm (FDCDLBOA) is proposed to solve it. First, a new adaptive fragrance is employed to optimize the instability caused by target differences and improve the convergence performance. Second, the proposed dimension differential learning strategy evolves the position of individuals with the help of superior dimensional information in the population, and this extensive learning exchange can balance global and local search, maintain diversity, and get rid of local optima. Third, the Fitness-Distance-Constraint (FDC) guide selection method is employed for the first time to handle the complex constraints of EED problems, enhancing the ability of individuals to bypass the infeasible search areas. After evaluating the proposed FDCDLBOA on CEC 2022 test suite, it is applied to solve 8 EED cases, encompassing small-, medium- and large-scale systems. Notably, the 280-generator case is the first large-scale test to exceed 200 generators. Compared with 9 representative algorithms, FDCDLBOA performs outstandingly in terms of robustness, improvement index (IF), mean constraint violation (MV), feasibility rate (FR) and Quade multiple comparison, among which IF, MV, FR, and Quade are all employed for evaluating the EED problem for the first time. The presented results confirm that the proposed method effectively enhances the robustness of high-quality solutions and the ability to handle complex constraints, demonstrating strong competitiveness and potential in solving the EED problem.

Multi-objective Approach for Dynamic Economic Emission Dispatch Problem Considering Power System Reliability and Transmission Loss Prediction Using Cascaded Forward Neural Network

This study addresses the significant problem of Dynamic Economic Emission Dispatch (DEED), a critical consideration in power systems from both economic and environmental protection viewpoints. Reliability stands as another vital facet, impacting maintenance and operation perspectives. The integration of Artificial Neural Network (ANN)-based transmission loss prediction into the DEED model is also essential to address specific limitations and enhance the overall performance of the dispatch process. Traditionally, the DEED model relies on a single B-loss coefficient to estimate transmission losses. While this approach simplifies calculations, it fails to account for the significant variations in demand that occur throughout the dispatch period and it leads to inaccuracies in loss prediction, especially in dynamic environments. Using a single coefficient, the model cannot adequately capture the complex, non-linear relationships between power generation, load, and transmission losses under different operating conditions. To overcome this limitation, this study introduces an ANN-based loss prediction method integrated into the DEED model and uses trained ANN to replace the process of finding B-loss coefficients during each dispatch period. This paper also introduces a strategy leveraging the multi-objective northern goshawk optimizer algorithm, characterized by a non-dominated sorting and crowding distance mechanism, to enhance DEED considerations incorporating reliability (DEEDR). This novel algorithm improves the solution space effectively, maintains high population diversity and enables an even distribution of individuals sharing the same rank in the objective space. The fundamental objective of this study is to balance fuel cost, emission, and system reliability in power system operations. Compared with a few existing multi-objective optimization algorithms, this study demonstrates superior performance in generating a series of non-dominated solutions. The experimental results highlight its competitive and potential as an efficient tool in the DEED and DEEDR problems, promising a synergistic coordination of economy, environmental protection, and system reliability benefits in power system management.

A Novel Hybrid Crow Search Arithmetic Optimization Algorithm for Solving Weighted Combined Economic Emission Dispatch with Load-Shifting Practice

The crow search arithmetic optimization algorithm (CSAOA) method is introduced in this article as a novel hybrid optimization technique. This proposed strategy is a population-based metaheuristic method inspired by crows’ food-hiding techniques and merged with a recently created simple yet robust arithmetic optimization algorithm (AOA). The proposed method’s performance and superiority over other existing methods is evaluated using six benchmark functions that are unimodal and multimodal in nature, and real-time optimization problems related to power systems, such as the weighted dynamic economic emission dispatch (DEED) problem. A load-shifting mechanism is also implemented, which reduces the system’s generation cost even further. An extensive technical study is carried out to compare the weighted DEED to the penalty factor-based DEED and arrive at a superior compromise option. The effects of CO2, SO2, and NOx are studied independently to determine their impact on system emissions. In addition, the weights are modified from 0.1 to 0.9, and the effects on generating cost and emission are investigated. Nonparametric statistical analysis asserts that the proposed CSAOA is superior and robust.

A new model of electrical cyber–physical systems considering stochastic communication link failures

This article establishes a model for electrical cyber–physical systems (ECPS), integrating the power grid, power information network and control network. The power grid is modelled based on DC power flow. The power information network enables the exchange of information between the power grid and control network. Stochastic communication link failure is a common problem in real control networks. To address this issue, this article models the control network as a Bernoulli network. The incorporation of an asynchronous gossip algorithm with price penalty factors enables the model to analyse multi-target combined economic emission dispatch problems (CEED) involving line losses in an imperfect control network. The effectiveness and validity of the model are illustrated through simulations.

Lévy arithmetic optimization for energy Management of Solar Wind Microgrid with multiple diesel generators for off-grid communities

This paper presents an improved optimization algorithm for the energy management of a renewable energy solar/wind microgrid with multiple diesel generators applied to off-grid remote communities. The main objective aims to solve the economic emission dispatch problem with a price penalty factor to minimize the energy cost and the emission level. An enhanced metaheuristic optimization algorithm, Lévy arithmetic algorithm, is applied to improve the searchability for optimal solution compared to the conventional arithmetic algorithm. The Lévy arithmetic method is used for the management of the microgrid and compared to other metaheuristic optimization algorithms for the same application. Comparative analysis demonstrates good cost savings using the Lévy arithmetic algorithm, compared to other optimization algorithms such as the arithmetic algorithm, crow search algorithm, hybrid modified grey wolf algorithm, interior search algorithm, cuckoo search algorithm, particle swarm algorithm, colony algorithm, and genetic algorithm.

An improved golden jackal optimization algorithm for combined economic emission dispatch problems

In this research paper, a new improved golden jackal optimization (IGJO) algorithm is applied to address the combined economic emission dispatch (CEED) problem, along with various thermal generator constraints such as valve point loading (VPL) effect, generator limits (GL) in power system. The hunting behavior of the golden jackals is mimicked in the golden jackal optimization (GJO) algorithm. The main aim of the CEED problem is to find the best optimal generation scheduling while minimizing both fuel cost and emission besides meeting the different power system constraints. The original GJO algorithm faces challenges when dealing with high-dimensional optimization problems, as it tends to get trapped in local optima. To address this issue the opposition-based learning (OBL) method was adopted in this GJO algorithm to obtain the global optimal solution and ensure enhanced performance in finding the solution for the CEED problems. To assess the competitiveness of the IGJO algorithm, it is used for various CEED test problems available in the literature, and results are contrasted with other recent heuristic optimization algorithms. Simulation results show that the proposed IGJO performs more effectively than the other compared algorithms in terms of solution quality, and robustness.

Multi-Objective Dynamic Economic and Emission Generation Scheduling of Coordinated Power System Considering Renewable Energy Sources and Pumped Storage Hydro Plants via Fuzzy Surrogate-Assisted Coronavirus Herd Immunity Optimization

Globally, the power generation from renewable energy sources (RES) has received considerable attention to reduce pollutant emissions and the total operating costs of power generation. In this context, this study aims to extend the multi-objective dynamic economic and emission dispatch (MODEED) problem by incorporating RES and pumped storage hydro plants. The complex constrained MODEED problem is solved by a fuzzy surrogate-assisted coronavirus herd immunity optimization (FSACHIO) algorithm in which a self-adaptive speed factor and Lévy flight mechanism are utilized to ensure populace diversity, prevent premature convergence and achieve an ideal stability among the exploration and exploitation of the algorithm. Surrogate worth tradeoff methodology is used to discover a solution that provides the optimal balance between the objectives such as operating expenses and emission pollutants. The performance of FSACHIO algorithm is validated on a small-scale and a large-scale test systems, involving 10-unit, and 40-unit test systems, and compared with that of the coronavirus herd immunity optimization, red fox optimizer, Remora optimization algorithm, and other erstwhile approaches. Besides, a fuzzy constraint handling method based on a dominance relationship is integrated to fulfill the restrictions of the MODEED problem. The simulation results reveal that: (i) the operating costs and emissions are reduced by 173785.54 $/day and 2992.1848 lb/day in the small-scale test system and by 6383.9903 $/day and 216631.4877 lb/day in the large-scale test system, respectively for the MODEED problem with the presence of RES and pumped storage hydro plants; (ii) the suggested approach may offer a well-distributed Pareto-optimal frontier and superior tradeoffs among the operating expenses and pollution objectives in comparison to the other approaches.

Modified Opposition-Based Particle Swarm Optimization for Combined Economic and Emission Dispatch Problem

Modification of the particle swarm optimization (PSO) method is proposed with an opposition-based learning strategy to find the optimal solution to electrical power dispatch problems. The objective of the proposed algorithm is to address the combined economic and emissions dispatch problem (CEED) of thermal power plants. This problem includes constraints such as the valve point effect, prohibited zones of operation, and ramp rate limits. In order to assess its performance, the proposed algorithm is first evaluated using a set of benchmark functions. Later, three thermal generating systems having 6, 10, and 40 units respectively are regarded as the test systems to validate the proposed method. The proposed method is tested, and a comparison of the results are made with popular optimization techniques reported in the literature such as PDE, MODE, NSGA II, and MOSSA. Promising results have been obtained with opposition-based PSO in comparison with their current equivalents. A comparison was made between the fuel cost, emissions, and CPU time of the proposed method with the two other PSO variants: inertia factor PSO (IFPSO) and constriction factor PSO (CFPSO). The results showed a decline in the overall cost by approximately 3.73% and a decrease in CPU time by as much as 2.6 s. Furthermore, the obtained predictions consistently exhibit a high level of accuracy, typically approaching 100%.

Multi-Objective Stochastic Paint Optimizer for Solving Dynamic Economic Emission Dispatch with Transmission Loss Prediction Using Random Forest Machine Learning Model

Dynamic economic emission dispatch problems are complex optimization tasks in power systems that aim to simultaneously minimize both fuel costs and pollutant emissions while satisfying various system constraints. Traditional methods often involve solving intricate nonlinear load flow equations or employing approximate loss formulas to account for transmission losses. These methods can be computationally expensive and may not accurately represent the actual transmission losses, affecting the overall optimization results. To address these limitations, this study proposes a novel approach that integrates transmission loss prediction into the dynamic economic emission dispatch (DEED) problem. A Random Forest machine learning model was offline-trained to predict transmission losses accurately, eliminating the need for repeated calculations during each iteration of the optimization process. This significantly reduced the computational burden of the algorithm and improved its efficiency. The proposed method utilizes a powerful multi-objective stochastic paint optimizer to solve the highly constrained and complex dynamic economic emission dispatch problem integrated with random forest-based loss prediction. A fuzzy membership-based approach was employed to determine the best compromise Pareto-optimal solution. The proposed algorithm integrated with loss prediction was validated on widely used five and ten-unit power systems with B-loss coefficients. The results obtained using the proposed algorithm were compared with seventeen algorithms available in the literature, demonstrating that the multi-objective stochastic paint optimizer (MOSPO) outperforms most existing algorithms. Notably, for the Institute of Electrical and Electronics Engineers (IEEE) thirty bus system, the proposed algorithm achieves yearly fuel cost savings of USD 37,339.5 and USD 3423.7 compared to the existing group search optimizer algorithm with multiple producers (GSOMP) and multi-objective multi-verse optimization (MOMVO) algorithms.

Integrating renewable energy sources and electric vehicles in dynamic economic emission dispatch: an oppositional-based equilibrium optimizer approach

ABSTRACT This article proposes a solution to the Dynamic Economic Emission Dispatch (DEED) problem, which incorporates wind, solar and plug-in electric vehicles (PEVs) into the optimization challenge. The new model, called Wind-Solar-Plug in Electric Vehicle (WSPEV) DEED, utilizes an optimization technique called the Oppositional-based Equilibrium Optimizer (OEO) method with the Weibull and Beta distributions to model wind and solar resources. The charging and discharging patterns of PEVs are also considered in the model. The proposed approach is evaluated through several scenarios involving Renewable Energy Sources (RESs) and PEVs, and the simulation results demonstrate the effectiveness of the proposed model in achieving a sustainable and cost-effective power system. The WSPEV DEED model provides a valuable solution to the DEED problem, which is crucial for successfully integrating RESs and PEVs into the power system for a sustainable future.

Multi-strategy enhanced kernel search optimization and its application in economic emission dispatch problems

Abstract The kernel search optimizer (KSO) is a recent metaheuristic optimization algorithm that is based on kernel theory, eliminating the need for hyper-parameter adjustments, and demonstrating excellent global search capabilities. However, the original KSO exhibits insufficient accuracy in local search, and there is a high probability that it may fail to achieve local optimization in complex tasks. Therefore, this paper proposes a multi-strategy enhanced KSO (MSKSO) to enhance the local search ability of the KSO. The MSKSO combines several control strategies, including chaotic initialization, chaotic local search mechanisms, the high-altitude walk strategy (HWS), and the Levy flight (LF), to effectively balance exploration and exploitation. The MSKSO is compared with ten well-known algorithms on 50 benchmark test functions to validate its performance, including single-peak, multi-peak, separable variable, and non-separable variable functions. Additionally, the MSKSO is applied to two real engineering economic emission dispatch (EED) problems in power systems. Experimental results demonstrate that the performance of the MSKSO nearly optimizes that of other well-known algorithms and achieves favorable results on the EED problem. These case studies verify that the MSKSO outperforms other algorithms and can serve as an effective optimization tool.

Application of the Slime Mould Algorithm on the Bi-Objective Environmental Economic Dispatch Problem

This paper investigates the performance of one of the latest metaheuristic swarm-based approaches called Slime Mould Algorithm (SMA). SMA is used here to solve the static bi-objective constrained Economic Emission Dispatch (EED) problem in the presence of renewable energy sources while considering the Valve-Point Effects (VPE). The SMA approach is applied to indicate the adequate optimal solutions for operating the committed thermal units under different operational constraints. The sought optimal solutions are the midpoint between cost saving and pollutant gas emission reduction. This study also examines the influence of integrating renewable energy sources (wind and solar) into the conventional power production network. SMA technique is applied on 3- and 6-unit IEEE test systems in several case studies. The simulation numerical results indicate that SMA has a high efficiency and a better performance compared to known state-of-the-art algorithms. The proposed approach was programmed and simulated in MATLAB.

A variegated GWO algorithm implementation in emerging power systems optimization problems

This paper proposes a novel hybrid algorithm which is mathematically modelled by amalgamating the superior features of recently developed Grey Wolf Optimizer (GWO), Sine Cosine Algorithm (SCA), and Crow Search Algorithm (CSA). Researchers have already implemented the aforementioned three algorithms and obtained superior quality results for solving diverse optimization problems. The novel hybrid Variegated GWO Algorithm (VGWO) developed in this proposed research work is initially realized and validated for solving IEEE CEC-C06 2019 benchmark functions. Thereafter, the proposed VGWO is utilized as an optimization tool to solve three emerging and complex power system optimization problems which includes energy management of microgrid systems operated in both islanded and grid-connected mode, dynamic economic emission dispatch and reactive power planning (RPP) problem. A comparative analysis of the proposed VGWO approach with other established metaheuristics is undertaken for each optimization problem. Numerical results show that the novel hybrid VGWO algorithm outperformed an ample number of optimization techniques in providing better quality solutions. The proposed hybrid algorithm yielded a 36.93% reduction in active power loss and 36.80% reduction in operating cost with respect to base case condition for RPP problem. Likewise while solving microgrid energy management problems 9–30% savings was realized in the generation cost compared to the ones mentioned in literature. The capability of handling many complex constraints within a minimum amount of computational time to provide consistently best solutions prioritize the proposed hybrid algorithm among its kinds. Statistical analysis validates the authenticity and viability of the proposed algorithm.

Combined heat and power economic emission dispatch using dynamic switched crowding based multi-objective symbiotic organism search algorithm

Combined heat and power economic emission dispatch (CHPEED) problem is a highly complex, non-linear, non-convex multi-objective optimization problem due to two conflicting objectives and various operational constraints such as valve-point loading effect, power transmission loss, prohibited operating zone, and the feasible operating region of combined heat and power unit. In order to overcome these challenges, it is necessary to design an algorithm that exhibits a search behavior, which is suitable for the characteristics of objective and constraint space of the CHPEED problem. For these reasons, a dynamic switched crowding based multi-objective symbiotic organism search (DSC-MOSOS) algorithm was designed to meet the requirements and geometric space of the CHPEED problem. By applying the DSC method in the MOSOS algorithm, it was aimed to improve the exploration ability, to strengthen exploitation-exploration balance, and to prevent the catching into local solution traps. A comprehensive experimental study was carried out to prove the performance of the proposed algorithm on IEEE CEC 2020 multi-modal multi-objective problems (MMOPs) and CHPEED problem. In the experimental study conducted among eleven versions of MOSOS variations created with DSC-method and the base MOSOS algorithm on IEEE CEC 2020 MMOPs, according to Friedman scores based on the four performance metrics, the base MOSOS algorithm ranked the last. In other experimental study, the best DSC-MOSOS variant was applied to solve the CHPEED problem, where 5-, 7-, 10- and 14-unit test systems and eight case studies were considered. The important points of this study were that 10-unit and 14-unit test systems were presented to the literature, and the prohibited operating zone was considered in CHPEED problem for the first time. According to the results obtained from eight case studies obtained from the DSC-MOSOS and fourteen competitor algorithms, while the improvement in cost was between 0.2% and 16.55%, the reduction of the emission value was between 0.2 kg and 42.97 kg compared to the competitor algorithms. On the other hand, the stability of the DSC-MOSOS and the base MOSOS was evaluated using stability analysis. While the MOSOS algorithms was not able to perform a success in any case study, the DSC-MOSOS was achieved an average success rate with 91.16%. Thus, the performance of the DSC-MOSOS over the MOSOS was verified by the results of experimental studies and analysis.

Decentralized Coordination of DERs for Dynamic Economic Emission Dispatch

This paper focuses on the dynamic economic emission dispatch (DEED) problem, to coordinate the distributed energy resources (DERs) in a power system and achieve economical and environmental operation. Distributed energy storages (ESs) are introduced into problem formulation in which charging/discharging efficiency is taken into account. By relaxing the nonconvexity induced by the charging/discharging model of ESs and network losses, we convert the non-convex DEED problem into its convex equivalency. Then, through a Lagrangian duality reformulation, an equivalent unconstrained consensus optimization model is established—a novel consensus-based decentralized algorithm, where the incremental cost is chosen as the consensus variable. At each iteration, only one primal variable requires sub-optimization, and it is completely locally updated. This is different from the well-known alternating direction method of multiplier (ADMM)-based algorithms where more than one subproblem needs to be solved at each iteration. The results of the comparative experiments also reflect the algorithm’s advantage in terms of computational efficiency. The simulation results validate the effectiveness of the proposed algorithm, achieving a balance between emissions and economic considerations.

Boosting Kernel Search Optimizer with Slime Mould Foraging Behavior for Combined Economic Emission Dispatch Problems

Boosting Kernel Search Optimizer with Slime Mould Foraging Behavior for Combined Economic Emission Dispatch Problems

Solving combined economic and emission dispatch problems using reinforcement learning-based adaptive differential evolution algorithm

Nowadays, economic and environmental concerns in production have become increasingly significant. To address these issues, the Combined Economic and Emission Dispatch (CEED) problem has been introduced to optimize the power generation process by considering fuel cost and emitted substances. However, due to the nonlinearity and nonconvexity of the objective function, the optimization of CEED remains a challenge. In this paper, we develop a Reinforcement Learning-based Adaptive Differential Evolution (RLADE) algorithm to enhance the optimization performance. The mutation strategy and crossover probability of RLADE are optimized using Reinforcement Learning (RL) to respectively ensure better convergence speed and searchability. Additionally, two modifications of RL, namely the adaptive population size-based state division and fitness-ranking-based reward mechanism, are proposed to improve the accuracy of state division and reward calculation in RL. The experiments conducted in this paper consider two objective formulation methods of CEED problems, namely the quadratic and cubic criterion functions. The mean values and standard deviations of the obtained solutions were utilized to assess the performance of RLADE, as well as other comparative algorithms, namely DE algorithm and two RL-based DE variants. The results clearly demonstrate that RLADE surpasses its counterparts with proportion of 100%, 85.7%, and 100% for the 6-unit and 11-unit quadratic CEED problems, as well as cubic criterion functions, in terms of both search accuracy and convergence ability. Furthermore, the significance of RLADE's superiority is confirmed through the Wilcoxon's signed rank test.