Adaptive Mutation Operator Research Articles

Multi-algorithm based evolutionary strategy with Adaptive Mutation Mechanism for Constraint Engineering Design Problems

This paper proposes a new multi-algorithm based evolution strategy with the addition of adaptive mutation operators for global optimization. The new algorithm namely Kepler meerkat naked (KMN) algorithm is based on Kepler’s optimization algorithm (KOA), meerkat optimization algorithm (MOA), and naked mole-rat algorithm (NMRA), as the core algorithms and, grey wolf optimizer (GWO) and cuckoo search (CS) inspired equations for enhanced exploration and exploitation. The proposed algorithm uses six new mutation operators for parametric enhancements, and follows an iterative division mechanism for a balanced operation. A comparative analysis is done with respect to classical benchmarks, CEC 2014, CEC 2017, CEC 2019 and CEC 2022 benchmark datasets for performance evaluation. Six engineering design problems are also used to test the performance of the proposed KMN algorithm for constraint optimization. Apart from that, a binary version of KMN namely bKMN is also proposed, and ten feature selection datasets are used for performance evaluation. Performance testing of the KMN and bKMN algorithm is done with success history-based DE (SHADE), LSHADE-SPACMA, self-adaptive DE (SaDE), fast opposition-based learning golden jackal optimization (FROBL-GJO), LSHADE-EpSin, jSO, EBOwithCMAR, among others. Experimental and statistical results are performed using Wilcoxon’s and Friedman’s tests, and it has been found that the proposed algorithms are highly competitive in contrast to other algorithms under study.

An Adaptive Multi-Objective Genetic Algorithm for Solving Heterogeneous Green City Vehicle Routing Problem

Intelligent scheduling plays a crucial role in minimizing transportation expenses and enhancing overall efficiency. However, most of the existing scheduling models fail to comprehensively account for the requirements of urban development, as exemplified by the vehicle routing problem with time windows (VRPTW), which merely specifies the minimization of path length. This paper introduces a new model of the heterogeneous green city vehicle routing problem with time windows (HGCVRPTW), addressing challenges in urban logistics. The HGCVRPTW model considers carriers with diverse attributes, recipients with varying tolerance for delays, and fluctuating road congestion levels impacting carbon emissions. To better deal with the HGCVRPTW, an adaptive multi-objective genetic algorithm based on the greedy initialization strategy (AMoGA-GIS) is proposed, which includes the following three advantages. Firstly, considering the impact of initial information on the search process, a greedy initialization strategy (GIS) is proposed to guide the overall evolution during the initialization phase. Secondly, the adaptive multiple mutation operators (AMMO) are introduced to improve the diversity of the population at different evolutionary stages according to their success rate of mutation. Moreover, we built a more tailored testing dataset that better aligns with the challenges faced by the HGCVRPTW. Our extensive experiments affirm the competitive performance of the AMoGA-GIS by comparing it with other state-of-the-art algorithms and prove that the GIS and AMMO play a pivotal role in advancing algorithmic capabilities tailored to the HGCVRPTW.

Complete Coverage Path Planning Based on Improved Genetic Algorithm for Unmanned Surface Vehicle

Complete Coverage Path Planning (CCPP) is a key technology for Unmanned Surface Vehicles (USVs) that require complete coverage on the water surface, such as water sample collection, garbage collection, water field patrol, etc. When facing complex and irregular boundaries, the traditional CCPP-based boustrophedon method may encounter many problems and challenges, such as multiple repeated regions, multiple turns, and the easy occurrence of local optima. The traditional genetic algorithm also has some shortcomings. The fixed fitness function, mutation operator and crossover operator are not conducive to the evolution of the population and the production of better offspring. In order to solve the above problems, this paper proposes a CCPP method based on an improved genetic algorithm, including a stretched fitness function, an adaptive mutation operator, and a crossover operator. The algorithm combines the key operators in the fireworks algorithm. Then, the turning and obstacle avoidance during the operation of the Unmanned Surface Vehicle are optimized. Simulation and experiments show that the improved genetic algorithm has higher performance than the exact unit decomposition method and the traditional genetic algorithm, and has more advantages in reducing the coverage path length and repeating the coverage area. This proves that the proposed CCPP method has strong adaptability to the environment and has practical application value in improving the efficiency and quality of USV related operations.

Accurate fault section diagnosis of power systems with a binary adaptive quadratic interpolation learning differential evolution

Fault section diagnosis (FSD) is essential for ensuring the effective operation of power systems. To determine the faulty sections accurately, we proposed an improved binary adaptive quadratic interpolation learning differential evolution called BAQILDE for solving the FSD problem. By comparing the received warning data with the anticipated states of circuit breakers and protective relays, an analytical 0–1 integer programming function is established. To tackle the resultant function accurately, the population in BAQILDE is directly encoded in binary instead of floating-point to facilitate the solving convenience. Besides, three enhanced strategies including adaptive mutation operator, time-varying crossover rate, and dual transformation operator are developed to equilibrate the population diversity and convergence well to strengthen BAQILDE. To evaluate BAQILDE's performance, four test systems were used for verification, including 4-substation power system, IEEE 118 bus system, and two actual failures that occurred in Guangzhou and Jilin power grids, China. The results show that BAQILDE can diagnose various failures within 0.12 s with 100 % success rate and 0 diagnosis error, consuming an average of 32.21 function evaluation times. It outperformed other well-known peer algorithms in success rate, diagnosis error, robustness, convergence, and statistical analysis, which demonstrates its strong competitiveness in solving the FSD problem.

Energy-efficient indoor hybrid deployment strategy for 5G mobile small-cell base stations using JAFR Algorithm

In the context of 5th-generation (5G) mobile communication technology, deploying indoor small-cell base stations (SBS) to serve visitors has become common. However, indoor SBS is constrained by factors such as service capacity, signal interference, and structural layout. Merchants within large buildings frequently host diverse activities to attract visitors, significantly increasing indoor traffic and crowd-gathering phenomenon. Consequently, SBS faces challenges of excessive energy consumption, compromised communication quality, and an inability to provide service to all visitors. Merchants aim to deploy SBS that can effectively curtail energy consumption costs while fulfilling visitor needs. However, due to the intermittent nature of high footfall situations, employing additional fixed SBS is not economically viable. Therefore, we address the challenge of maintaining service quality and mitigating energy consumption of SBS during footfall fluctuations by proposing an SBS model with a dynamic sleep mechanism. We simulate the internal structure of a three-dimensional (3D) building and the footfall over time. Within this model, we leverage the flexibility of mobile small-cell base stations (MSBS) to seamlessly traverse service regions. We compute the transmission power and location of SBS and MSBS based on energy efficiency (EE), combining their strengths to tackle the challenge. This approach maintains SBS communication quality while curbing energy consumption. We attain the optimal hybrid deployment strategy by enhancing the adaptive differential evolution with optional external archive (JADE) algorithm and incorporating the final fitness formula, the adaptive ranking mutation operator strategy, and the disorder replacement strategy (DRS) in it to form the proposed joint adaptive fusion with ranking (JAFR) algorithm. Our comparative simulation experiments demonstrate the effectiveness of JAFR in addressing the challenges against conventional methods, recent differential evolution algorithms, and mobile base station (MBS) deployment approaches posed by this model. The results indicate that the JAFR algorithm yields superior SBS deployment strategies in most cases.

Handling dynamic capacitated vehicle routing problems based on adaptive genetic algorithm with elastic strategy

With the development of e-commerce platforms, the logistics industry is also booming. The transportation process is at the core of the logistics industry, which influences the timeliness and rationality of logistics distribution. In the real world, there are many dynamic demands in logistics distribution, so logistics distribution should deal with dynamic demands quickly to realize more effective route planning. This paper proposes an adaptive genetic algorithm (AGA) with elastic strategy (AGA-ES) to solve the dynamic capacitated vehicle routing problems (DCVRPs). Firstly, AGA designs an adaptive local search operator, which can adaptively adjust the quantity of nodes that need local search, according to the fitness value of different individuals. At the same time, AGA develops adaptive crossover and mutation operators, which can automatically adjust the crossover and mutation probability based on the different fitness values. The experimental results verify the better performance of AGA on the traditional capacitated vehicle routing problems (CVRPs). After that, AGA combines elastic strategy (AGA-ES) to solve DCVRPs. This paper mainly concerns three types of actual demand information in DCVRPs: distribution nodes increase, distribution nodes decrease, and distribution road conditions change, according to the actual background. AGA-ES could interact with demand information and judge the types of different demands, and then adaptively plan new and reasonable routes after receiving one or more of the above demand information. The verification of benchmark data sets shows that AGA-ES can effectively deal with DCVRPs. Furthermore, this paper collects the longitude and latitude coordinates of 100 SF express stations in Xi’an, constructs the distribution information of these express stations, and verifies that AGA-ES can solve the DCVRPs under the actual background.

A priority-based self-guided serial–parallel genetic algorithm for low-dose computed tomography

Computed tomography (CT) is a non-destructive evaluation technique to know the internal structure of the objects under scan. It has numerous applications in engineering as well as in the medical field. The prime objective of this manuscript is to reduce the radiation dose to the object under scanning and to reconstruct the low-noise CT images, even in limited-view projections data scenarios. The present manuscript proposes a novel priority-based self-guided serial-parallel hybrid genetic algorithm for low-dose CT reconstruction. The current algorithm combines serial and parallel processing elements to reduce the loss of diversity in the population and increase the convergence rate. The proposed algorithm uses a novel priority-based self-guided competition operator. It consists of two approaches for maintaining exploration and exploitation tradeoffs. Here, the first approach uses serial processing, whereas the second approach uses parallel processing. The algorithm also uses priority-based hybrid crossover (PHCO) and adaptive priority-based mutation operator (PMO) to generate the most suitable offspring in every generation. Experimental results reveal that the presented algorithm produces satisfactory results with limited-view projections. The presented algorithm also outperforms other limited-view CT reconstruction algorithms.

MOEA with adaptive operator based on reinforcement learning for weapon target assignment

<abstract><p>Weapon target assignment (WTA) is a typical problem in the command and control of modern warfare. Despite the significance of the problem, traditional algorithms still have shortcomings in terms of efficiency, solution quality, and generalization. This paper presents a novel multi-objective evolutionary optimization algorithm (MOEA) that integrates a deep Q-network (DQN)-based adaptive mutation operator and a greedy-based crossover operator, designed to enhance the solution quality for the multi-objective WTA (MO-WTA). Our approach (NSGA-DRL) evolves NSGA-II by embedding these operators to strike a balance between exploration and exploitation. The DQN-based adaptive mutation operator is developed for predicting high-quality solutions, thereby improving the exploration process and maintaining diversity within the population. In parallel, the greedy-based crossover operator employs domain knowledge to minimize ineffective searches, focusing on exploitation and expediting convergence. Ablation studies revealed that our proposed operators significantly boost the algorithm performance. In particular, the DQN mutation operator shows its predictive effectiveness in identifying candidate solutions. The proposed NSGA-DRL outperforms state-and-art MOEAs in solving MO-WTA problems by generating high-quality solutions.</p></abstract>

An adaptive hybrid mutated differential evolution feature selection method for low and high-dimensional medical datasets

Feature selection (FS) constitutes a crucial endeavor in classification procedures, aiming to identify the minimal subset of features that maximizes classification accuracy. In the realm of combinatorial NP-hard challenges, FS assumes significance, prompting the utilization of robust metaheuristics as efficient wrapper-based FS strategies. However, the application of these wrapper metaheuristics to high-dimensional datasets, characterized by an abundance of features and a scarcity of samples, often results in a decline in effectiveness and escalated computational costs. Addressing these limitations, this study introduces the Adaptive Hybrid-Mutated Differential Evolution (A-HMDE) method, targeting the inherent drawbacks of the Differential Evolution (DE) algorithm. The A-HMDE incorporates four distinct strategies. Firstly, it integrates the mechanics of the Spider Wasp Optimization (SWO) algorithm into DE’s mutation strategies, yielding enhanced performance marked by high accuracy and swift convergence towards global optima. Secondly, adaptive mechanisms are applied to key DE parameters, amplifying the efficiency of the search process. Thirdly, an adaptive mutation operator ensures a harmonious balance between global exploration and local exploitation during optimization. Lastly, the concept of Enhanced Solution Quality (ESQ), rooted in the RUN algorithm, guides DE to elude local optima, thus heightening the accuracy of obtained solutions. The efficiency of the A-HMDE approach is assessed by employing it as a FS method across diverse datasets encompassing the UCI repository, microarray data, and skin disease image dataset. The experimental results accentuate the method’s remarkable ability to overcome challenges related to local minima and hasten the convergence process. A comprehensive comparison against contemporary cutting-edge algorithms highlights the considerable advancements achieved by the proposed method, with recorded accuracy ranging from 0.88 to 1.00.

An efficient adaptive-mutated Coati optimization algorithm for feature selection and global optimization

The feature selection (FS) problem has occupied a great interest of scientists lately since the highly dimensional datasets might have many redundant and irrelevant features. FS aims to eliminate such features and select the most important ones that affect classification performance. Metaheuristic algorithms are the best choice to solve this combinatorial problem. Recent researchers invented and adapted new algorithms, hybridized many algorithms, or enhanced existing ones by adding some operators to solve the FS problem. In our paper, we added some operators to the Coati optimization algorithm (CoatiOA). The first operator is the adaptive s-best mutation operator to enhance the balance between exploration and exploitation. The second operator is the directional mutation rule that opens the way to discover the search space thoroughly. The final enhancement is controlling the search direction toward the global best. We tested the proposed mCoatiOA algorithm in solving) in solving challenging problems from the CEC'20 test suite. mCoatiOA performance was compared with Dandelion Optimizer (DO), African vultures optimization algorithm (AVOA), Artificial gorilla troops optimizer (GTO), whale optimization algorithm (WOA), Fick's Law Algorithm (FLA), Particle swarm optimization (PSO), Harris hawks optimization (HHO), and Tunicate swarm algorithm (TSA). According to the average fitness, it can be observed that the proposed method, mCoatiOA, performs better than the other optimization algorithms on 8 test functions. It has lower average standard deviation values compared to the competitive algorithms. Wilcoxon test showed that the results obtained by mCoatiOA are significantly different from those of the other rival algorithms. mCoatiOA has been tested as a feature selection algorithm. Fifteen benchmark datasets of various types were collected from the UCI machine-learning repository. Different evaluation criteria are used to determine the effectiveness of the proposed method. The proposed mCoatiOA achieved better results in comparison with other published methods. It achieved the mean best results on 75% of the datasets.

Path Planning of an Electric Vehicle for Logistics Distribution Considering Carbon Emissions and Green Power Trading

As environmental awareness continues to grow and government policies provide incentives, electric vehicles (EVs) are becoming more widely used in logistics distribution. Considering green power trading and carbon emissions, this paper addresses the green vehicle routing problem (GVRP) and constructs an electric vehicle path model with time windows to minimize the total cost. To solve the model, a hybrid adaptive genetic algorithm (HAGA) is proposed. An improved nearest-neighbor algorithm is adopted to improve the quality of the initial population, and the adaptive crossover and mutation operators are introduced to achieve the better solution. In addition, based on the Schneider case, HAGA is used to solve the models with and without considering green power trading separately, and the results show that considering green power trading can reduce the total cost by 3.22% and carbon emissions by 23.38 kg. Finally, the experimental simulations further prove that with the increase in case size, HAGA can effectively reduce total cost. And it is beneficial for the popularization of electric vehicles in logistics distribution.

A novel multi-agent genetic algorithm for limited-view computed tomography

Computed tomography (CT) is a non-invasive testing technique to generate the internal image of any object. It has various applications belonging to medical imaging and other engineering applications. The present article proposes a novel multiagent genetic algorithm based on hill-climbing for limited-view computed tomography (MAGAH-CT). The MAGAH combines a multi-agent system based on a genetic algorithm (MAGA) and a hill-climbing approach. The MAGAH uses multiple operators to refine the agent population during evolution. These operators are neighborhood-based competition, hybrid crossover, adaptive mutation, and self-learning. MAGAH-CT explores better solutions in neighborhood-based competition and cooperation operators. The self-learning operator learns through the agent’s population generated by adaptive mutation and hybrid crossover operator, ensuring the results’ continuity. The proposed algorithm has been tested on a Shepp-Logan head phantom with limited view projection data. The algorithm can accurately reconstruct the low-noise CT image using limited data constraints. Experimental results reveal that the presented MAGAH-CT algorithm is efficient and computationally reasonable. The presented algorithm is suitable for low-noise CT reconstruction and out-performs other limited-view CT reconstruction algorithms.

A robust method based on reinforcement learning and differential evolution for the optimal photovoltaic parameter extraction

It is crucial to identify the optimal parameters of Photovoltaic (PV) models with the purpose of evaluating, controlling, and improving PV systems. Lots of optimization algorithms have been developed to solve the problem and achieve better results. But, the performance of most algorithms is greatly influenced by their parameters. A Reinforcement Learning-based Adaptive Parameter and Mutation operator Differential Evolution algorithm (RLAPMDE) is developed, in which the parameters of algorithms are randomly set in [0,1], and the mutation operator is adaptively adjusted between Rand/1 and Best/1. Rand/1 is mainly responsible for exploration, while Best/1 is to implement exploitation. Exploration and exploitation are well balanced. RL technique is used to realize the process through interaction with the environment. The RLAPMDE is employed to identify the optimal parameters of PV. The dataset used in experiments is Single Diode Model (SDM), Double Diode Model (DDM) and PV module. The results of the best RMSE obtained by RLAPMDE are 9.8602E-4, 9.8248E-4, 2.4251E-3, 1.7298E-3 and 1.6601E-2, which are the minimum when compared with the conventional DE, five DE variants, six latest meta-heuristic algorithms and some reported results. The proposed PLAPMDE algorithm is one of the alternative algorithms when estimating the parameters of PV systems.

An Efficient and Improved Coronavirus Herd Immunity Algorithm Using Knowledge-Driven Variable Neighborhood Search for Flexible Job-Shop Scheduling Problems

By addressing the flexible job shop scheduling problem (FJSP), this paper proposes a new type of algorithm for the FJSP. We named it the hybrid coronavirus population immunity optimization algorithm. Based on the characteristics of the problem, firstly, this paper redefined the discretized two-stage individual encoding and decoding scheme. Secondly, in order to realize the multi-scale search of the solution space, a multi-population update mechanism is designed, and a collaborative learning method is proposed to ensure the diversity of the population. Then, an adaptive mutation operation is introduced to enrich the diversity of the population, relying on the adaptive adjustment of the mutation operator to balance global search and local search capabilities. In order to realize a directional and efficient neighborhood search, this algorithm proposed a knowledge-driven variable neighborhood search strategy. Finally, the algorithm’s performance comparison experiment is carried out. The minimum makespans on the MK06 medium-scale case and MK10 large-scale case are 58 and 201, respectively. The experimental results verify the effectiveness of the hybrid algorithm.

Innovative Design Method of Hydro-Pneumatic Suspension for Large High-Clearance Sprayer Based on Improved NSGA-II Algorithm

Large high-clearance sprayers are widely used in the field of plant protection due to their high work efficiency. Influenced by the characteristics of a large ground clearance, fast driving speed and constantly changing sprung mass, how to solve the contradiction between the vibration reduction performance of a large sprayer and the friendliness of farmland roads has become a current research hotspot. In order to improve the driving performance of the sprayers, the design, optimization and verification scheme of the hydro-pneumatic suspension of a large sprayer based on the improved NSGA-II algorithm was completely constructed in this study. The hydro-pneumatic suspension system of a sprayer was mainly designed and a real-time time-varying model under field road excitation was established. The NSGA-II algorithm was improved by introducing the adaptive crossover operator and DE mutation operator, and a real-time interactive interface between the time-varying model was established for multi-objective optimization. Finally, system simulation analysis was conducted and a vibration test bench was built for experimental verification. The results show that vibration reduction indicators improved by 19.4%, 10.7% and 4.0%, respectively, compared with those before optimization. The performance of the designed hydro-pneumatic suspension was better than that of the ordinary suspension.

Optimising Characteristics of an Intelligent Transport System Using a Real-Coded Genetic Algorithm Based on Adaptive Mutation

A novel real-coded genetic algorithm (FCGA-AM) that uses the proposed adaptive mutation (AM) operator is presented. The algorithm is designed to optimise the characteristics of the developed intelligent transportation system. The performance of the proposed genetic algorithm was evaluated in comparison with other methods of multicriteria heuristic optimization with the use of various test instances and well-known quality metrics for Pareto frontiers. At the next stage, the FCGA-AM was applied to find the best road safety trade-offs involving unmanned ground vehicles (UAVs) interacting with conventional ground vehicles (UTVs), pedestrians and other agents

Operation Optimization of Circulating Cooling Water System Based on Adaptive Differential Evolution Algorithm

The circulating cooling water system (CCWS) is a commonly used auxiliary system in industrial production, and it is also one of the main energy-consuming systems. The operating conditions of the system vary with the temperature changes caused by seasons, day and night, causing different energy consumption. If the system still maintains conditions when the actual conditions change, energy would be wasted. Operation optimization for the system can improve the operation effect of the system, reduce energy consumption, and increase operating efficiency. Therefore, through operation mechanism analysis for the main energy-consuming components of the CCWS that has been put into use, an operation optimization model is established integrating the domain knowledge. After that, an adaptive differential evolution (ADE) algorithm is proposed by introducing the adaptive mutation and crossover operator to solve the model. According to the minimum circulating water volume and air volume required by the system under different working conditions, the optimal start-up combination mode and operating frequency of the water pumps and fans are determined. And then, the optimal opening values of the regulating valves and baffles in the system are determined, thereby saving the energy of the system. Considering system operation knowledge, the synchronous optimization of the operation mode and operation status of the components in the system is realized. Finally, the effectiveness of the optimization method is verified through a case study.

Parameter identification method of J–A hysteresis model based on improved sparrow search algorithm

Aiming at the weak capacity of the parameter identification methods of Jiles–Atherton (J–A) hysteresis model, such as slow convergence speed and low convergence accuracy, an improved sparrow search algorithm (IM-SSA) is proposed based on mutation crossover operator and T-distribution perturbation strategy in this paper to improve the convergence speed and accuracy of parameter identification method. Firstly, the initial population of the sparrow search algorithm is enriched by Tent chaotic sequence, which expand the search area. Then, the adaptive crossover and mutation operator is introduced into the finders population to enrich the diversity of the finders population and balance the global and local search ability of the algorithm. Secondly, the T-distribution perturbation or differential mutation is used to perturb the population after each iteration according to the individual characteristics, which can avoid the population singularity in the later stage of the algorithm and enhance the ability of jump out of the local optimal value of the algorithm. Finally, the proposed parameter identification method is used to identify the parameters of the J–A hysteresis model, which are used to simulate the magnetic properties of Non-oriented silicon steel sheets with different magnetic induction intensity. The calculation result is compared with the experiment ones. The results proved that the proposed method has faster convergence speed and higher convergence accuracy.

Multi-Objective Vehicle Routing Problem for Waste Classification and Collection with Sustainable Concerns: The Case of Shanghai City

With the promotion of an ecological civilization philosophy and a sustainable development strategy, solid waste classification and collection has become an emerging issue in China. Based on the three dimensions of sustainable development, namely economy, society, and environment, the route optimization model of waste collection and transportation is constructed. In order to solve the model aiming to maximize the benefits of sanitation companies under the constraints of workload balance, transportation cleanliness, and route changes due to cost factors, we combine the non-dominated sorting genetic algorithm III with simulated annealing. According to the characteristics of the problem, the probabilistic insertion method is incorporated to generate the initial solution, and the adaptive mutation operator is added to improve the population diversity. Finally, a real case in Xuhui District, Shanghai, a megacity taking the lead in 2019 in mandating a separated collection policy, is presented to verify the proposed model’s performance. The results provide a decision solution for dispatching the collection route of vehicles with some references for sanitary companies.

Design and Implementation of Energy-Saving Logistics Management System for Route Optimization

In order to effectively solve the problem of vehicle routing, a design and implementation method of an energy-saving logistics management system oriented to routing optimization is proposed. From the perspective of optimal calculation, this research uses the improved Dixie algorithm and clustering algorithm to design and implement a logistics company’s distribution center location and distribution path planning system. First of all, the authors analyze the common models of the LRP problem in detail and give the mathematical model and calculation method of positioning rationing and the transportation route planning problem. Secondly, in view of the shortcomings of traditional evolutionary algorithms, the authors propose a series of improvement measures. The authors adopt a natural number coding scheme combined with an adaptive crossover mutation operator to improve the search ability of the solution space; the authors also introduce a penalty function to deal with constraints and take corresponding measures for illegal individuals generated in the evolution process, reducing premature convergence. Possibility. It has been verified that the design and development of the system saves investment costs for small and medium-sized logistics enterprises and reduces the cost of goods distribution by 80%. The effect is remarkable, which verifies the effectiveness, accuracy, and superiority of the algorithm.