A novel discrete zeroing neural network for online solving time-varying nonlinear optimization problems.

To reduce transportation time, a discrete zeroing neural network (DZNN) method is proposed to solve the shortest path planning problem with a single starting point and a single target point. The shortest path planning problem is reformulated as an optimization problem, and a discrete nonlinear function related to the energy function is established so that the lowest-energy state corresponds to the optimal path solution. Theoretical analyzes demonstrate that the discrete ZNN model (DZNNM) exhibits zero stability, effectiveness, and real-time performance in handling time-varying nonlinear optimization problems (TVNOPs). Simulations with various parameters confirm the efficiency and real-time performance of the developed DZNNM for TVNOPs, indicating its suitability and superiority for solving the shortest path planning problem in real time.

Hierarchical path planning from speech instructions with spatial concept-based topometric semantic mapping.

Assisting individuals in their daily activities through autonomous mobile robots is a significant concern, especially for users without specialized knowledge. Specifically, the capability of a robot to navigate to destinations based on human speech instructions is crucial. Although robots can take different paths toward the same objective, the shortest path is not always the most suitable. A preferred approach would be to accommodate waypoint specifications flexibly for planning an improved alternative path even with detours. Furthermore, robots require real-time inference capabilities. In this sense, spatial representations include semantic, topological, and metric-level representations, each capturing different aspects of the environment. This study aimed to realize a hierarchical spatial representation using a topometric semantic map and path planning with speech instructions by including waypoints. Thus, we present a hierarchical path planning method called spatial concept-based topometric semantic mapping for hierarchical path planning (SpCoTMHP), which integrates place connectivity. This approach provides a novel integrated probabilistic generative model and fast approximate inferences with interactions among the hierarchy levels. A formulation based on "control as probabilistic inference" theoretically supports the proposed path planning algorithm. We conducted experiments in a home environment using the Toyota human support robot on the SIGVerse simulator and in a lab-office environment with the real robot Albert. Here, the user issues speech commands that specify the waypoint and goal, such as "Go to the bedroom via the corridor." Navigation experiments were performed using speech instructions with a waypoint to demonstrate the performance improvement of the SpCoTMHP over the baseline hierarchical path planning method with heuristic path costs (HPP-I) in terms of the weighted success rate at which the robot reaches the closest target (0.590) and passes the correct waypoints. The computation time was significantly improved by 7.14 s with the SpCoTMHP than the baseline HPP-I in advanced tasks. Thus, hierarchical spatial representations provide mutually understandable instruction forms for both humans and robots, thus enabling language-based navigation.

Global Path Planning for Articulated Steering Tractor Based on Multi-Objective Hybrid Algorithm.

With the development of smart agriculture, autopilot technology is being used more and more widely in agriculture. Because most of the current global path planning only considers the shortest path, it is difficult to meet the articulated steering tractor operation needs in the orchard environment and address other issues, so this paper proposes a hybrid algorithm of an improved bidirectional search A* algorithm and improved differential evolution genetic algorithm(AGADE). First, the integrated priority function and search method of the traditional A* algorithm are improved by adding weight influence to the integrated priority, and the search method is changed to a bidirectional search. Second, the genetic algorithm fitness function and search strategy are improved; the fitness function is set as the path tree row center offset factor; the smoothing factor and safety coefficient are set; and the search strategy adopts differential evolution for cross mutation. Finally, the shortest path obtained by the improved bidirectional search A* algorithm is used as the initial population of an improved differential evolution genetic algorithm, optimized iteratively, and the optimal path is obtained by adding kinematic constraints through a cubic B-spline curve smoothing path. The convergence of the AGADE hybrid algorithm and GA algorithm on four different maps, path length, and trajectory curve are compared and analyzed through simulation tests. The convergence speed of the AGADE hybrid algorithm on four different complexity maps is improved by 92.8%, 64.5%, 50.0%, and 71.2% respectively. The path length is slightly increased compared with the GA algorithm, but the path trajectory curve is located in the center of the tree row, with fewer turns, and it meets the articulated steering tractor operation needs in the orchard environment, proving that the improved hybrid algorithm is effective.

Improved A* Algorithm for Mobile Robots under Rough Terrain Based on Ground Trafficability Model and Ground Ruggedness Model.

Considering that the existing path planning algorithms for mobile robots under rugged terrain do not consider the ground flatness and the lack of optimality, which leads to the instability of the center of mass of the mobile robot, this paper proposes an improved A* algorithm for mobile robots under rugged terrain based on the ground accessibility model and the ground ruggedness model. Firstly, the ground accessibility and ruggedness models are established based on the elevation map, expressing the ground flatness. Secondly, the elevation cost function that can obtain the optimal path is designed based on the two types of models combined with the characteristics of the A* algorithm, and the continuous cost function is established by connecting with the original distance cost function, which avoids the center-of-mass instability caused by the non-optimal path. Finally, the effectiveness of the improved algorithm is verified by simulation and experiment. The results show that compared with the existing commonly used path planning algorithms under rugged terrain, the enhanced algorithm improves the smoothness of paths and the optimization degree of paths in the path planning process under rough terrain.

Rescue path planning for urban flood: A deep reinforcement learning-based approach.

Urban flooding is among the costliest natural disasters worldwide. Timely and effective rescue path planning is crucial for minimizing loss of life and property. However, current research on path planning often fails to adequately consider the need to assess area risk uncertainties and bypass complex obstacles in flood rescue scenarios, presenting significant challenges for developing optimal rescue paths. This study proposes a deep reinforcement learning (RL) algorithm incorporating four main mechanisms to address these issues. Dual-priority experience replays and backtrack punishment mechanisms enhance the precise estimation of area risks. Concurrently, random noisy networks and dynamic exploration techniques encourage the agent to explore unknown areas in the environment, thereby improving sampling and optimizing strategies for bypassing complex obstacles. The study constructed multiple grid simulation scenarios based on real-world rescue operations in major urban flood disasters. These scenarios included uncertain risk values for all passable areas and an increased presence of complex elements, such as narrow passages, C-shaped barriers, and jagged paths, significantly raising the challenge of path planning. The comparative analysis demonstrated that only the proposed algorithm could bypass all obstacles and plan the optimal rescue path across nine scenarios. This research advances the theoretical progress for urban flood rescue path planning by extending the scale of scenarios to unprecedented levels. It also develops RL mechanisms adaptable to various extremely complex obstacles in path planning. Additionally, it provides methodological insights into artificial intelligence to enhance real-world risk management.

Multi-area collision-free path planning and efficient task scheduling optimization for autonomous agricultural robots.

Collision-free path planning and task scheduling optimization in multi-region operations of autonomous agricultural robots present a complex coupled problem. In addition to considering task access sequences and collision-free path planning, multiple factors such as task priorities, terrain complexity of farmland, and robot energy consumption must be comprehensively addressed. This study aims to explore a hierarchical decoupling approach to tackle the challenges of multi-region path planning. Firstly, we conduct path planning based on the A* algorithm to traverse paths for all tasks and obtain multi-region connected paths. Throughout this process, factors such as path length, turning points, and corner angles are thoroughly considered, and a cost matrix is constructed for subsequent optimization processes. Secondly, we reformulate the multi-region path planning problem into a discrete optimization problem and employ genetic algorithms to optimize the task sequence, thus identifying the optimal task execution order under energy constraints. We finally validate the feasibility of the multi-task planning algorithm proposed by conducting experiments in an open environment, a narrow environment and a large-scale environment. Experimental results demonstrate the method's capability to find feasible collision-free and cost-optimal task access paths in diverse and complex multi-region planning scenarios.

Evolutionary optimization for risk-aware heterogeneous multi-agent path planning in uncertain environments.

Cooperative multi-agent systems make it possible to employ miniature robots in order to perform different experiments for data collection in wide open areas to physical interactions with test subjects in confined environments such as a hive. This paper proposes a new multi-agent path-planning approach to determine a set of trajectories where the agents do not collide with each other or any obstacle. The proposed algorithm leverages a risk-aware probabilistic roadmap algorithm to generate a map, employs node classification to delineate exploration regions, and incorporates a customized genetic framework to address the combinatorial optimization, with the ultimate goal of computing safe trajectories for the team. Furthermore, the proposed planning algorithm makes the agents explore all subdomains in the workspace together as a formation to allow the team to perform different tasks or collect multiple datasets for reliable localization or hazard detection. The objective function for minimization includes two major parts, the traveling distance of all the agents in the entire mission and the probability of collisions between the agents or agents with obstacles. A sampling method is used to determine the objective function considering the agents' dynamic behavior influenced by environmental disturbances and uncertainties. The algorithm's performance is evaluated for different group sizes by using a simulation environment, and two different benchmark scenarios are introduced to compare the exploration behavior. The proposed optimization method establishes stable and convergent properties regardless of the group size.

Autonomous navigation and control of magnetic microcarriers using potential field algorithm and adaptive non-linear PID.

Microparticles are increasingly employed as drug carriers inside the human body. To avoid collision with environment, they reach their destination following a predefined trajectory. However, due to the various disturbances, tracking control of microparticles is still a challenge. In this work, we propose to use an Adaptive Nonlinear PID (A-NPID) controller for trajectory tracking of microparticles. A-NPID allows the gains to be continuously adjusted to satisfy the performance requirements at different operating conditions. An in-vitro study is conducted to verify the proposed controller where a microparticle of 100 µ m diameter is put to navigate through an open fluidic reservoir with virtual obstacles. Firstly, a collision-free trajectory is generated using a path-planning algorithm. Secondly, the microparticle dynamic model, when moving under the influence of external forces, is derived, and employed to design the A-NPID control law. The proposed controller successfully allowed the particle to navigate autonomously following the reference collision-free trajectory in presence of varying environmental conditions. Moreover, the particle could reach its targeted position with a minimal steady-state error of 4 µ m. A degradation in the performance was observed when only a PID controller was used in the absence of adaptive terms. The results have been verified by simulation and experimentally.

Adaptive approach for tracking movements of biological targets: application to robot-based intervention for prostate cancer.

Introduction: In this paper, we introduce an advanced robotic system integrated with an adaptive optimization algorithm, tailored for Brachytherapy in prostate cancer treatment. The primary innovation of the system is the algorithm itself, designed to dynamically adjust needle trajectories in response to the real-time movements of the prostate gland during the local intervention. Methods: The system employs real-time position data extracted from Magnetic Resonance Imaging (MRI) to ensure precise targeting of the prostate, adapting to its constant motion and deformation. This precision is crucial in Brachytherapy, where the accurate placement of radioactive seeds directly impacts the efficacy of the treatment and minimizes damage to surrounding safe tissues. Results: Our results demonstrate a marked improvement in the accuracy of radiation seed placement, directly correlating to more effective radiation delivery. The adaptive nature of the algorithm significantly reduces the number of needle insertions, leading to a less invasive treatment experience for patients. This reduction in needle insertions also contributes to lower risks of infection and shorter recovery times. Discussion: This novel robotic system, enhanced by the adaptive optimization algorithm, improves the coverage of targets reached by a traditional combinatorial approach by approximately 15% with fewer required needles. The improved precision and reduced invasiveness highlight the potential of this system to enhance the overall effectiveness and patient experience in prostate cancer Brachytherapy.

Real-time path planning for autonomous vehicle off-road driving.

Background: Autonomous driving is a growing research area that brings benefits in science, economy, and society. Although there are several studies in this area, currently there is no a fully autonomous vehicle, particularly, for off-road navigation. Autonomous vehicle (AV) navigation is a complex process based on application of multiple technologies and algorithms for data acquisition, management and understanding. Particularly, a self-driving assistance system supports key functionalities such as sensing and terrain perception, real time vehicle mapping and localization, path prediction and actuation, communication and safety measures, among others. Methods: In this work, an original approach for vehicle autonomous driving in off-road environments that combines semantic segmentation of video frames and subsequent real-time route planning is proposed. To check the relevance of the proposal, a modular framework for assistive driving in off-road scenarios oriented to resource-constrained devices has been designed. In the scene perception module, a deep neural network is used to segment Red-Green-Blue (RGB) images obtained from camera. The second traversability module fuses Light Detection And Ranging (LiDAR) point clouds with the results of segmentation to create a binary occupancy grid map to provide scene understanding during autonomous navigation. Finally, the last module, based on the Rapidly-exploring Random Tree (RRT) algorithm, predicts a path. The Freiburg Forest Dataset (FFD) and RELLIS-3D dataset were used to assess the performance of the proposed approach. The theoretical contributions of this article consist of the original approach for image semantic segmentation fitted to off-road driving scenarios, as well as adapting the shortest route searching A* and RRT algorithms to AV path planning. Results: The reported results are very promising and show several advantages compared to previously reported solutions. The segmentation precision achieves 85.9% for FFD and 79.5% for RELLIS-3D including the most frequent semantic classes. While compared to other approaches, the proposed approach is faster regarding computational time for path planning.

Model Predictive Control with Variational Autoencoders for Signal Temporal Logic Specifications.

This paper presents a control strategy synthesis method for dynamical systems with differential constraints, emphasizing the prioritization of specific rules. Special attention is given to scenarios where not all rules can be simultaneously satisfied to complete a given task, necessitating decisions on the extent to which each rule is satisfied, including which rules must be upheld or disregarded. We propose a learning-based Model Predictive Control (MPC) method designed to address these challenges. Our approach integrates a learning method with a traditional control scheme, enabling the controller to emulate human expert behavior. Rules are represented as Signal Temporal Logic (STL) formulas. A robustness margin, quantifying the degree of rule satisfaction, is learned from expert demonstrations using a Conditional Variational Autoencoder (CVAE). This learned margin is then applied in the MPC process to guide the prioritization or exclusion of rules. In a track driving simulation, our method demonstrates the ability to generate behavior resembling that of human experts and effectively manage rule-based dilemmas.

Research on path planning for clear aligner flexible manufacturing.

In recent years, clear aligner can enhance individual appearance with dental defects, so it used more and more widely. However, in manufacturing process, there are still some problems, such as low degree of automation and high equipment cost. The problem of coordinate system mismatch between gingival curve point cloud and dental CAD model is faced to. The PCA-ICP registration algorithm is proposed, which includes coarse match algorithm and improve-ICP registration algorithm. The principal component analysis (PCA) based method can roughly find the posture relationship between the two point clouds. Using z-level dynamic hierarchical, the ICP registration can accurately find the posture between these two clouds. The final registration maximum distance error is 0.03 mm, which is smaller than robot machining error. Secondly, the clear aligner machining process is conducted to verify the registration effectiveness. Before machining, the path is generated based on the well registered gingival curve. After full registration, the tool path is calculated by establishing a local coordinate system between the workpiece and the tool to avoid interference. This path is calculated and generated as an executable program for ABB industrial robots. Finally, the robot was used for flexible cutting of clear aligners and was able to extract products, ensuring the effectiveness of the proposed research. This method can effectively solve the limitations of traditional milling path planning under such complex conditions.

Research on Path Planning Algorithm of Driverless Ferry Vehicles Combining Improved A* and DWA.

In view of the fact that the global planning algorithm cannot avoid unknown dynamic and static obstacles and the local planning algorithm easily falls into local optimization in large-scale environments, an improved path planning algorithm based on the integration of A* and DWA is proposed and applied to driverless ferry vehicles. Aiming at the traditional A* algorithm, the vector angle cosine value is introduced to improve the heuristic function to enhance the search direction; the search neighborhood is expanded and optimized to improve the search efficiency; aiming at the problem that there are many turning points in the A* algorithm, a cubic quasi-uniform B-spline curve is used to smooth the path. At the same time, fuzzy control theory is introduced to improve the traditional DWA so that the weight coefficient of the evaluation function can be dynamically adjusted in different environments, effectively avoiding the problem of a local optimal solution. Through the fusion of the improved DWA and the improved A* algorithm, the key nodes in global planning are used as sub-target punctuation to guide the DWA for local planning, so as to ensure that the ferry vehicle avoids obstacles in real time. Simulation results show that the fusion algorithm can avoid unknown dynamic and static obstacles efficiently and in real time on the basis of obtaining the global optimal path. In different environment maps, the effectiveness and adaptability of the fusion algorithm are verified.

Path Planning of Unmanned Aerial Vehicles Based on an Improved Bio-Inspired Tuna Swarm Optimization Algorithm.

The Sine-Levy tuna swarm optimization (SLTSO) algorithm is a novel method based on the sine strategy and Levy flight guidance. It is presented as a solution to the shortcomings of the tuna swarm optimization (TSO) algorithm, which include its tendency to reach local optima and limited capacity to search worldwide. This algorithm updates locations using the Levy flight technique and greedy approach and generates initial solutions using an elite reverse learning process. Additionally, it offers an individual location optimization method called golden sine, which enhances the algorithm's capacity to explore widely and steer clear of local optima. To plan UAV flight paths safely and effectively in complex obstacle environments, the SLTSO algorithm considers constraints such as geographic and airspace obstacles, along with performance metrics like flight environment, flight space, flight distance, angle, altitude, and threat levels. The effectiveness of the algorithm is verified by simulation and the creation of a path planning model. Experimental results show that the SLTSO algorithm displays faster convergence rates, better optimization precision, shorter and smoother paths, and concomitant reduction in energy usage. A drone can now map its route far more effectively thanks to these improvements. Consequently, the proposed SLTSO algorithm demonstrates both efficacy and superiority in UAV route planning applications.

Multi-UAV Cooperative Coverage Search for Various Regions Based on Differential Evolution Algorithm.

In recent years, remotely controlling an unmanned aerial vehicle (UAV) to perform coverage search missions has become increasingly popular due to the advantages of the UAV, such as small size, high maneuverability, and low cost. However, due to the distance limitations of the remote control and endurance of a UAV, a single UAV cannot effectively perform a search mission in various and complex regions. Thus, using a group of UAVs to deal with coverage search missions has become a research hotspot in the last decade. In this paper, a differential evolution (DE)-based multi-UAV cooperative coverage algorithm is proposed to deal with the coverage tasks in different regions. In the proposed algorithm, named DECSMU, the entire coverage process is divided into many coverage stages. Before each coverage stage, every UAV automatically plans its flight path based on DE. To obtain a promising flight trajectory for a UAV, a dynamic reward function is designed to evaluate the quality of the planned path in terms of the coverage rate and the energy consumption of the UAV. In each coverage stage, an information interaction between different UAVs is carried out through a communication network, and a distributed model predictive control is used to realize the collaborative coverage of multiple UAVs. The experimental results show that the strategy can achieve high coverage and a low energy consumption index under the constraints of collision avoidance. The favorable performance in DECSMU on different regions also demonstrate that it has outstanding stability and generality.

Research on detection method of photovoltaic cell surface dirt based on image processing technology.

In view of the reduced power generation efficiency caused by ash or dirt on the surface of photovoltaic panels, and the problems of heavy workload and low efficiency faced by manual detection, this study proposes a method to detect dust or dust on the surface of photovoltaic cells with the help of image processing technology to timely eliminate hidden dangers and improve power generation efficiency.This paper introduces image processing methods based on mathematical morphology, such as image enhancement, image sharpening, image filtering and image closing operation, which makes the image better highlight the target to be recognized. At the same time, it also solves the problem of uneven image binarization caused by uneven illumination in the process of image acquisition. By using the image histogram equalization, the gray level concentration area of the original image is opened or the gray level is evenly distributed, so that the dynamic range of the pixel gray level is increased, so that the image contrast or contrast is increased, the image details are clear, to achieve the purpose of enhancement. When identifying the target area, the method of calculating the proportion of the dirt area to the whole image area is adopted, and the ratio exceeding a certain threshold is judged as a fault. In addition, the improved A* path planning algorithm is adopted in this study, which greatly improves the efficiency of the unmanned aerial vehicle detection of photovoltaic cell dirt, saves time and resources, reduces operation and maintenance costs, and improves the operation and maintenance level of photovoltaic units.

A multi-strategy improved rime optimization algorithm for three-dimensional USV path planning and global optimization.

The RIME optimization algorithm (RIME) represents an advanced optimization technique. However, it suffers from issues such as slow convergence speed and susceptibility to falling into local optima. In response to these shortcomings, we propose a multi-strategy enhanced version known as the multi-strategy improved RIME optimization algorithm (MIRIME). Firstly, the Tent chaotic map is utilized to initialize the population, laying the groundwork for global optimization. Secondly, we introduce an adaptive update strategy based on leadership and the dynamic centroid, facilitating the swarm's exploitation in a more favorable direction. To address the problem of population scarcity in later iterations, the lens imaging opposition-based learning control strategy is introduced to enhance population diversity and ensure convergence accuracy. The proposed centroid boundary control strategy not only limits the search boundaries of individuals but also effectively enhances the algorithm's search focus and efficiency. Finally, to demonstrate the performance of MIRIME, we employ CEC 2017 and CEC 2022 test suites to compare it with 11 popular algorithms across different dimensions, verifying its effectiveness. Additionally, to assess the method's practical feasibility, we apply MIRIME to solve the three-dimensional path planning problem for unmanned surface vehicles. Experimental results indicate that MIRIME outperforms other competing algorithms in terms of solution quality and stability, highlighting its superior application potential.

Hybrid Path Generation Method for Multi-Axis Laser Metal Deposition of Overhanging Thin-Walled Structures.

Additive manufacturing has advantages over other traditional manufacturing technologies for the fabrication of complex thin-walled parts. Previous correlation path strategies, when applied to laser metal deposition processes, suffer from contour deposition transboundary and surface "scar" type overstacking. Therefore, this paper proposes a hybrid path generation method for the laser metal deposition process. First, the topological logic of the STL model of the part is restored to reduce redundant calculations at the stage of obtaining the layered contour. Then, the path points are planned on the basis of the offset contours in a helical upward trend to form a globally continuous composite path in space considering the melt channel width. Finally, vectors that adaptively fit to the model surface are generated for the path points as tool orientations and they are optimized by smoothing the rotation angles. The results of experiments conducted on a multi-axis machine equipped with a laser metal deposition module show that the path generated by the proposed method is not only capable of thin-walled structures with overhanging and curved surface features but also improves the surface imperfections of the part due to sudden changes in the angle of rotation while ensuring the boundary dimensions.

Mobile Sensor Path Planning for Kalman Filter Spatiotemporal Estimation.

The estimation of spatiotemporal data from limited sensor measurements is a required task across many scientific disciplines. In this paper, we consider the use of mobile sensors for estimating spatiotemporal data via Kalman filtering. The sensor selection problem, which aims to optimize the placement of sensors, leverages innovations in greedy algorithms and low-rank subspace projection to provide model-free, data-driven estimates. Alternatively, Kalman filter estimation balances model-based information and sparsely observed measurements to collectively make better estimation with limited sensors. It is especially important with mobile sensors to utilize historical measurements. We show that mobile sensing along dynamic trajectories can achieve the equivalent performance of a larger number of stationary sensors, with performance gains related to three distinct timescales: (i) the timescale of the spatiotemporal dynamics, (ii) the velocity of the sensors, and (iii) the rate of sampling. Taken together, these timescales strongly influence how well-conditioned the estimation task is. We draw connections between the Kalman filter performance and the observability of the state space model and propose a greedy path planning algorithm based on minimizing the condition number of the observability matrix. This approach has better scalability and computational efficiency compared to previous works. Through a series of examples of increasing complexity, we show that mobile sensing along our paths improves Kalman filter performance in terms of better limiting estimation and faster convergence. Moreover, it is particularly effective for spatiotemporal data that contain spatially localized structures, whose features are captured along dynamic trajectories.

SDC-Net++: End-to-End Crash Detection and Action Control for Self-Driving Car Deep-IoT-Based System.

Few prior works study self-driving cars by deep learning with IoT collaboration. SDC-Net, which is an end-to-end multitask self-driving car camera cocoon IoT-based system, is one of the research areas that tackles this direction. However, by design, SDC-Net is not able to identify the accident locations; it only classifies whether a scene is a crash scene or not. In this work, we introduce an enhanced design for the SDC-Net system by (1) replacing the classification network with a detection one, (2) adapting our benchmark dataset labels built on the CARLA simulator to include the vehicles' bounding boxes while keeping the same training, validation, and testing samples, and (3) modifying the shared information via IoT to include the accident location. We keep the same path planning and automatic emergency braking network, the digital automation platform, and the input representations to formulate the comparative study. The SDC-Net++ system is proposed to (1) output the relevant control actions, especially in case of accidents: accelerate, decelerate, maneuver, and brake, and (2) share the most critical information to the connected vehicles via IoT, especially the accident locations. A comparative study is also conducted between SDC-Net and SDC-Net++ with the same input representations: front camera only, panorama and bird's eye views, and with single-task networks, crash avoidance only, and multitask networks. The multitask network with a BEV input representation outperforms the nearest representation in precision, recall, f1-score, and accuracy by more than 15.134%, 12.046%, 13.593%, and 5%, respectively. The SDC-Net++ multitask network with BEV outperforms SDC-Net multitask with BEV in precision, recall, f1-score, accuracy, and average MSE by more than 2.201%, 2.8%, 2.505%, 2%, and 18.677%, respectively.