A Survey on Randomized Sampling-Based Path Optimization Methods

2013 ◽  
Vol 853 ◽  
pp. 652-660
Author(s):  
Fu Yu Yan ◽  
Fan Wu ◽  
Fei Peng ◽  
Zhi Jie Zhu
Keyword(s):  
Path Length ◽  
Quality Measures ◽  
Optimization Methods ◽  
Path Optimization ◽  
Free Motion ◽  
Configuration Spaces ◽  
High Dimensional ◽  
Practical Applications ◽  
Randomized Sampling ◽  
Motion Paths

Randomized sampling-based motion planners could efficiently generate collision-free motion paths. However, these paths have some quality problems (with respect to quality measures, such as path length, clearance and smoothness), especially in high dimensional configuration spaces. Thus, researchers studied some path optimization methods to improve path quality and to make paths suitable for practical applications. This paper reviews some of the most influential path optimization methods and gives an overall perspective on the most widely used ideas in the field.

scholarly journals Data Quality Measures and Efficient Evaluation Algorithms for Large-Scale High-Dimensional Data

2021 ◽  
Vol 11 (2) ◽  
pp. 472
Author(s):  
Hyeongmin Cho ◽  
Sangkyun Lee
Keyword(s):  
Machine Learning ◽  
Data Quality ◽  
Large Scale ◽  
High Dimensional Data ◽  
Quality Measures ◽  
Training Data ◽  
Measure Data ◽  
High Dimensional ◽  
Small Scale ◽  
Class Separability

Machine learning has been proven to be effective in various application areas, such as object and speech recognition on mobile systems. Since a critical key to machine learning success is the availability of large training data, many datasets are being disclosed and published online. From a data consumer or manager point of view, measuring data quality is an important first step in the learning process. We need to determine which datasets to use, update, and maintain. However, not many practical ways to measure data quality are available today, especially when it comes to large-scale high-dimensional data, such as images and videos. This paper proposes two data quality measures that can compute class separability and in-class variability, the two important aspects of data quality, for a given dataset. Classical data quality measures tend to focus only on class separability; however, we suggest that in-class variability is another important data quality factor. We provide efficient algorithms to compute our quality measures based on random projections and bootstrapping with statistical benefits on large-scale high-dimensional data. In experiments, we show that our measures are compatible with classical measures on small-scale data and can be computed much more efficiently on large-scale high-dimensional datasets.

scholarly journals Double-Arc Parallel Coordinates and its Axes re-Ordering Methods

2020 ◽  
Vol 25 (4) ◽  
pp. 1376-1391
Author(s):  
Liangfu Lu ◽  
Wenbo Wang ◽  
Zhiyuan Tan
Keyword(s):  
High Dimensional Data ◽  
Two Dimensions ◽  
High Dimensional ◽  
Data Sets ◽  
Parallel Coordinates ◽  
Practical Applications ◽  
Data Volume ◽  
Visual Clutter ◽  
Correlation Information ◽  
Value Decomposition

AbstractThe Parallel Coordinates Plot (PCP) is a popular technique for the exploration of high-dimensional data. In many cases, researchers apply it as an effective method to analyze and mine data. However, when today’s data volume is getting larger, visual clutter and data clarity become two of the main challenges in parallel coordinates plot. Although Arc Coordinates Plot (ACP) is a popular approach to address these challenges, few optimization and improvement have been made on it. In this paper, we do three main contributions on the state-of-the-art PCP methods. One approach is the improvement of visual method itself. The other two approaches are mainly on the improvement of perceptual scalability when the scale or the dimensions of the data turn to be large in some mobile and wireless practical applications. 1) We present an improved visualization method based on ACP, termed as double arc coordinates plot (DACP). It not only reduces the visual clutter in ACP, but use a dimension-based bundling method with further optimization to deals with the issues of the conventional parallel coordinates plot (PCP). 2)To reduce the clutter caused by the order of the axes and reveal patterns that hidden in the data sets, we propose our first dimensional reordering method, a contribution-based method in DACP, which is based on the singular value decomposition (SVD) algorithm. The approach computes the importance score of attributes (dimensions) of the data using SVD and visualize the dimensions from left to right in DACP according the score in SVD. 3) Moreover, a similarity-based method, which is based on the combination of nonlinear correlation coefficient and SVD algorithm, is proposed as well in the paper. To measure the correlation between two dimensions and explains how the two dimensions interact with each other, we propose a reordering method based on non-linear correlation information measurements. We mainly use mutual information to calculate the partial similarity of dimensions in high-dimensional data visualization, and SVD is used to measure global data. Lastly, we use five case scenarios to evaluate the effectiveness of DACP, and the results show that our approaches not only do well in visualizing multivariate dataset, but also effectively alleviate the visual clutter in the conventional PCP, which bring users a better visual experience.

scholarly journals Bounding on rough terrain with the LittleDog robot

2010 ◽  
Vol 30 (2) ◽  
pp. 192-215 ◽  
Author(s):  
Alexander Shkolnik ◽  
Michael Levashov ◽  
Ian R. Manchester ◽  
Russ Tedrake
Keyword(s):  
State Space ◽  
Open Loop ◽  
Random Trees ◽  
Configuration Spaces ◽  
High Dimensional ◽  
Rough Terrain ◽  
Task Space ◽  
Motion Primitive ◽  
Dimensional State Space ◽  
Planning Algorithm

A motion planning algorithm is described for bounding over rough terrain with the LittleDog robot. Unlike walking gaits, bounding is highly dynamic and cannot be planned with quasi-steady approximations. LittleDog is modeled as a planar five-link system, with a 16-dimensional state space; computing a plan over rough terrain in this high-dimensional state space that respects the kinodynamic constraints due to underactuation and motor limits is extremely challenging. Rapidly Exploring Random Trees (RRTs) are known for fast kinematic path planning in high-dimensional configuration spaces in the presence of obstacles, but search efficiency degrades rapidly with the addition of challenging dynamics. A computationally tractable planner for bounding was developed by modifying the RRT algorithm by using: (1) motion primitives to reduce the dimensionality of the problem; (2) Reachability Guidance, which dynamically changes the sampling distribution and distance metric to address differential constraints and discontinuous motion primitive dynamics; and (3) sampling with a Voronoi bias in a lower-dimensional “task space” for bounding. Short trajectories were demonstrated to work on the robot, however open-loop bounding is inherently unstable. A feedback controller based on transverse linearization was implemented, and shown in simulation to stabilize perturbations in the presence of noise and time delays.

scholarly journals Meta-Heuristic Optimization Methods for Quaternion-Valued Neural Networks

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 938
Author(s):  
Jeremiah Bill ◽  
Lance Champagne ◽  
Bruce Cox ◽  
Trevor Bihl
Keyword(s):  
Neural Networks ◽  
Optimization Methods ◽  
Network Size ◽  
High Dimensional ◽  
Proof Of Concept ◽  
Activation Functions ◽  
Hypercomplex Numbers ◽  
Neural Network Structure ◽  
Future Work ◽  
High Dimensional Datasets

In recent years, real-valued neural networks have demonstrated promising, and often striking, results across a broad range of domains. This has driven a surge of applications utilizing high-dimensional datasets. While many techniques exist to alleviate issues of high-dimensionality, they all induce a cost in terms of network size or computational runtime. This work examines the use of quaternions, a form of hypercomplex numbers, in neural networks. The constructed networks demonstrate the ability of quaternions to encode high-dimensional data in an efficient neural network structure, showing that hypercomplex neural networks reduce the number of total trainable parameters compared to their real-valued equivalents. Finally, this work introduces a novel training algorithm using a meta-heuristic approach that bypasses the need for analytic quaternion loss or activation functions. This algorithm allows for a broader range of activation functions over current quaternion networks and presents a proof-of-concept for future work.

Mode-Pursuing Sampling Method Using Discriminative Coordinate Perturbation for High-Dimensional Expensive Black-Box Optimization

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Yufei Wu ◽  
Teng Long ◽  
Renhe Shi ◽  
G. Gary Wang
Keyword(s):  
Design Optimization ◽  
Sampling Method ◽  
Sequential Sampling ◽  
Computational Cost ◽  
Optimization Methods ◽  
Black Box ◽  
High Dimensional ◽  
Beam Design ◽  
Convergence Performance ◽  
Coordinate Perturbation

Abstract This article presents a novel mode-pursuing sampling method using discriminative coordinate perturbation (MPS-DCP) to further improve the convergence performance of solving high-dimensional, expensive, and black-box (HEB) problems. In MPS-DCP, a discriminative coordinate perturbation strategy is integrated into the original mode-pursuing sampling (MPS) framework for sequential sampling. During optimization, the importance of variables is defined by approximated global sensitivities, while the perturbation probabilities of variables are dynamically adjusted according to the number of optimization stalling iterations. Expensive points considering both optimality and space-filling property are selected from cheap points generated by perturbing the current best point, which balances between global exploration and local exploitation. The convergence property of MPS-DCP is theoretically analyzed. The performance of MPS-DCP is tested on several numerical benchmarks and compared with state-of-the-art metamodel-based design optimization methods for HEB problems. The results indicate that MPS-DCP generally outperforms the competitive methods regarding convergence and robustness performances. Finally, the proposed MPS-DCP is applied to a stepped cantilever beam design optimization problem and an all-electric satellite multidisciplinary design optimization (MDO) problem. The results demonstrate that MPS-DCP can find better feasible optima with the same or less computational cost than the competitive methods, which demonstrates its effectiveness and practicality in solving real-world engineering problems.

scholarly journals An Empirical Study on Low Emission Taxiing Path Optimization of Aircrafts on Airport Surfaces from the Perspective of Reducing Carbon Emissions

Energies ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 1649 ◽  
Author(s):  
Nan Li ◽  
Yu Sun ◽  
Jian Yu ◽  
Jian-Cheng Li ◽  
Hong-fei Zhang ◽  
...  
Keyword(s):  
Real Time ◽  
Emission Reduction ◽  
Trajectory Optimization ◽  
Optimization Methods ◽  
Optimization Method ◽  
Path Optimization ◽  
Pollutant Emissions ◽  
Future Research ◽  
Aircraft Emissions ◽  
Fuel Consumption And Emissions

Aircraft emissions are the main cause of airport air pollution. One of the keys to achieving airport energy conservation and emission reduction is to optimize aircraft taxiing paths. The traditional optimization method based on the shortest taxi time is to model the aircraft under the assumption of uniform speed taxiing. Although it is easy to solve, it does not take into account the change of the velocity profile when the aircraft turns. In view of this, this paper comprehensively considered the aircraft’s taxiing distance, the number of large steering times and collision avoidance in the taxi, and established a path optimization model for aircraft taxiing at airport surface with the shortest total taxi time as the target. The genetic algorithm was used to solve the model. The experimental results show that the total fuel consumption and emissions of the aircraft are reduced by 35% and 46%, respectively, before optimization, and the taxi time is greatly reduced, which effectively avoids the taxiing conflict and reduces the pollutant emissions during the taxiing phase. Compared with traditional optimization methods that do not consider turning factors, energy saving and emission reduction effects are more significant. The proposed method is faster than other complex algorithms considering multiple factors, and has higher practical application value. It is expected to be applied in the more accurate airport surface real-time running trajectory optimization in the future. Future research will increase the actual interference factors of the airport, comprehensively analyze the actual situation of the airport’s inbound and outbound flights, dynamically adjust the taxiing path of the aircraft and maintain the real-time performance of the system, and further optimize the algorithm to improve the performance of the algorithm.

scholarly journals Mobile Robot Path Planning Based on a Generalized Wavefront Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Sifan Wu ◽  
Yu Du ◽  
Yonghua Zhang
Keyword(s):  
Path Planning ◽  
Mobile Robot ◽  
Path Length ◽  
Computation Time ◽  
Target Point ◽  
Multiple Target ◽  
Robot Path Planning ◽  
Practical Applications ◽  
Real Time Applications ◽  
Robot Path

This study develops a generalized wavefront algorithm for conducting mobile robot path planning. The algorithm combines multiple target point sets, multilevel grid costs, logarithmic expansion around obstacles, and subsequent path optimization. The planning performances obtained with the proposed algorithm, the A∗ algorithm, and the rapidly exploring random tree (RRT) algorithm optimized using a Bézier curve are compared using simulations with different grid map environments comprising different numbers of obstacles with varying shapes. The results demonstrate that the generalized wavefront algorithm generates smooth and safe paths around obstacles that meet the required kinematic conditions associated with the actual maneuverability of mobile robots and significantly reduces the planned path length compared with the results obtained with the A∗ algorithm and the optimized RRT algorithm with a computation time acceptable for real-time applications. Therefore, the generated path is not only smooth and effective but also conforms to actual robot maneuverability in practical applications.

Concept of Neighborhood Degree and its Application to Switching Plural Optimization Methods in Scheduling

2010 ◽  
Vol 14 (1) ◽  
pp. 21-27
Author(s):  
Fangyan Dong ◽  
◽  
Kewei Chen ◽  
Kaoru Hirota ◽  
Keyword(s):  
Simulated Annealing ◽  
Tabu Search ◽  
Vehicle Routing ◽  
Optimization Methods ◽  
Optimization Process ◽  
Scheduling Problems ◽  
Solution Quality ◽  
Practical Applications ◽  
Benchmark Data

A concept of neighborhood degree is proposed to evaluate the quality of solutions to scheduling problems such as vehicle routing, scheduling, and dispatching problems. It is possible to apply it to the optimization process of scheduling problems in order to switch between various optimization methods by considering convergence speed and solution quality. In the experiments on TSP benchmark data, two optimization methods, i.e., tabu search and simulated annealing, are switched effectively by observing the variation of the neighborhood degree. Directions for Practical applications are also mentioned.

scholarly journals Deterministic Agent-Based Path Optimization by Mimicking the Spreading of Ripples

2016 ◽  
Vol 24 (2) ◽  
pp. 319-346 ◽  
Author(s):  
Xiao-Bing Hu ◽  
Ming Wang ◽  
Mark S. Leeson ◽  
Ezequiel A. Di Paolo ◽  
Hao Liu
Keyword(s):  
Evolutionary Computation ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Path Optimization ◽  
Agent Based ◽  
Optimization Principle ◽  
Global Optimal ◽  
Effectiveness And Efficiency ◽  
Distinguishing Features ◽  
Theoretical Foundations

Inspirations from nature have contributed fundamentally to the development of evolutionary computation. Learning from the natural ripple-spreading phenomenon, this article proposes a novel ripple-spreading algorithm (RSA) for the path optimization problem (POP). In nature, a ripple spreads at a constant speed in all directions, and the node closest to the source is the first to be reached. This very simple principle forms the foundation of the proposed RSA. In contrast to most deterministic top-down centralized path optimization methods, such as Dijkstra’s algorithm, the RSA is a bottom-up decentralized agent-based simulation model. Moreover, it is distinguished from other agent-based algorithms, such as genetic algorithms and ant colony optimization, by being a deterministic method that can always guarantee the global optimal solution with very good scalability. Here, the RSA is specifically applied to four different POPs. The comparative simulation results illustrate the advantages of the RSA in terms of effectiveness and efficiency. Thanks to the agent-based and deterministic features, the RSA opens new opportunities to attack some problems, such as calculating the exact complete Pareto front in multiobjective optimization and determining the kth shortest project time in project management, which are very difficult, if not impossible, for existing methods to resolve. The ripple-spreading optimization principle and the new distinguishing features and capacities of the RSA enrich the theoretical foundations of evolutionary computation.

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