The Traveling Salesman Problem: An Analysis and Comparison of Metaheuristics and Algorithms

One of the most investigated topics in operations research is the Traveling Salesman Problem (TSP) and the algorithms that can be used to solve it. Despite its relatively simple formulation, its computational difficulty keeps it and potential solution methods at the forefront of current research. This paper defines and analyzes numerous proposed solutions to the TSP in order to facilitate understanding of the problem. Additionally, the efficiencies of different heuristics are studied and compared to the aforementioned algorithms’ accuracy, as a quick algorithm is often formulated at the expense of an exact solution

Temporal Action Segmentation: An Analysis of Modern Techniques

Temporal action segmentation (TAS) in videos aims at densely identifying video frames in minutes-long videos with multiple action classes. As a long-range video understanding task, researchers have developed an extended collection of methods and examined their performance using various benchmarks. Despite the rapid growth of TAS techniques in recent years, no systematic survey has been conducted in these sectors. This survey analyzes and summarizes the most significant contributions and trends. In particular, we first examine the task definition, common benchmarks, types of supervision, and prevalent evaluation measures. In addition, we systematically investigate two essential techniques of this topic, i.e., frame representation and temporal modeling, which have been studied extensively in the literature. We then conduct a thorough review of existing TAS works categorized by their levels of supervision and conclude our survey by identifying and emphasizing several research gaps. In addition, we have curated a list of TAS resources, which is available at https://github.com/nus-cvml/awesome-temporal-action-segmentation.Comment: 19 pages, 9 figures, 8 table

Sparse octree algorithms for scalable dense volumetric tracking and mapping

This thesis is concerned with the problem of Simultaneous Localisation and Mapping (SLAM), the task of localising an agent within an unknown environment and at the same time building a representation of it. In particular, we tackle the fundamental scalability limitations of dense volumetric SLAM systems. We do so by proposing a highly efficient hierarchical data-structure based on octrees together with a set of algorithms to support the most compute-intensive operations in typical volumetric reconstruction pipelines. We employ our hierarchical representation in a novel dense pipeline based on occupancy probabilities. Crucially, the complete space representation encoded by the octree enables to demonstrate a fully integrated system in which tracking, mapping and occupancy queries can be performed seamlessly on a single coherent representation. While achieving accuracy either at par or better than the current state-of-the-art, we demonstrate run-time performance of at least an order of magnitude better than currently available hierarchical data-structures. Finally, we introduce a novel multi-scale reconstruction system that exploits our octree hierarchy. By adaptively selecting the appropriate scale to match the effective sensor resolution in both integration and rendering, we demonstrate better reconstruction results and tracking accuracy compared to single-resolution grids. Furthermore, we achieve much higher computational performance by propagating information up and down the tree in a lazy fashion, which allow us to reduce the computational load when updating distant surfaces. We have released our software as an open-source library, named supereight, which is freely available for the benefit of the wider community. One of the main advantages of our library is its flexibility. By carefully providing a set of algorithmic abstractions, supereight enables SLAM practitioners to freely experiment with different map representations with no intervention on the back-end library code and crucially, preserving performance. Our work has been adopted by robotics researchers in both academia and industry.Open Acces

Super-Resolution of Unmanned Airborne Vehicle Images with Maximum Fidelity Stochastic Restoration

Super-resolution (SR) refers to reconstructing a single high resolution (HR) image from a set of subsampled, blurred and noisy low resolution (LR) images. One may, then, envision a scenario where a set of LR images is acquired with sensors on a moving platform like unmanned airborne vehicles (UAV). Due to the wind, the UAV may encounter altitude change or rotational effects which can distort the acquired as well as the processed images. Also, the visual quality of the SR image is affected by image acquisition degradations, the available number of the LR images and their relative positions. This dissertation seeks to develop a novel fast stochastic algorithm to reconstruct a single SR image from UAV-captured images in two steps. First, the UAV LR images are aligned using a new hybrid registration algorithm within subpixel accuracy. In the second step, the proposed approach develops a new fast stochastic minimum square constrained Wiener restoration filter for SR reconstruction and restoration using a fully detailed continuous-discrete-continuous (CDC) model. A new parameter that accounts for LR images registration and fusion errors is added to the SR CDC model in addition to a multi-response restoration and reconstruction. Finally, to assess the visual quality of the resultant images, two figures of merit are introduced: information rate and maximum realizable fidelity. Experimental results show that quantitative assessment using the proposed figures coincided with the visual qualitative assessment. We evaluated our filter against other SR techniques and its results were found to be competitive in terms of speed and visual quality

PREDICTIVE MATURITY OF INEXACT AND UNCERTAIN STRONGLY COUPLED NUMERICAL MODELS

The Computer simulations are commonly used to predict the response of complex systems in many branches of engineering and science. These computer simulations involve the theoretical foundation, numerical modeling and supporting experimental data, all of which contain their associated errors. Furthermore, real-world problems are generally complex in nature, in which each phenomenon is described by the respective constituent models representing different physics and/or scales. The interactions between such constituents are typically complex in nature, such that the outputs of a particular constituent may be the inputs for one or more constituents. Thus, the natural question then arises concerning the validity of these complex computer model predictions, especially in cases where these models are executed in support of high-consequence decision making. The overall accuracy and precision of the coupled system is then determined by the accuracy and precision of both the constituents and the coupling interface. Each constituent model has its own uncertainty and bias error. Furthermore, the coupling interface also brings in a similar spectrum of uncertainties and bias errors due to unavoidably inexact and incomplete data transfer between the constituents. This dissertation contributes to the established knowledge of partitioned analysis by investigating the numerical uncertainties, validation and uncertainty quantification of strongly coupled inexact and uncertain models. The importance of this study lies in the urgent need for gaining a better understanding of the simulations of coupled systems, such as those in multi-scale and multi-physics applications, and to identify the limitations due to uncertainty and bias errors in these models

Numerical Treatment of Non-Linear System for Latently Infected CD4+T Cells: A Swarm- Optimized Neural Network Approach

Swarm-inspired computing techniques are the best candidates for solving various nonlinear problems. The current study aims to exploit the swarm intelligence technique known as Particle Swarm Optimization (PSO) for the numerical investigation of a nonlinear system of latently infected CD4+T cells. The strength of the Mexican Hat Wavelet (MHW) based unsupervised Feed Forward Artificial Neural Network (FFANN) is used to solve the nonlinear system of latently infected CD4+T cells. The function approximation of unsupervised ANN is used to construct the mathematical model of the latently infected CD4+T cells by defining the error function in the mean square manner. The adjustable parameters called the unknowns of the network are optimized by using the Particle Swarm Optimization (PSO), Nedler Mead Simplex Method (NMSM), and their hybrid PSO-NMSM. The PSO applied for the global optimization of weights aided by the NMSM algorithm for rapid local search. Finally, a Comprehensive Monte Carlo simulation and statistical analysis of the analytical method, numerical Range Kutta (RK) method, ANN optimized with Genetic Algorithm (GA) aided with Sequential Quadratic Programming (SQP) known as GA-SQP, ANN-PSO-SQP and the proposed MHW-HIVFFANN-PSO-NMSM are performed to validate the effectiveness, stability, convergence, and computational complexity of each scheme. It is observed that the proposed MHW-FFANN-HIVPSO-NMSM scheme has converged in all classes at 10 −6 , 10−7 , and 10 −8 and solved the nonlinear system of latently infected CD4+ T cells more accurately and effectively. The absolute error lies in 10−3 , 10−4 , 10−4 , and 10−5 for numerical, ANN-GA-SQP, ANN-PSO-SQP, and proposed MHW-ANN-PSO-NMSM respectively. Moreover, the proposed scheme is stable for the large number of independent runs. The values for global statistical indicators’ global mean squared error are lies 8.15E-09, 3.25E-10, 4.15E-09, and 3.15E-10 for class X(t), W(t), Y(t), and V(t) respectively whereas the global mean absolute deviation lies in range 7.35E-09, 8.50E-10, 2.10E-10 and 7.10E-09

Modeling Electrokinetic Flows with the Discrete Ion Stochastic Continuum Overdamped Solvent Algorithm

In this article we develop an algorithm for the efficient simulation of electrolytes in the presence of physical boundaries. In previous work the Discrete Ion Stochastic Continuum Overdamped Solvent (DISCOS) algorithm was derived for triply periodic domains, and was validated through ion-ion pair correlation functions and Debye-H{\"u}ckel-Onsager theory for conductivity, including the Wien effect for strong electric fields. In extending this approach to include an accurate treatment of physical boundaries we must address several important issues. First, the modifications to the spreading and interpolation operators necessary to incorporate interactions of the ions with the boundary are described. Next we discuss the modifications to the electrostatic solver to handle the influence of charges near either a fixed potential or dielectric boundary. An additional short-ranged potential is also introduced to represent interaction of the ions with a solid wall. Finally, the dry diffusion term is modified to account for the reduced mobility of ions near a boundary, which introduces an additional stochastic drift correction. Several validation tests are presented confirming the correct equilibrium distribution of ions in a channel. Additionally, the methodology is demonstrated using electro-osmosis and induced charge electro-osmosis, with comparison made to theory and other numerical methods. Notably, the DISCOS approach achieves greater accuracy than a continuum electrostatic simulation method. We also examine the effect of under-resolving hydrodynamic effects using a `dry diffusion' approach, and find that considerable computational speedup can be achieved with a negligible impact on accuracy.Comment: 27 pages, 15 figure