Variation In Greedy Approach To Set Covering Problem

The weighted set covering problem is to choose a number of subsets to cover all the elements in a universal set at the lowest cost. It is a well-studied classical problem with applications in various fields like machine learning, planning, information retrieval, facility allocation, etc. Deep web crawling refers to the process of gathering documents that have been structured into a data source and can be retrieved through a search interface. Its query selection process calls for an efficient solution to the set covering problem

Assignment Algorithms for Multi-Robot Task Allocation in Uncertain and Dynamic Environments

Multi-robot task allocation is a general approach to coordinate a team of robots to complete a set of tasks collectively. The classical works adopt relevant theories from other disciplines (e.g., operations research, economics), but oftentimes they are not adequately rich to deal with the properties from the robotics domain such as perception that is local and communication which is limited. This dissertation reports the efforts on relaxing the assumptions, making problems simpler and developing new methods considering the constraints or uncertainties in robot problems. We aim to solve variants of classical multi-robot task allocation problems where the team of robots operates in dynamic and uncertain environments. In some of these problems, it is adequate to have a precise model of nondeterministic costs (e.g., time, distance) subject to change at run-time. In some other problems, probabilistic or stochastic approaches are adequate to incorporate uncertainties into the problem formulation. For these settings, we propose algorithms that model dynamics owing to robot interactions, new cost representations incorporating uncertainty, algorithms specialized for the representations, and policies for tasks arriving in an online manner. First, we consider multi-robot task assignment problems where costs for performing tasks are interrelated, and the overall team objective need not be a standard sum-of costs (or utilities) model, enabling straightforward treatment of the additional costs incurred by resource contention. In the model we introduce, a team may choose one of a set of shared resources to perform a task (e.g., several routes to reach a destination), and resource contention is modeled when multiple robots use the same resource. We propose efficient task assignment algorithms that model this contention with different forms of domain knowledge and compute an optimal assignment under such a model. Second, we address the problem of finding the optimal assignment of tasks to a team of robots when the associated costs may vary, which arises when robots deal with uncertain situations. We propose a region-based cost representation incorporating the cost uncertainty and modeling interrelationships among costs. We detail how to compute a sensitivity analysis that characterizes how much costs may change before optimality is violated. Using this analysis, robots are able to avoid unnecessary re-assignment computations and reduce global communication when costs change. Third, we consider multi-robot teams operating in probabilistic domains. We represent costs by distributions capturing the uncertainty in the environment. This representation also incorporates inter-robot couplings in planning the team’s coordination. We do not have the assumption that costs are independent, which is frequently used in probabilistic models. We propose algorithms that help in understanding the effects of different characterizations of cost distributions such as mean and Conditional Value-at-Risk (CVaR), in which the latter assesses the risk of the outcomes from distributions. Last, we study multi-robot task allocation in a setting where tasks are revealed sequentially and where it is possible to execute bundles of tasks. Particularly, we are interested in tasks that have synergies so that the greater the number of tasks executed together, the larger the potential performance gain. We provide an analysis of bundling, giving an understanding of the important bundle size parameter. Based on the qualitative basis, we propose multiple simple bundling policies that determine how many tasks the robots bundle for a batched planning and execution

Monte Carlo Method with Heuristic Adjustment for Irregularly Shaped Food Product Volume Measurement

Volume measurement plays an important role in the production and processing of food products. Various methods have been proposed to measure the volume of food products with irregular shapes based on 3D reconstruction. However, 3D reconstruction comes with a high-priced computational cost. Furthermore, some of the volume measurement methods based on 3D reconstruction have a low accuracy. Another method for measuring volume of objects uses Monte Carlo method. Monte Carlo method performs volume measurements using random points. Monte Carlo method only requires information regarding whether random points fall inside or outside an object and does not require a 3D reconstruction. This paper proposes volume measurement using a computer vision system for irregularly shaped food products without 3D reconstruction based on Monte Carlo method with heuristic adjustment. Five images of food product were captured using five cameras and processed to produce binary images. Monte Carlo integration with heuristic adjustment was performed to measure the volume based on the information extracted from binary images. The experimental results show that the proposed method provided high accuracy and precision compared to the water displacement method. In addition, the proposed method is more accurate and faster than the space carving method

Mathematical optimization for the visualization of complex datasets

This PhD dissertation focuses on developing new Mathematical Optimization models and solution approaches which help to gain insight into complex data structures arising in Information Visualization. The approaches developed in this thesis merge concepts from Multivariate Data Analysis and Mathematical Optimization, bridging theoretical mathematics with real life problems. The usefulness of Information Visualization lies with its power to improve interpretability and decision making from the unknown phenomena described by raw data, as fully discussed in Chapter 1. In particular, datasets involving frequency distributions and proximity relations, which even might vary over the time, are the ones studied in this thesis. Frameworks to visualize such enclosed information, which make use of Mixed Integer (Non)linear Programming and Difference of Convex tools, are formally proposed. Algorithmic approaches such as Large Neighborhood Search or Difference of Convex Algorithm enable us to develop matheuristics to handle such models. More specifically, Chapter 2 addresses the problem of visualizing a frequency distribution and an adjacency relation attached to a set of individuals. This information is represented using a rectangular map, i.e., a subdivision of a rectangle into rectangular portions so that their areas reflect the frequencies, and the adjacencies between portions represent the adjacencies between the individuals. The visualization problem is formulated as a Mixed Integer Linear Programming model, and a matheuristic that has this model at its heart is proposed. Chapter 3 generalizes the model presented in the previous chapter by developing a visualization framework which handles simultaneously the representation of a frequency distribution and a dissimilarity relation. This framework consists of a partition of a given rectangle into piecewise rectangular portions so that the areas of the regions represent the frequencies and the distances between them represent the dissimilarities. This visualization problem is formally stated as a Mixed Integer Nonlinear Programming model, which is solved by means of a matheuristic based on Large Neighborhood Search. Contrary to previous chapters in which a partition of the visualization region is sought, Chapter 4 addresses the problem of visualizing a set of individuals, which has attached a dissimilarity measure and a frequency distribution, without necessarily cov-ering the visualization region. In this visualization problem individuals are depicted as convex bodies whose areas are proportional to the given frequencies. The aim is to determine the location of the convex bodies in the visualization region. In order to solve this problem, which generalizes the standard Multidimensional Scaling, Difference of Convex tools are used. In Chapter 5, the model stated in the previous chapter is extended to the dynamic case, namely considering that frequencies and dissimilarities are observed along a set of time periods. The solution approach combines Difference of Convex techniques with Nonconvex Quadratic Binary Optimization. All the approaches presented are tested in real datasets. Finally, Chapter 6 closes this thesis with general conclusions and future lines of research.Esta tesis se centra en desarrollar nuevos modelos y algoritmos basados en la Optimización Matemática que ayuden a comprender estructuras de datos complejas frecuentes en el área de Visualización de la Información. Las metodologías propuestas fusionan conceptos de Análisis de Datos Multivariantes y de Optimización Matemática, aunando las matemáticas teóricas con problemas reales. Como se analiza en el Capítulo 1, una adecuada visualización de los datos ayuda a mejorar la interpretabilidad de los fenómenos desconocidos que describen, así como la toma de decisiones. Concretamente, esta tesis se centra en visualizar datos que involucran distribuciones de frecuencias y relaciones de proximidad, pudiendo incluso ambas variar a lo largo del tiempo. Se proponen diferentes herramientas para visualizar dicha información, basadas tanto en la Optimización (No) Lineal Entera Mixta como en la optimización de funciones Diferencia de Convexas. Además, metodologías como la Búsqueda por Entornos Grandes y el Algoritmo DCA permiten el desarrollo de mateheurísticas para resolver dichos modelos. Concretamente, el Capítulo 2 trata el problema de visualizar simultáneamente una distribución de frequencias y una relación de adyacencias en un conjunto de individuos. Esta información se representa a través de un mapa rectangular, es decir, una subdivisión de un rectángulo en porciones rectangulares, de manera que las áreas de estas porciones representen las frecuencias y las adyacencias entre las porciones representen las adyacencias entre los individuos. Este problema de visualización se formula con la ayuda de la Optimización Lineal Entera Mixta. Además, se propone una mateheurística basada en este modelo como método de resolución. En el Capítulo 3 se generaliza el modelo presentado en el capítulo anterior, construyendo una herramienta que permite visualizar simultáneamente una distribución de frecuencias y una relación de disimilaridades. Dicha visualización se realiza mediante la partición de un rectángulo en porciones rectangulares a trozos de manera que el área de las porciones refleje la distribución de frecuencias y las distancias entre las mismas las disimilaridades. Se plantea un modelo No Lineal Entero Mixto para este problema de visualización, que es resuelto a través de una mateheurística basada en la Búsqueda por Entornos Grandes. En contraposición a los capítulos anteriores, en los que se busca una partición de la región de visualización, el Capítulo 4 trata el problema de representar una distribución de frecuencias y una relación de disimilaridad sobre un conjunto de individuos, sin forzar a que haya que recubrir dicha región de visualización. En este modelo de visualización los individuos son representados como cuerpos convexos cuyas áreas son proporcionales a las frecuencias dadas. El objetivo es determinar la localización de dichos cuerpos convexos dentro de la región de visualización. Para resolver este problema, que generaliza el tradicional Escalado Multidimensional, se utilizan técnicas de optimización basadas en funciones Diferencia de Convexas. En el Capítulo 5, se extiende el modelo desarrollado en el capítulo anterior para el caso en el que los datos son dinámicos, es decir, las frecuencias y disimilaridades se observan a lo largo de varios instantes de tiempo. Se emplean técnicas de optimización de funciones Diferencias de Convexas así como Optimización Cuadrática Binaria No Convexa para la resolución del modelo. Todas las metodologías propuestas han sido testadas en datos reales. Finalmente, el Capítulo 6 contiene las conclusiones a esta tesis, así como futuras líneas de investigación.Premio Extraordinario de Doctorado U

Network modeling and optimization for energy and sustainable transit

Energy and transportation systems are integral to our infrastructure. Along with other types of networks, critical challenges constantly arise, particularly with regard to accessibility, efficiency, optimality, and sustainability. In this dissertation, we use mixed integer programming, data mining and mixed complementarity techniques to address some of these challenges. We have developed an improved schematic mapping algorithm to facilitate the process of network representation for a variety of systems beyond transportation. We also discover fundamental patterns in bicycle ownership on a global scale with implications for sustainable urban planning and public health outcomes. Finally, we model the fast-growing crude oil market in North America, implementing scenarios that point to integrated approaches to exports, pipeline investments and targeted rail restrictions as most viable for addressing medium-term oil transportation concerns. The methods we employ are generalizable to other types of energy and transit systems, and beyond. Finally, we discuss the importance of these methods to newer applications