Theses
http://hdl.handle.net/10012/6
Sun, 20 May 2018 22:27:42 GMT2018-05-20T22:27:42ZThe Capacitated Matroid Median Problem
http://hdl.handle.net/10012/13331
The Capacitated Matroid Median Problem
Kalhan, Sanchit
In this thesis, we study the capacitated generalization of the Matroid Median Problem which is a generalization of the classical clustering problem called the k-Median problem. In the capacitated matroid median problem, we are given a set F of facilities, a set D of clients and a common metric defined on F ∪ D, where the cost of connecting client j to facility i is denoted as c_{ij}. Each client j ∈ D has a demand of d_j, and each facility i ∈ F has an opening cost of f_i and a capacity u_i which limits the amount of demand that can be assigned to facility i. Moreover, there is a matroid M = (F,I) defined on the set of facilities. A solution to the capacitated matroid median problem involves opening a set of facilities F' ⊆ F such that F' ∈ I, and figuring out an assignment i(j) ∈ F' for every j ∈ D such that each facility i ∈ F' is assigned at most u_i demand. The cost associated with such a solution is : Σ_{i∈F} f_i + Σ_{j∈D} d_j c_{i(j)j}. Our goal is to find a solution of minimum cost.
As the Matroid Median Problem generalizes the classical NP-Hard problem called k- median, it also is NP-Hard. We provide a bi-criteria approximation algorithm for the capacitated Matroid Median Problem with uniform capacities based on rounding the natural LP for the problem. Our algorithm achieves an approximation guarantee of 76 and violates the capacities by a factor of at most 6. We complement this result by providing two integrality gap results for the natural LP for capacitated matroid median.
Fri, 18 May 2018 00:00:00 GMThttp://hdl.handle.net/10012/133312018-05-18T00:00:00ZData Driven Efficiency for E-Warehousing: Descriptive and Prescriptive Analytics
http://hdl.handle.net/10012/13330
Data Driven Efficiency for E-Warehousing: Descriptive and Prescriptive Analytics
Ugur, Yildiz
Based on data provided by a warehouse logistics management company, we analyze the warehousing operation and its major processes of order picking and order consolidation. Without access to the actual layouts and process flow diagrams, we analyze the data to describe the processes in detail, and prescribe changes to improve the operation.
We investigate the characteristics of the order preparation process and the order consolidation operation. We find that products from different orders are mixed for effective picking. Similar products from different orders are picked together in containers called totes. Full totes are stored in a buffer area, and then routed to a conveyor system where products are sorted. The contents of the totes are then consolidated into orders. This order consolidation process depends on the sequence in which totes are processed and has a huge impact on the order completion time. OCP is a new problem for both the warehouse management system and the parallel machine scheduling literature. We provide mathematical formulations for the problem and devise two solution methods. The first is a simulated annealing metaheuristic, while the second is an exact branch-and-price method.
We test the solutions on both random and industry data. Simulated Annealing is found to achieve near optimal solutions within 0.01 % of optimality. For the branch-and-price approach, we use a set partitioning formulation and a column generation method where the subproblems are single machine scheduling problems that are solved using dynamic programming. We also devise a new branching rule and new dynamic programming algorithm to solve the subproblem after branching. To assess the efficiency of the proposed branch-and-price methodology, we compare against the branch-and-price approach of Chen and Powell (1999) for the parallel machine scheduling problem. We take advantage of the fact that OCP is a generalization of the parallel machine scheduling problem. The proposed, more general, branch-and-price approach achieves the same solution quality, but takes more time.
Fri, 18 May 2018 00:00:00 GMThttp://hdl.handle.net/10012/133302018-05-18T00:00:00ZMath Information Retrieval using a Text Search Engine
http://hdl.handle.net/10012/13329
Math Information Retrieval using a Text Search Engine
Dallas, Fraser
Combining text and mathematics when searching in a corpus with extensive mathematical
notation remains an open problem. Recent results for math information retrieval systems
on the math and text retrieval task at NTCIR-12, for example, show room for improvement,
even though formula retrieval appears to be fairly successful.
This thesis explores how to adapt the state-of-the-art BM25 text ranking method to
work well when searching for math and text together. Symbol layout trees are used to
represent math formulas, and features are extracted from the trees, which are then used
as search terms for BM25. This thesis explores various features of symbol layout trees and
explores their effects on retrieval performance. Based on the results, a set of features are
recommended that can be used effectively in a conventional text-based retrieval engine.
The feature set is validated using various NTCIR math only benchmarks.
Various proximity measures show math and text are closer in documents deemed rel-
evant than documents deemed non-relevant for NTCIR queries. Therefore it would seem
that proximity could improve ranking for math information retrieval systems when search-
ing for both math and text. Nevertheless, two attempts to include proximity when scoring
matches were unsuccessful in improving retrieval effectiveness.
Finally, the BM25 ranking of both math and text using the feature set designed for
formula retrieval is validated by various NTCIR math and text benchmarks.
Fri, 18 May 2018 00:00:00 GMThttp://hdl.handle.net/10012/133292018-05-18T00:00:00ZRule Derivation for Agent-Based Models of Complex Systems: Nuclear Waste Management and Road Networks Case Studies
http://hdl.handle.net/10012/13325
Rule Derivation for Agent-Based Models of Complex Systems: Nuclear Waste Management and Road Networks Case Studies
Garcia Hernandez, Jorge Andres
This thesis explores the relation between equation-based models (EBMs) and agent-based models (ABMs), in particular, the derivation of agent rules from equations such that agent collective behavior produces results that match or are close to those from EBMs.
This allows studying phenomena using both approaches and obtaining an understanding of the aggregate behavior as well as the individual mechanisms that produce them. The use of ABMs allows the inclusion of more realistic features that would not be possible (or would be difficult to include) using EBMs.
The first part of the thesis studies the derivation of molecule displacement probabilities from the diffusion equation using cellular automata. The derivation is extended to include reaction and advection terms. This procedure is later applied to estimate lifetimes of nuclear waste containers for various scenarios of interest and the inclusion of uncertainty.
The second part is concerned with the derivation of a Bayesian state algorithm that consolidates collective real-time information about the state of a given system and outputs a probability density function of state domain, from which the most probable state can be computed at any given time. This estimation is provided to agents so that they can choose the best option for them. The algorithm includes a diffusion or diffusion-like term to account for the deterioration of information as time goes on. This algorithm is applied to a couple of road networks where drivers, prior to selecting a route, have access to current information about the traffic and are able to decide which path to follow.
Both problems are complex due to heterogeneous components, nonlinearities, and stochastic behavior; which make them difficult to describe using classical equation models such as the diffusion equation or optimization models. The use of ABMs allowed for the inclusion of such complex features in the study of their respective systems.
Fri, 18 May 2018 00:00:00 GMThttp://hdl.handle.net/10012/133252018-05-18T00:00:00Z