UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.
More information is available at Theses and Dissertations at University of Maryland Libraries.
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Item Stabilizing Column Generation via Dual Optimal Inequalities with Applications in Logistics and Robotics(2020) Haghani, Naveed; Balan, Radu; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This work addresses the challenge of stabilizing column generation (CG) via dual optimal inequalities (DOI). We present two novel classes of DOI for the general context of set cover problems. We refer to these as Smooth DOI (S-DOI) and Flexible DOI (F-DOI). S-DOI can be interpreted as allowing for the undercovering of items at the cost of overcovering others and incurring an objective penalty. SDOI leverage the fact that dual values associated with items should change smoothly over space. F-DOI can be interpreted as offering primal objective rewards for the overcovering of items. We combine these DOI to produce a joint class of DOI called Smooth-Flexible DOI (SF-DOI). We apply these DOI to three classical problems in logistics and operations research: the Single Source Capacitated Facility Location Problem, the Capacitated p-Median Problem, and the Capacitated Vehicle Routing Problem. We prove that these DOI are valid and are guaranteed to not alter the optimal solution of CG. We also present techniques for their use in the case of solvingCG with relaxed column restrictions. This work also introduces a CG approach to Multi-Robot Routing (MRR). MRR considers the problem of routing a fleet of robots in a warehouse to collectively complete a set of tasks while prohibiting collisions. We present two distinct formulations that tackle unique problem variants. The first we model as a set packing problem, while the second we model as a set cover problem. We show that the pricing problem for both approaches amounts to an elementary resource constrained shortest path problem (ERCSPP); an NP-hard problem commonly studied in other CG problem contexts. We present an efficient implementation of our CG approach that radically reduces the state size of the ERCSPP. Finally, we present a novel heuristic algorithm for solving the ERCSPP and offer probabilistic guarantees forits likelihood to deliver the optimal solution.Item Solving the integrated school bell time, and bus routing and scheduling optimization problem under the deterministic and stochastic conditions(2019) Wang, Zhongxiang; Haghani, Ali; Civil Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The school bus planning problem (SBPP) has drawn significant attention in research and practice because of its importance in pupil transportation. The major task of the SBPP is to simultaneously optimize the school bell times, the routing plan (a set of trips) and the scheduling plan (the assignment of buses to serve these trips) while maintaining the minimum level-of-service requirements with the objective that the total number of buses and the total vehicle time are both minimized. Many subproblems of the SBPP have been well studied, but the integrated problem lacks much research due to its complexity. A Mixed Integer Programming (MIP) model is proposed for the integrated SBPP. A novel decomposition method is developed to solve the model. It distinguishes itself from the literature with the consideration of trip compatibility in the routing stage, which is a piece of essential information in the following scheduling stage. This ‘look ahead’ strategy finds a new balance between the model integration and decomposition, which solves the problem efficiently as a decomposed problem but with the high solution quality as the integrated model. Three heuristic algorithms are proposed to solve the deterministic SBPP with the trip compatibility. Then, two mathematical programming models and a Column Generation-based algorithm are proposed for the SBPP under traffic congestion and stochastic travel time in a real uncertain world. These innovative algorithms incorporate the merits of the Simulated Annealing, Tabu Search, Insertion Algorithm, and Greedy Randomized Adaptive Search Procedure and gain the computational power that the existing methods do not have. The experiments are conducted on randomly generated datasets, benchmark problems, and real-world cases. The results show that the proposed models and algorithms outperform the state-of-the-art method in all test problems by up to 25%. In a real-world case study, after the bell time adjustment, up to 41% of current buses can be saved with even better service with respect to the higher punctuality and shorter student ride time.Item Models for Budget Constrained Auctions: An Application to Sponsored Search & Other Auctions(2010) Pani, Abhishek; Raghavan, Subramanian; Business and Management: Decision & Information Technologies; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The last decade has seen the emergence of auction mechanisms for pricing and allocating goods on the Internet. A successful application area for auctions has been sponsored search. Search firms like Google, Bing and Yahoo have shown stellar revenue growths due to their ability to run large number of auctions in a computationally efficient manner. The online advertisement market in the U.S. is estimated to be around $41 billion in 2010 and expected to grow to $50 billion by 2011 (http://www.marketingcharts.com/interactive/us-online-advertising-market-to-reach-50b-in-2011-3128/). The paid search component is estimated to account for nearly 50% of online advertising spend. This dissertation considers two problems in the sponsored search auction domain. In sponsored search, the search operator solves a multi-unit allocation and pricing problem with the specified bidder values and budgets. The advertisers, on the other hand, regularly solve a bid determination problem for the different keywords, given their budget and other business constraints. We develop a model for the auctioneer that allows the bidders to place differing bids for different advertisement slots for any keyword combination. Despite the increased complexity, our model is solved in polynomial time. Next, we develop a column-generation procedure for large advertisers to bid optimally in the sponsored search auctions. Our focus is on solving large-scale versions of the problem. Multi-unit auctions have also found a number of applications in other areas that include supply chain coordination, wireless spectrum allocation and transportation. Current research in the multi-unit auction domain ignores the budget constraint faced by participants. We address the computational issues faced by the auctioneer when dealing with budget constraints in a multi-unit auction. We propose an optimization model and solution approach to ensure that the allocation and prices are in the core. We develop an algorithm to determine an allocation and Walrasian equilibrium prices (when they exist) under additive bidder valuations where the auctioneer's goal is social welfare maximization and extend the approach to address general package auctions. We, also, demonstrate the applicability of the Benders decomposition technique to model and solve the revenue maximization problem from an auctioneer's standpoint.Item Column Generation in Infeasible Predictor-Corrector Methods for Solving Linear Programs(2009) Nicholls, Stacey Oneeta; O'Leary, Dianne P.; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Primal &ndash dual interior &ndash point methods (IPMs) are distinguished for their exceptional theoretical properties and computational behavior in solving linear programming (LP) problems. Consider solving the primal &ndash dual LP pair using an IPM such as a primal &ndash dual Affine &ndash Scaling method, Mehrotra's Predictor &ndash Corrector method (the most commonly used IPM to date), or Potra's Predictor &ndash Corrector method. The bulk of the computation in the process stems from the formation of the normal equation matrix, AD2A T, where A \in \Re {m times n} and D2 = S{-1}X is a diagonal matrix. In cases when n >> m, we propose to reduce this cost by incorporating a column generation scheme into existing infeasible IPMs for solving LPs. In particular, we solve an LP problem based on an iterative approach where we select a &ldquo small &rdquo subset of the constraints at each iteration with the aim of achieving both feasibility and optimality. Rather than n constraints, we work with k = |Q| \in [m,n] constraints at each iteration, where Q is an index set consisting of the k most nearly active constraints at the current iterate. The cost of the formation of the matrix, AQ DQ2 AQT, reduces from &theta(m2 n) to &theta(m2 k) operations, where k is relatively small compared to n. Although numerical results show an occasional increase in the number of iterations, the total operation count and time to solve the LP using our algorithms is, in most cases, small compared to other &ldquo reduced &rdquo LP algorithms.Item Air Express Network Design with Hub Sorting(2007-11-05) Ngamchai, Somnuk; Schonfeld, Paul M.; Civil Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation examines an innovative strategic operation for next day air package delivery. The proposed system, in which some packages are sorted twice at two distinct hubs before arriving at their destinations, is investigated for its potential savings. A two-stage sorting operation is proposed and compared to the currently operated single-stage sorting operation. By considering the endogenous optimization of hub sorting and storage capacities, cost minimization models are developed for both operations and used for performance comparison. Two solution approaches are presented in this study, namely the Column Generation (CG) approach and the Genetic Algorithm (GA) approach. The first method is implemented to optimize the problem by means of linear programming (LP) relaxation, in which the resulting model is then embedded into a branch-and-bound approach to generate an integer solution. However, for solving realistic problem sizes, the model is intractable with the conventional time-space formulation. Therefore, a Genetic Algorithm is developed for solving a large-scale problem. The GA solution representation is classified into two parts, a grouping representation for hub assignment and an aircraft route representation for aircraft route cycles. Several genetic operators are specifically developed based on the problem characteristics to facilitate the search. After optimizing the solution, we compare not only the potential cost saving from the proposed system, but also the system's reliability based on its slack. To provide some insights on the effects of two-stage operation, several factors are explored such as the location of regional hubs, single and multiple two-stage routings and aircraft mix. Sensitivity analyses are conducted under different inputs, including different demand levels, aircraft operating costs and hub operating costs. Additional statistics on aircraft utilization, hub capacity utilization, circuity factor, average transfers per package, and system slack gain/loss by commodity, are analyzed to elucidate the changes in system characteristics.