Browsing by Author "Shu-Cherng Fang, Committee Member"

Now showing 1 - 6 of 6

Exact and Heuristic Algorithms for the q-mode Problem
(2005-05-18) Kulkarni, Girish; Stephen Roberts, Committee Member; Shu-Cherng Fang, Committee Member; Carla Savage, Committee Member; Yahya Fathi, Committee Chair
In this dissertation we focus on the development of exact and inexact (i.e., heuristic) algorithms for the q-mode problem. The exact algorithms are based on integer programming models for the q-mode problem. We discuss the theoretical properties of an existing IP model and propose several enhancements. We also propose a new IP model for the problem and investigate these models through a comprehensive computational experiment. The experiment reveals that, in practice, the IP models are more effective for instances with strong natural clusters but less effective for instances containing weak natural clusters. We also propose exact algorithms based on the Benders decomposition for one of the IP models. The heuristic algorithm that we propose for the q-mode problem is a local improvement algorithm that is based on a very large scale neighborhood structure. We evaluate the algorithm through a computational experiment and empirically demonstrate its effectiveness.
Long-Term Spatial Load Forecasting Using Human-Machine Co-construct Intelligence Framework
(2008-10-28) Hong, Tao; Shu-Cherng Fang, Committee Member; Yahya Fathi, Committee Member; Simon M. Hsiang, Committee Chair
This thesis presents a formal study of the long-term spatial load forecasting problem: given small area based electric load history of the service territory, current and future land use information, return forecast load of the next 20 years. A hierarchical S-curve trending method is developed to conduct the basic forecast. Due to uncertainties of the electric load data, the results from the computerized program may conflict with the nature of the load growth. Sometimes, the computerized program is not aware of the local development because the land use data lacks such information. A human-machine co-construct intelligence framework is proposed to improve the robustness and reasonability of the purely computerized load forecasting program. The proposed algorithm has been implemented and applied to several utility companies to forecast the long-term electric load growth in the service territory and to get satisfying results.
The Nearest Point Problem in a Polyhedral Cone and Its Extensions
(2009-08-07) Liu, Zhe; Shu-Cherng Fang, Committee Member; Yahya Fathi, Committee Chair; Brian T. Denton, Committee Member; Richard H. Bernhard, Committee Member
The problem of finding the nearest point in a polyhedral cone to a given point in n-dimensional space can be formulated as a convex quadratic programming problem with special structure. This problem has applications in a wide range of areas, such as robotics, computer graphics, optimal control, and stochastic programming. In this research we study the geometrical structure of the nearest point problem in a polyhedral cone, and propose an efficient algorithm for solving this problem. We refer to this algorithm as the active index algorithm. In particular, we show that, given the index of one active constraint of the nearest point problem in a polyhedral cone, the order of the problem (number of variables and number of constraints) can be reduced by one. Further, by exploiting the relationship between the nearest point problem in a polyhedral cone and the nearest point problem in a pos cone, we design an efficient procedure to either find the optimal solution to the problem or find one of its active constraints. We also propose several strategies for efficient implementation of this algorithm. Furthermore, we show how we can use the active index algorithm to solve an instance of the nearest point problem in a polyhedral set. And finally we show how to extend the reach of this algorithm to solve any strictly convex quadratic programming problem with linear inequality constraints. In addition, we construct a large collection of instances using a random data generator. We then solve those instances using our proposed algorithm as well as the three solvers of Cplex 11 (Barrier solver, Primal Simplex solver, and Dual Simplex solver), and compare the corresponding execution times. Computational results show that for this collection of instances our proposed algorithm has a smaller execution time than any of the three solvers of Cplex 11.
Parameter Identification in Lumped Compartment Cardiorespiratory Models
(2009-04-13) Pope, Scott R.; C. T. Kelley, Committee Chair; Mette Olufsen, Committee Member; Shu-Cherng Fang, Committee Member; Ilse Ipsen, Committee Member
The parameter identification problem attempts to find parameter values that cause the solution of a predictive model to match data. In this work, parameters in cardiovascular and respiratory models are identified. This workÃ¢â‚¬â„¢s main contribution is in its application of gradient based optimization techniques and insight into methods to identify parameters that can be estimated given subject specific data. The models presented in this paper are lumped compartment models of the cardiovascular and respiratory systems. Lumped compartment models treat the cardiovascular and respiratory systems as collections of interconnected compartments transporting blood and exchanging oxygen and carbon dioxide. Using these compartments, a system of ordinary differential equations (ODE) is generated that incorporates several physiological parameters representing vascular resistances, compliances, and tissue metabolic rates. The solution to this ODE system is used to predict cerebral blood flow, systemic arterial blood pressure, and expired carbon dioxide partial pressures, which are then compared to subject data. Minimizing the two-norm difference between between the result of the predictive model and the experimental data is a non-linear least squares problem. Although the least squares problem is overdetermined, the data do not contain enough information to determine all model parameters. A combination of sensitivity analysis, expert knowledge, and subset selection techniques reduce the number of model parameters estimated.
A Price Trajectory Algorithm for Solving Iterative Auction Problems
(2006-12-11) Zhong, Jie; Carla D. Savage, Committee Member; Yahya Fathi, Committee Member; Shu-Cherng Fang, Committee Member; Peter R. Wurman, Committee Chair
A variety of auctions exist in the literature such as the English auction, the Dutch auction, and the Vickrey auction. The underlying problem in an auction is to find the winners and the corresponding payments. Proxy bidding has proven useful in solving auction problems in many real–world auction formats, most notably eBay. It has been proposed for several iterative combinatorial auctions, such as the Ascending Package auction, the Ascending k-Bundle auction, and the iBundle auction. In this dissertation, a new type of iterative auction called the Simple Combinatorial Proxy auction is proposed. The winners of the new auction are the same as that of the Ascending k-Bundle auction. Simulating the incremental bidding decisions of the agents is a popular method to solve proxy-enabled version of the auction problems. This approach has some disadvantages. First, the outcome depends upon implementation details. Second, the accuracy of the outcome relies on the bid increment. Third, the running time is sensitive to the magnitude of values, the ordering of agents, and the tie–breaking rules. In this dissertation, a new approach called the Price Trajectory Algorithm is presented to solve iterative combinatorial auctions with proxy bidding. This approach computes the agents' allocation of their attention across the bundles only at "inflection points" — the points at which agents change their behavior. Inflections are caused by one the following reasons: (1) an introduction of a new bundle into an agent's demand set, (2) a change in the set of current competitive allocations, or (3) a withdrawal of an agent from the set of active agents. The proposed algorithm tracks the behavior of agents and the competitive allocations of items to establish a connection between the demand set and competitive allocations. With the allocation of agents' attention, one can compute the slopes of price curves to get the bundle prices and speed up the computation by jumping from one inflection point to the next. The price trajectory algorithm can solve the Simple Combinatorial Proxy Auction and the Ascending Package Auction. It has several advantages over alternatives: (1) it computes exact solutions; (2) the solutions are independent of the bid increment or tie-breaking rules; and (3) the solutions are invariant to the magnitude of the bids. For the security consideration, a cryptographic protocol is presented for the price trajectory algorithm. It guarantees that only the auctioneer obtains the correct and necessary information from the agents and there is no leak of private information between agents. The detection of fraud by the auctioneer is also discussed.
A Sample-path Optimization Approach for Optimal Resource Allocation in Stochastic Projects
(2007-03-13) Morgan, Clayton; Salah Elmaghraby, Committee Chair; Xiuli Chao, Committee Member; Shu-Cherng Fang, Committee Member
The purpose of this research has been to develop an optimization method that can be utilized to determine optimal resource allocations for projects in an uncertain (stochastic) environment. The project under consideration is modeled as a stochastic activity network (SAN) where the workload requirements for each activity are assumed to be random with some specified distribution. Our concern is the time/cost tradeoff problem where the project manager can affect the duration of each activity in the project by allocating more or less of a scarce resource to the competing activities (at some cost). The objective is therefore to minimize the total expected cost of the project by assigning the resource to the various activities while simultaneously respecting precedence relationships among the activities and constraints on the total resource available. In particular we would like to analyze stochastic projects of reasonable size (>100 activities) and provide an optimization tool that achieves results in sufficiently small amount of time to make its application practical for realistic project management scenarios.