Browsing by Author "Desai, Jitamitra"

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    A Discrete Optimization Approach to Solve a Reader Location Problem for Estimating Travel Times
    Desai, Jitamitra (Virginia Tech, 2002-04-26)
    Traffic incidents routinely impact the flow of vehicles on roadways. These incidents need to be identified, and responded to in a timely fashion in order to keep traffic moving safely and efficiently. One of the main areas of transportation research that remains of contemporary interest is the study of travel times. Travel time information technologies, until very recently, have not been efficient enough to provide instantaneous information for managing traffic flow. The Virginia Department of Transportation (VDOT) currently operates a number of surveillance technologies. Of particular interest to us are Automatic Vehicle Identification (AVI) tag readers to assimilate travel time information. One of VDOT's latest research thrusts has been to develop efficient algorithms for estimating link travel times using such advanced technologies. To achieve this purpose, VDOT is currently monitoring volunteer tagged cars by using AVI tag readers fixed at certain specific locations. This thesis focuses on devising an efficient methodology to capture as much travel time information as possible, by solving a Reader Location Problem that maximizes the benefit accruing from measuring travel time variability with respect to freeways. This problem is formulated as a quadratic 0-1 optimization problem. The objective function parameters in the optimization problem represent certain benefit factors resulting from the ability to measure travel time variability along various origin-destination paths. A simulation study using the INTEGRATION package is performed to derive these benefit factors for various types of freeway sections, and two composite functions that measure benefits for O-D paths that are comprised of several such sections are presented. The simulation results are presented as generic look-up tables, and can be used for any freeway section for the purpose of computing the associated benefit factor coefficient. An optimization approach based on the Reformulation-Linearization Technique coupled with Semidefinite Programming concepts is designed to solve the formulated reader location problem. This approach can be used to derive alternative equivalent formulations of the problem that vary in the degree of tightness of their underlying linear programming relaxations. Four such model representations are explored by using the software package, AMPL-CPLEX 6.5.3, to solve them for some sample transportation networks. The sensitivity of the reader locations to the different proposed benefit factor composite functions is also investigated. The results indicate that the first level continuous RLT relaxation to problem RL produces a tight underlying representation and that the optimal solution obtained for this relaxation tends to be very close to the actual integer optimum. Moreover, it is found that the optimal locations of the readers are insensitive to either the traffic, or the benefit factor used, or the density of the graph, when these factors are considered individually. However, a combination of two or more of these factors can lead to a change in the optimal locations of the readers.
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    Solving Factorable Programs with Applications to Cluster Analysis, Risk Management, and Control Systems Design
    Desai, Jitamitra (Virginia Tech, 2005-06-28)
    Ever since the advent of the simplex algorithm, linear programming (LP) has been extensively used with great success in many diverse fields. The field of discrete optimization came to the forefront as a result of the impressive developments in the area of linear programming. Although discrete optimization problems can be viewed as belonging to the class of nonconvex programs, it has only been in recent times that optimization research has confronted the more formidable class of continuous nonconvex optimization problems, where the objective function and constraints are often highly nonlinear and nonconvex functions, defined in terms of continuous (and bounded) decision variables. Typical classes of such problems involve polynomial, or more general factorable functions. This dissertation focuses on employing the Reformulation-Linearization Technique (RLT) to enhance model formulations and to design effective solution techniques for solving several practical instances of continuous nonconvex optimization problems, namely, the hard and fuzzy clustering problems, risk management problems, and problems arising in control systems. Under the umbrella of the broad RLT framework, the contributions of this dissertation focus on developing models and algorithms along with related theoretical and computational results pertaining to three specific application domains. In the basic construct, through appropriate surrogation schemes and variable substitution strategies, we derive strong polyhedral approximations for the polynomial functional terms in the problem, and then rely on the demonstrated (robust) ability of the RLT for determining global optimal solutions for polynomial programming problems. The convergence of the proposed branch-and-bound algorithm follows from the tailored branching strategy coupled with consistency and exhaustive properties of the enumeration tree. First, we prescribe an RLT-based framework geared towards solving the hard and fuzzy clustering problems. In the second endeavor, we examine two risk management problems, providing novel models and algorithms. Finally, in the third part, we provide a detailed discussion on studying stability margins for control systems using polynomial programming models along with specialized solution techniques.