Date of Award
M.S. in Engineering Science
Paul M. Goggans
In the thesis, we study the theory of Markov Chain Monte Carlo (MCMC) and its application in statistical optimization. The MCMC method is a class of evolutionary algorithms for generating samples from given probability distributions. In the thesis, we first focus on the methods of slice sampling and simulated annealing. While slice sampling has a merit to generate samples based on the underlying distribution with adjustable step size, simulated annealing can facilitate samples to jump out of local optima and converge quickly to the global optimum. With this MCMC method, we then solve two practical optimization problems. The first problem is image transmission over varying channels. Existing work in media transmission generally assumes that channel condition is stationary. However, communication channels are often varying with time in practice. Adaptive design needs frequent feedback for channel updates, which is often impractical due to the complexity and delay. In this application, we design an unequal error protection scheme for image transmission over noisy varying channels based on MCMC. First, the problem cost function is mapped into a multi-variable probability distribution. Then, with the “detailed balance", MCMC is used to generate samples from the mapped stationary distribution so that the optimal solution is the one that gives the lowest data distortion. We also show that the final rate allocation designed with this method works better than a conventional design that considers the mean value of the channel. In the second application, we consider a terminal-location-planning problem for intermodal transportation systems. With a given number of potential locations, it needs to find the most appropriate number of terminals and their locations to provide the economically most efficient operation when multiple service pairs exist simultaneously. The problem also has an inherent issue that for a particular planning, the optimal route paths must be determined for the co-existing service pairs. To solve this NP-hard problem, we design a MCMC-based two-layer method. The lower-layer is an optimal routing design for all service pairs given a particular planning that considers both efficiency and fairness. The upper-layer is finding the optimal planning based on MCMC with the stationary distribution that is mapped from the cost function. The effectiveness of this method is demonstrated through computer simulations and comparison with one state-of-the-art method. The work of this thesis has shown that a MCMC-method, consisting of both slice sampling and simulated annealing, can be successfully applied to solving practical optimization problems. Particularly, the method has advantages in dealing with high-dimensional problems with large searching spaces.
Wu, Xiaobin, "Mcmc- Based Optimization And Application" (2015). Electronic Theses and Dissertations. 522.
Emphasis: Electrical Engineering