Three essays on sequencing and routing problems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2005.Includes bibliographical references (leaves 157-162).In this thesis we study different combinatorial optimization problems. These problems arise in many practical settings where there is a need for finding good solutions fast. The first class of problems we study are vehicle routing problems, and the second type of problems are sequencing problems. We study approximation algorithms and local search heuristics for these problems. First, we analyze the Vehicle Routing Problem (VRP) with and without split deliveries. In this problem, we have to route vehicles from the depot to deliver the demand to the customers while minimizing the total traveling cost. We present a lower bound for this problem, improving a previous bound of Haimovich and Rinnooy Kan. This bound is then utilized to improve the worst-case approximation algorithm of the Iterated Tour Partitioning (ITP) heuristic when the capacity of the vehicles is constant. Second, we analyze a particular case of the VRP, when the customers are uniformly distributed i.i.d. points on the unit square of the plane, and have unit demand. We prove that there exists a constant c > 0 such that the ITP heuristic is a 2 - c approximation algorithm with probability arbitrarily close to one as the number of customers goes to infinity. This result improves the approximation factor of the ITP heuristic under the worst-case analysis, which is 2. We also generalize this result and previous ones to the multi-depot case. Third, we study a language to generate Very Large Scale Neighborhoods for sequencing problems. Local search heuristics are among the most popular approaches to solve hard optimization problems.(cont.) Among them, Very Large Scale Neighborhood Search techniques present a good balance between the quality of local optima and the time to search a neighborhood. We develop a language to generate exponentially large neighborhoods for sequencing problems using grammars. We develop efficient generic dynamic programming solvers that determine the optimal neighbor in a neighborhood generated by a grammar for a list of sequencing problems, including the Traveling Salesman Problem and the Linear Ordering Problem. This framework unifies a variety of previous results on exponentially large neighborhoods for the Traveling Salesman Problem.by Agustín Bompadre.Ph.D

Using grammars to generate very large scale neighborhoods for the traveling salesman problem and other sequencing problems

Local search heuristics are among the most popular approaches to solve hard optimization problems. Among them, Very Large Scale Neighborhood Search techniques present a good balance between the quality of local optima and the time to search a neighborhood. We develop a language to generate exponentially large neighborhoods for sequencing problems using grammars. We develop efficient generic dynamic programming solvers that determine the optimal neighbor in a neighborhood generated by a grammar for sequencing problems such as the Traveling Salesman Problem or the Linear Ordering Problem. This framework unifies a variety of previous results on exponentially large neighborhood for the Traveling Salesman Problem and generalizes them to other sequencing problems

An algorithmic approach to system architecting using shape grammar-cellular automata

Thesis (Ph. D.)--Massachusetts Institute of Technology, Engineering Systems Division, 2008.Includes bibliographical references (p. 404-417).This thesis expands upon the understanding of the fundamentals of system architecting in order to more effectively apply this process to engineering systems. The universal concern about the system architecting process is that the needs and wants of the stakeholders are not being fully satisfied, primarily because too few design alternatives are created and ambiguity exists in the information required. At the same time, it is noted that nature offers a superb example of system architecting and therefore should be considered as a guide for the engineering of systems. Key features of nature's architecting processes include self-generation, diversity, emergence, least action (balance of kinetic and potential energy), system-of-systems organization, and selection for stability. Currently, no human-friendly method appears to exist that addresses the problems in the field of system architecture while at the same time emulating nature's processes. By adapting nature's self-generative approach, a systematic means is offered to more rigorously conduct system architecting and better satisfy stakeholders. After reviewing generative design methods, an algorithmic methodology is developed to generate a space of architectural solutions satisfying a given specification, local constraints, and physical laws. This approach combines a visually oriented human design interface (shape grammar) that provides an intuitive design language with a machine (cellular automata) to execute the system architecture's production set (algorithm). The manual output of the flexible shape grammar, the set of design rules, is transcribed into cellular automata neighborhoods as a sequenced production set that may include other simple programs (such as combinatoric instructions).(cont.) The resulting catalog of system architectures can be unmanageably large, so selection criteria (e.g., stability, matching interfaces, least action) are defined by the architect to narrow the solution space for stakeholder review. The shape grammar-cellular automata algorithmic approach was demonstrated across several domains of study. This methodology improves on the design's clarification and the number of design alternatives produced, which should result in greater stakeholder satisfaction. Of additional significance, this approach has shown value both in the study of the system architecting process, leading to the proposal of normative principles for system architecture, and in the modeling of systems for better understanding.by Thomas H. Speller, Jr.Ph.D

Evolutionary Computation

This book presents several recent advances on Evolutionary Computation, specially evolution-based optimization methods and hybrid algorithms for several applications, from optimization and learning to pattern recognition and bioinformatics. This book also presents new algorithms based on several analogies and metafores, where one of them is based on philosophy, specifically on the philosophy of praxis and dialectics. In this book it is also presented interesting applications on bioinformatics, specially the use of particle swarms to discover gene expression patterns in DNA microarrays. Therefore, this book features representative work on the field of evolutionary computation and applied sciences. The intended audience is graduate, undergraduate, researchers, and anyone who wishes to become familiar with the latest research work on this field

Towards hybrid methods for solving hard combinatorial optimization problems

Tesis doctoral leída en la Escuela Politécnica Superior de la Universidad Autónoma de Madrid el 4 de septiembre de 200

Tracking the Temporal-Evolution of Supernova Bubbles in Numerical Simulations

The study of low-dimensional, noisy manifolds embedded in a higher dimensional space has been extremely useful in many applications, from the chemical analysis of multi-phase flows to simulations of galactic mergers. Building a probabilistic model of the manifolds has helped in describing their essential properties and how they vary in space. However, when the manifold is evolving through time, a joint spatio-temporal modelling is needed, in order to fully comprehend its nature. We propose a first-order Markovian process that propagates the spatial probabilistic model of a manifold at fixed time, to its adjacent temporal stages. The proposed methodology is demonstrated using a particle simulation of an interacting dwarf galaxy to describe the evolution of a cavity generated by a Supernov

Distributed Learning, Prediction and Detection in Probabilistic Graphs.

Critical to high-dimensional statistical estimation is to exploit the structure in the data distribution. Probabilistic graphical models provide an efficient framework for representing complex joint distributions of random variables through their conditional dependency graph, and can be adapted to many high-dimensional machine learning applications. This dissertation develops the probabilistic graphical modeling technique for three statistical estimation problems arising in real-world applications: distributed and parallel learning in networks, missing-value prediction in recommender systems, and emerging topic detection in text corpora. The common theme behind all proposed methods is a combination of parsimonious representation of uncertainties in the data, optimization surrogate that leads to computationally efficient algorithms, and fundamental limits of estimation performance in high dimension. More specifically, the dissertation makes the following theoretical contributions: (1) We propose a distributed and parallel framework for learning the parameters in Gaussian graphical models that is free of iterative global message passing. The proposed distributed estimator is shown to be asymptotically consistent, improve with increasing local neighborhood sizes, and have a high-dimensional error rate comparable to that of the centralized maximum likelihood estimator. (2) We present a family of latent variable Gaussian graphical models whose marginal precision matrix has a “low-rank plus sparse” structure. Under mild conditions, we analyze the high-dimensional parameter error bounds for learning this family of models using regularized maximum likelihood estimation. (3) We consider a hypothesis testing framework for detecting emerging topics in topic models, and propose a novel surrogate test statistic for the standard likelihood ratio. By leveraging the theory of empirical processes, we prove asymptotic consistency for the proposed test and provide guarantees of the detection performance.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/110499/1/mengzs_1.pd

Machine intelligence and robotics: Report of the NASA study group

Opportunities for the application of machine intelligence and robotics in NASA missions and systems were identified. The benefits of successful adoption of machine intelligence and robotics techniques were estimated and forecasts were prepared to show their growth potential. Program options for research, advanced development, and implementation of machine intelligence and robot technology for use in program planning are presented