Polynomial-time highest-gain augmenting path algorithms for the generalized circulation problem

Includes bibliographical references (p. 15-16).Supported in part by NSF. DMS 94-14438 DMS 95-27124 Supported in part by DOE. DE-FG02-92ER25126 Supported as well by grants from UPS and ONR. N00014-96-1-0051by Donald Goldfarb, Zhiying Jin, James B. Orlin

An E-relaxation method for separable convex cost generalized network flow problems

Cover title. "The extended abstract of this article appeared in the proceedings of the 5th International IPCO Conference, Vancouver, June 1996."--P. 1.Includes bibliographical references (p. 18-21).Supported by the National Science Foundation. CCR-9311621, DMI-9300494by Paul Tseng, Dimitri P. Bertsekas

Auction algorithms for generalized nonlinear network flow problems

Thesis (Ph.D.)--Boston UniversityNetwork flow is an area of optimization theory concerned with optimization over networks with a range of applicability in fields such as computer networks, manufacturing, finance, scheduling and routing, telecommunications, and transportation. In both linear and nonlinear networks, a family of primal-dual algorithms based on "approximate" Complementary Slackness (ε-CS) is among the fastest in centralized and distributed environments. These include the auction algorithm for the linear assignment/transportation problems, ε-relaxation and Auction/Sequential Shortest Path (ASSP) for the min-cost flow and max-flow problems. Within this family, the auction algorithm is particularly fast, as it uses "second best" information, as compared to using the more generic ε-relaxation for linear assignment/transportation. Inspired by the success of auction algorithms, we extend them to two important classes of nonlinear network flow problems. We start with the nonlinear Resource Allocation Problem (RAP). This problem consists of optimally assigning N divisible resources to M competing missions/tasks each with its own utility function. This simple yet powerful framework has found applications in diverse fields such as finance, economics, logistics, sensor and wireless networks. RAP is an instance of generalized network (networks with arc gains) flow problem but it has significant special structure analogous to the assignment/transportation problem. We develop a class of auction algorithms for RAP: a finite-time auction algorithm for both synchronous and asynchronous environments followed by a combination of forward and reverse auction with ε-scaling to achieve pseudo polynomial complexity for any non-increasing generalized convex utilities including non-continuous and/ or non-differentiable functions. These techniques are then generalized to handle shipping costs on allocations. Lastly, we demonstrate how these techniques can be used for solving a dynamic RAP where nodes may appear or disappear over time. In later part of the thesis, we consider the convex nonlinear min-cost flow problem. Although E-relaxation and ASSP are among the fastest available techniques here, we illustrate how nonlinear costs, as opposed to linear, introduce a significant bottleneck on the progress that these algorithms make per iteration. We then extend the core idea of the auction algorithm, use of second best to make aggressive steps, to overcome this bottleneck and hence develop a faster version of ε-relaxation. This new algorithm shares the same theoretical complexity as the original but outperforms it in our numerical experiments based on random test problem suites

Finding the minimum test set with the optimum number of internal probe points.

by Kwan Wai Wing Eric.Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.Includes bibliographical references.ABSTRACTACKNOWLEDGMENTLIST OF FIGURESLIST OF TABLESChapter Chapter 1 --- IntroductionChapter 1.1 --- Background --- p.1-1Chapter 1.2 --- E-Beam testing and test generation algorithm --- p.1-2Chapter 1.3 --- Motivation of this research --- p.1-4Chapter 1.4 --- Out-of-kilter Algorithm --- p.1-6Chapter 1.5 --- Outline of the remaining chapter --- p.1-7Chapter Chapter 2 --- Electron Beam TestingChapter 2.1 --- Background and Theory --- p.2-1Chapter 2.2 --- Principles and Instrumentation --- p.2-4Chapter 2.3 --- Implication of internal IC testing --- p.2-6Chapter 2.4 --- Advantage of Electron Beam Testing --- p.2-7Chapter Chapter 3 --- An exhaustive method to minimize test setsChapter 3.1 --- Basic Principles --- p.3-1Chapter 3.1.1 --- Controllability and Observability --- p.3-1Chapter 3.1.2 --- Single Stuck at Fault Model --- p.3-2Chapter 3.2 --- Fault Dictionary --- p.3-4Chapter 3.2.1 --- Input Format --- p.3-4Chapter 3.2.2 --- Critical Path Generation --- p.3-6Chapter 3.2.3 --- Probe point insertion --- p.3-8Chapter 3.2.4 --- Formation of Fault Dictionary --- p.3-9Chapter Chapter 4 --- Mathematical Model - Out-of-kilter algorithmChapter 4.1 --- Network Model --- p.4-1Chapter 4.2 --- Linear programming model --- p.4-3Chapter 4.3 --- Kilter states --- p.4-5Chapter 4.4 --- Flow change --- p.4-7Chapter 4.5 --- Potential change --- p.4-9Chapter 4.6 --- Summary and Conclusion --- p.4-10Chapter Chapter 5 --- Apply Mathematical Method to minimize test setsChapter 5.1 --- Implementation of OKA to the Fault Dictionary --- p.5-1Chapter 5.2 --- Minimize test set and optimize internal probings / probe points --- p.5-5Chapter 5.2.1 --- Minimize the number of test vectors --- p.5-5Chapter 5.2.2 --- Find the optimum number of internal probings --- p.5-8Chapter 5.2.3 --- Find the optimum number of internal probe points --- p.5-11Chapter 5.3 --- Fixed number of internal probings/probe points --- p.5-12Chapter 5.4 --- True minimum test set and optimum probing/ probe point --- p.5-14Chapter Chapter 6 --- Implementation and work examplesChapter 6.1 --- Generation of Fault Dictionary --- p.6-1Chapter 6.2 --- Finding the minimum test set without internal probe point --- p.6-5Chapter 6.3.1 --- Finding the minimum test set with optimum internal probing --- p.6-10Chapter 6.3.2 --- Finding the minimum test set with optimum internal probe point --- p.6-24Chapter 6.4 --- Finding the minimum test set by fixing the number of internal probings at 2 --- p.6-26Chapter 6.5 --- Program Description --- p.6-35Chapter Chapter 7 --- Realistic approach to find the minimum solutionChapter 7.1 --- Problem arising in exhaustive method --- p.7-1Chapter 7.2 --- Improvement work on existing test generation algorithm --- p.7-2Chapter 7.3 --- Reduce the search set --- p.7-5Chapter 7.3.1 --- Making the Fault Dictionary from existing test generation algorithm --- p.7-5Chapter 7.3.2 --- Making the Fault Dictionary by random generation --- p.7-9Chapter Chapter 8 --- ConclusionsChapter 8.1 --- Summary of Results --- p.8-1Chapter 8.2 --- Further Research --- p.8-5REFERENCES --- p.R-1Chapter Appendix A --- Fault Dictionary of circuit SC1 --- p.A-1Chapter Appendix B --- Fault Dictionary of circuit SC7 --- p.B-1Chapter Appendix C --- Simple Circuits Layout --- p.C-

A Generalized Network Model for Freight Car Distribution

We consider the empty freight car distribution problem (DP) at DB Schenker Rail Deutschland AG under a wide range of application relevant constraints and real data sets. The (DP) is an online assignment problem between geographically distributed empty freight car supplies and customer demands for such cars in preparation of good transport. The objective is to minimize transport costs for empty cars while distributing them effectively with respect to the constraints. In our case, one major constraint is given by prescheduled freight trains: obviously a supply can only be assigned to a demand if it reaches the latter in time. Further, the variety of goods (bulk cargo, steel coils, etc.) to be transported requires distinct types of freight cars. Freight cars of a certain type can be exchanged by cars of other types with respect to a given substitution scheme and different 'exchange rates'. Allowed substitutions are therefore another major constraint of the (DP). We describe further `hard' and `soft' constraints and sketch the current work flow at DB Schenker Rail Deutschland AG to find an adequate solution for the (DP) on a daily base in practice. The (DP) is currently solved separately for groups of car types and in several steps. Moreover, some steps contain manual pre- and post-processing to ensure certain constraints. Hence global sub-optimal distributions can occur. We therefore integrate all constraints into a generalized network flow model for the (DP). A global optimal distribution is then provided by an integral minimum cost flow in the network. To find such a flow is NP-hard in general. We show that a general substitution scheme makes our notion of the (DP) also NP-hard. Hence independent of the applied model and with respect to practical runtime requirements, we have to find a compromise between solution time and quality. We do so in two ways. Instances of the (DP) which correspond to classical flow networks are solved by an integral minimum cost flow, which can be obtained in polynomial time. We use such instances to polynomially obtain minimum cost flows of fixed bounded fractionality for certain general instances. For those instances occurring in the application we obtain half-integral flows, which can be rounded to approximate or heuristic distributions in linear time. Moreover, we develop a network-based reoptimization approach, which yields optimal solutions for subsequent instances with few changes very fast. This thesis was inspired and funded by a 2-year research and development project of DB Schenker Rail Deutschland AG in cooperation with the work group Faigle/Schrader of the University of Cologne and the work group of Prof. Dr. Sven O. Krumke at the Technical University of Kaiserslautern. The project included the implementation of the generalized network model and the reoptimization, approximation and heuristic methods. The software is designed as a future optimization kernel for the (DP) at DB Schenker Rail Deutschland AG