A Dual Ascent Procedure for Large Scale Uncapacitated Network Design

The fixed-charge network design problem arises in a variety of problem contexts including transportation, communication, and production scheduling.We develop a family of dual ascent algorithms for this problem. This approach generalizes known ascent procedures for solving shortest path, plant location,Steiner network and directed spanning tree problems. Our computational results for several classes of test problems with up to 500 integer and 1.98 million continuous variables and constraints shows that the dual ascent procedure and an associated drop-add heuristic generates solutions that, in almost all cases, are guaranteed to be within 1 to 3 percent of optimality. Moreover, the procedure requires no more than 150 seconds on an IBM 3083 computer. The test problems correspond to dense and sparse networks,including some models arising in freight transport

Inter-domain router placement and traffic engineering

The Internet is organized as an interconnection of separate administrative domains called Autonomous Systems (AS). The Border Gateway Protocol (BGP) is the de facto standard for controlling the routing of traffic across different ASs. It supports scalable distribution of reachability and routing policy information among different ASs. In this paper, we study a network design problem which determines (1) the optimal placement of border router(s) within a domain and (2) the corresponding inter-and intra-domain traffic patterns within an AS. Practical constraints imposed by BGP and other standard shortest-path-based intra-domain routing protocols are considered. The problem is formulated as a variant of the uncapacitated network design problem (UNDP). While it is feasible to use a brute-force, integer-programming-based approach for tackling small instances of this problem, we have resorted to a dual-ascent approximation approach for mid/large-scale instances. The quality of the approximation approach is evaluated in terms of its computational efficiency and network cost sub-optimality. Sensitivity analysis w.r.t. various network/traffic parameters are also conducted. We then describe how one can apply our optimization results to better configure BGP as well as other intra-domain routing protocols. This serves as a first-step towards the auto-configuration of Internet routing protocols, BGP in particular, which is "well-known" for its tedious and error-prone configuration needs.published_or_final_versio

A dual-based algorithm for multi-level network design

Includes bibliographical references.Supported in part by a grant from the AT&T Research Fund.Anantaram Balakrishnan, Thomas L. Magnanti, Prakash Mirchandani

Primal-dual variable neighborhood search for the simple plant-location problem

Copyright @ 2007 INFORMSThe variable neighborhood search metaheuristic is applied to the primal simple plant-location problem and to a reduced dual obtained by exploiting the complementary slackness conditions. This leads to (i) heuristic resolution of (metric) instances with uniform fixed costs, up to n = 15,000 users, and m = n potential locations for facilities with an error not exceeding 0.04%; (ii) exact solution of such instances with up to m = n = 7,000; and (iii) exact solutions of instances with variable fixed costs and up to m = n = 15, 000.This work is supported by NSERC Grant 105574-02; NSERC Grant OGP205041; and partly by the Serbian Ministry of Science, Project 1583

A Dual-Based Algorithm for Multi-Level Network Design

Given an undirected network with L possible facility types for each edge, and a partition of the nodes into L levels, the Multi-level Network Design (MLND) problem seeks a fixed cost minimizing design that spans all the nodes and connects the nodes at each level by facilities of the corresponding or higher type. This problem generalizes the well-known Steiner network problem and the hierarchical network design problem, and has applications in telecommunication, transportation, and electric power distribution network design. In a companion paper we introduced the problem, studied alternative model formulations, and analyzed the worst-case performance of heuristics based on Steiner network and spanning tree solutions. This paper develops and tests a dual-based algorithm for the Multi-level Network Design (MLND) problem. The method first performs problem preprocessing to fix certain design variables, and then applies a dual ascent procedure to generate upper and lower bounds on the optimal value. We report extensive computational results on large, random networks (containing up to 500 nodes, and 5000 edges) with varying cost structures. The integer programming formulation of the largest of these problems has 20,000 integer variables and over 5 million constraints. Our tests indicate that the dualbased algorithm is very effective, producing solutions guaranteed to be within 0 to 0.9% of optimality

File Allocation and Join Site Selection Problem in Distributed Database Systems.

There are two important problems associated with the design of distributed database systems. One is the file allocation problem, and the other is the query optimization problem. In this research a methodology that considers both these aspects is developed that determines the optimal location of files and join sites for given queries simultaneously. Using this methodology, three different mixed integer programming models that describe three cases of the file allocation and join site selection problem are developed. Dual-based procedures are developed for each of the three mixed integer programming models. Extensive computational testing is performed which shows that the dual-based algorithms developed are able to generate solutions which are very close to the optimal. Also, these near optimal solutions are found very quickly, even for large scale problems

Separable Concave Optimization Approximately Equals Piecewise-Linear Optimization

We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our main result is that when the feasible set is a polyhedron, the number of resulting pieces is polynomial in the input size of the polyhedron and linear in 1/epsilon. For many practical concave cost problems, the resulting piecewise-linear cost problem can be formulated as a well-studied discrete optimization problem. As a result, a variety of polynomial-time exact algorithms, approximation algorithms, and polynomial-time heuristics for discrete optimization problems immediately yield fully polynomial-time approximation schemes, approximation algorithms, and polynomial-time heuristics for the corresponding concave cost problems. We illustrate our approach on two problems. For the concave cost multicommodity flow problem, we devise a new heuristic and study its performance using computational experiments. We are able to approximately solve significantly larger test instances than previously possible, and obtain solutions on average within 4.27% of optimality. For the concave cost facility location problem, we obtain a new 1.4991+epsilon approximation algorithm.Comment: Full pape

Network hub locations problems: the state of the art

Cataloged from PDF version of article.Hubs are special facilities that serve as switching, transshipment and sorting points in many-to-many distribution systems. The hub location problem is concerned with locating hub facilities and allocating demand nodes to hubs in order to route the traffic between origin-destination pairs. In this paper we classify and survey network hub location models. We also include some recent trends on hub location and provide a synthesis of the literature. (C) 2007 Elsevier B.V. All rights reserved

Dual-Based Local Search for Deterministic, Stochastic and Robust Variants of the Connected Facility Location Problem

In this dissertation, we propose the study of a family of network design problems that arise in a wide range of practical settings ranging from telecommunications to data management. We investigate the use of heuristic search procedures coupled with lower bounding mechanisms to obtain high quality solutions for deterministic, stochastic and robust variants of these problems. We extend the use of well-known methods such as the sample average approximation for stochastic optimization and the Bertsimas and Sim approach for robust optimization with heuristics and lower bounding mechanisms. This is particular important for NP-complete problems where even deterministic and small instances are difficult to solve to optimality. Our extensions provide a novel way of applying these techniques while using heuristics; which from a practical perspective increases their usefulness