Thomas L. Magnanti

Massachusetts Institute of Technology, Cambridge, Massachusetts, United States

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Publications (111)98.3 Total impact

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    ABSTRACT: The Stochastic User Equilibrium (SUE) model predicts traffic equilibrium flow assuming that users choose their perceived maximum utility paths (or perceived shortest paths) while accounting for the effects of congestion that arise due to users sharing links. Inspired by recent work on distributionally robust optimization, specifically a Cross Moment (CMM) choice model, we develop a new SUE model that uses the mean and covariance information on path utilities but does not assume the particular form of the distribution. Robustness to distributional assumptions is obtained in this model by minimizing the worst-case expected cost over all distributions with fixed two moments. We show that under mild conditions, the CMM-SUE (Cross Moment-Stochastic User Equilibrium) exists and is unique. By combining a simple projected gradient ascent method to evaluate path choice probabilities with a gradient descent method to find flows, we show that the CMM-SUE is efficiently computable. CMM-SUE provides both modeling flexibility and computational advantages over approaches such as the well-known MNP-SUE (Multinomial Probit-Stochastic User Equilibrium) model that require distributional (normality) assumptions to model correlation effects from overlapping paths. In particular, it avoids the use of simulation methods employed in computations for the distribution-based MNP-SUE model. Preliminary computational results indicate that CMM-SUE provides a practical distributionally robust alternative to MNP-SUE.
    No preview · Article · Mar 2015 · Transportation Research Part B Methodological
  • Maria Teresa Godinho · Luis Gouveia · Thomas L. Magnanti · Pierre Pesneau

    No preview · Article · Mar 2014
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    ABSTRACT: The vehicles of education have seen significant broadening with the proliferation of new technologies such as social media, microblogs, online references, multimedia, and interactive teaching tools. This paper summarizes research on the effect of using active learning methods to facilitate student learning and describes our experiences implementing group activities for a calculus course for first year university students at Singapore University of Technology and Design, a new design-centric university established in collaboration with Massachusetts Institute of Technology (MIT). We describe the educational impact of different pedagogical techniques, such as real-time response tools, hands on activities, mathematical modeling, visualization activities and motivational competitions on students with differing learning preferences in a unique cohort classroom setting. Based on faculty reflection and survey data, we provide guidelines on how to adopt the right set of active and group learning techniques to handle the changing learning preferences in the current and future generation of students.
    No preview · Conference Paper · Mar 2013
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    Thomas L. Magnanti · Dan Stratila
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    ABSTRACT: We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge counterpart is a well-studied combinatorial optimization problem. Our technique preserves constant factor approximation ratios, as well as ratios that depend only on certain problem parameters, and exact algorithms yield exact algorithms. Using our technique, we obtain a new 1.61-approximation algorithm for the concave cost facility location problem. For inventory problems, we obtain a new exact algorithm for the economic lot-sizing problem with general concave ordering costs, and a 4-approximation algorithm for the joint replenishment problem with general concave individual ordering costs.
    Preview · Article · Feb 2012
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    Thomas L. Magnanti · Dan Stratila
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    ABSTRACT: 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.
    Preview · Article · Jan 2012 · Lecture Notes in Computer Science
  • Anant Balakrishnan · Thomas L. Magnanti
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    ABSTRACT: This paper studies a core optimization model--the survivable network design (SND) problem--that incorporates cost and survivability. Given an undirected network G: (N,E) with nodes N, nonnegative costs for each edge in E, and nonnegative integer connectivity requirements specifying the minimum number of edge-disjoint paths needed between pairs of nodes, the SND problem seeks the minimum cost network that satisfies all the connectivity requirements. Although simple to describe, this model captures, as special cases, many classic, but difficult, optimization problems like the Steiner tree problem and the traveling salesman problem. In this paper, we develop a family of new formulations for the SND problem, and show that these formulations are stronger than the traditional cutset formulation of the problem. Our proposed connectivity-splitting formulations have intuitive special cases that motivate the design and analysis of specialized heuristics for the survivable network design problem
    No preview · Article · Apr 2009
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    Teresa Maria · Godinho · Luís Gouveia · Thomas L Magnanti · Pierre Pesneau · José Pires

    Full-text · Article · Apr 2009
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    Maria Teresa Godinho · Luis Gouveia · Thomas L. Magnanti
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    ABSTRACT: We consider two types of hop-indexed models for the unit-demand asymmetric Capacitated Vehicle Routing Problem (CVRP): (a) capacitated models guaranteeing that the number of commodities (paths) traversing any given arc does not exceed a specified capacity; and (b) hop-constrained models guaranteeing that any route length (number of nodes) does not exceed a given value. The latter might, in turn, be divided into two classes: (b1) those restricting the length of the path from the depot to any node k, and (b2) those restricting the length of the circuit passing through any node k. Our results indicate that formulations based upon circuit lengths (b2) lead to models with a linear programming relaxation that is tighter than the linear programming relaxation of models based upon path lengths (b1), and that combining features from capacitated models with those of circuit lengths can lead to formulations for the CVRP with a tight linear programming bound. Computational results on a small number of problem instances with up to 41 nodes and 440 edges show that the combined model with capacities and circuit lengths produce average gaps of less than one percent. We also briefly examine the asymmetric travelling salesman problem (ATSP), showing the potential use of the ideas developed for the vehicle routing problem to derive models for the ATSP with a linear programming relaxation bound that is tighter than the linear programming relaxation bound of the standard Dantzig, Fulkerson and Johnson [G. Dantzig, D. Fulkerson, D. Johnson, Solution of large-scale travelling salesman problem, Operations Research 2 (1954) 393–410] formulation.
    Full-text · Article · May 2008 · Discrete Optimization
  • Ravindra K. Ahuja · Thomas L. Magnanti · James B. Orlin

    No preview · Article · Jan 2008
  • Ravindra K. Ahuja · Thomas L. Magnanti · James B. Orlin
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    ABSTRACT: Keywords Applications Distribution Problems Airplane Hopping Problem Directed Chinese Postman Problem Preliminaries Assumptions Graph Notation Residual Network Order Notation Cycle-Canceling Algorithm Successive Shortest Path Algorithm Network Simplex Algorithm See also References
    No preview · Article · Jan 2008
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    Keely L. Croxton · Bernard Gendron · Thomas L. Magnanti
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    ABSTRACT: The function need not be continuous; it can have positive or negative jumps, though we do assume that the function is lower semi-continuous, that is, g a (x a ) lim inf x # a #xa g a (x # a ) for 1 any sequence x # a that approaches x a . Without loss of generality, we also assume, through a simple translation of the costs if necessary, that g a (0) = 0. Such a piecewise linear function can be fully characterized by its segments. On each arc a, each segment s of the function has a non-negative variable cost, c a (the slope), a non-negative fixed cost, f a (the intercept), and upper and lower bounds, b a and b a , on the flow of that segment. Since the total flow on each arc can always be bounded from above by either the arc capacity or the total demand flowing through the network, we assume that there is a finite number of segments on each arc a, which we represent by the set S a . We further introduce the following notation: K denotes the set of commodities, N is the |V
    Full-text · Article · Feb 2007 · Operations Research
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    Maria Teresa Godinho · Luis Gouveia · Thomas L. Magnanti · Pierre Pesneau

    Full-text · Article · Jan 2007
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    B. L. Golden · T. L. Magnanti · H. Q. Nguyen
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    ABSTRACT: Heuristic programming algorithms frequently address large problems and require manipulation and operation on massive data sets. The algorithms can be improved by using efficient data structures. With this in mind, we consider heuristic algorithms for vehicle routing, comparing techniques of Clarke and Wright, Gillett and Miller, and Tyagi, and presenting modifications and extensions which permit problems involving hundreds of demand points to be solved in a matter of seconds. In addition, a multi-depot routing algorithm is developed. The results are illustrated with a routing study for an urban newspaper with an evening circulation exceeding 100,000.
    Preview · Article · Oct 2006 · Networks
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    B. L. Golden · T. L. Magnanti
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    ABSTRACT: "7-102-77." Includes author index. Cover title. Supported in part by the U.S. Deaprtment of Transportation, Transportation Advanced Research Program (TARP) contract no. DOT-TSC-1058 by Bruce L. Golden and Thomas L. Magnanti.
    Preview · Article · Oct 2006 · Networks
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    Luis Gouveia · Thomas L. Magnanti · Cristina Requejo
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    ABSTRACT: In a previous paper, Gouveia and Magnanti (2003) found diameter-constrained minimal spanning and Steiner tree problems to be more difficult to solve when the tree diameter D is odd. In this paper, we provide an alternate modeling approach that views problems with odd diameters as the superposition of two problems with even diameters. We show how to tighten the resulting formulation to develop a model with a stronger linear programming relaxation. The linear programming gaps for the tightened model are very small, typically less than 0.5–, and are usually one third to one tenth of the gaps of the best previous model described in Gouveia and Magnanti (2003). Moreover, the new model permits us to solve large Euclidean problem instances that are not solvable by prior approaches.
    Preview · Article · Sep 2006 · Annals of Operations Research
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    Thomas L. Magnanti · Zuo-Jun Max Shen · Jia Shu · David Simchi-Levi · Chung-Piaw Teo
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    ABSTRACT: By adding a set of redundant constraints, and by iteratively refining the approximation, we show that a commercial solver is able to routinely solve moderate-size strategic safety stock placement problems to optimality. The speed-up arises because the solver automatically generates strong flow cover cuts using the redundant constraints.
    Full-text · Article · Mar 2006 · Operations Research Letters
  • Thomas L. Magnanti
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    ABSTRACT: This paper is an edited transcription of the author’s lecture given on February 25th, 2006, in honor of Saul Gass.
    No preview · Chapter · Dec 2005
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    Thomas L. Magnanti · S. Raghavan
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    ABSTRACT: The network design problem with connectivity requirements (NDC) models a wide variety of celebrated combinatorial optimization problems including the minimum span- ning tree, Steiner tree, and survivable network design problems. We develop strong for- mulations for two versions of the edge-connectivity NDC problem: unitary problems re- quiring connected network designs, and nonunitary problems permitting non-connected networks as solutions. We (i) present a new directed formulation for the unitary NDC problem that is stronger than a natural undirected formulation, (ii) project out several classes of valid inequalities—partition inequalities, odd-hole inequalities, and combi- natorial design inequalities—that generalize known classes of valid inequalities for the Steiner tree problem to the unitary NDC problem, and (iii) show how to strengthen and direct nonunitary problems. Our results provide a unifying framework for strengthening formulations for NDC problems, and demonstrate the strength and power of ßow-based formulations for net- work design problems with connectivity requirements.
    Preview · Article · Mar 2005 · Networks
  • Thomas L. Magnanti · Georgia Perakis
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    ABSTRACT: We introduce a general adaptive line search framework for solving fixed point and variational inequality problems. Our goals are to develop iterative schemes that (i) compute solutions when the underlying map satisfies properties weaker than contractiveness, for example, weaker forms of nonexpansiveness, (ii) are more efficient than the classical methods even when the underlying map is contractive, and (iii) unify and extend several convergence results from the fixed point and variational inequality literatures. To achieve these goals, we introduce and study joint compatibility conditions imposed upon the underlying map and the iterative step sizes at each iteration and consider line searches that optimize certain potential functions. As a special case, we introduce a modified steepest descent method for solving systems of equations that does not require a previous condition from the literature (the square of the Jacobian matrix is positive definite). Since the line searches we propose might be difficult to perform exactly, we also consider inexact line searches.
    No preview · Article · Dec 2004 · Mathematical Programming
  • Luis Gouveia · Thomas L. Magnanti · Cristina Requejo
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    ABSTRACT: In a previous article, using underlying graph theoretical properties, Gouveia and Magnanti (2003) described several network flow-based formulations for diameter-constrained tree problems. Their computational results showed that, even with several enhancements, models for situations when the tree diameter D is odd proved to be more difficult to solve than those when D is even. In this article we provide an alternative modeling approach for the situation when D is odd. The approach views the diameter-constrained minimum spanning tree as being composed of a variant of a directed spanning tree (from an artificial root node) together with two constrained paths, a shortest and a longest path, from the root node to any node in the tree. We also show how to view the feasible set of the linear programming relaxation of the new formulation as the intersection of two integer polyhedra, a so-called triangle-tree polyhedron and a constrained path polyhedron. This characterization improves upon a model of Gouveia and Magnanti (2003) whose linear programming relaxation feasible set is the intersection of three rather than two integer polyhedra. The linear programming gaps for the tightened model are very small, typically less than 0.5%, and are usually one third to one tenth of the gaps of the best previous model described in Gouveia and Magnanti (2003). Moreover, using the new model, we have been able to solve large Euclidean problem instances that are not solvable by the previous approaches. © 2004 Wiley Periodicals, Inc.
    No preview · Article · Dec 2004 · Networks

Publication Stats

9k Citations
98.30 Total Impact Points

Institutions

  • 1974-2015
    • Massachusetts Institute of Technology
      • • Department of Electrical Engineering and Computer Science
      • • School of Engineering
      • • MIT Sloan School of Management
      Cambridge, Massachusetts, United States
  • 1994-1995
    • University of Pittsburgh
      Pittsburgh, Pennsylvania, United States
  • 1991
    • Indian Institute of Technology Kanpur
      Cawnpore, Uttar Pradesh, India
  • 1988
    • Texas A&M University
      College Station, Texas, United States
  • 1987
    • Cambridge Healthtech Institute
      Needham, Massachusetts, United States
  • 1981
    • Troy University
      Троя, Alabama, United States
  • 1976
    • University of São Paulo
      San Paulo, São Paulo, Brazil