Giacomo Nannicini

A solution algorithm for chance-constrained problems with integer second-stage recourse decisions

  • Andrea Lodi
  • Enrico Malaguti
  • Michele Monaci
  • Giacomo Nannicini
  • Paolo Paronuzzi
    • Categories (Mixed) Integer Nonlinear Programming, Stochastic Programming

    We study a class of chance-constrained two-stage stochastic optimization problems where the second-stage recourse decisions belong to mixed-integer convex sets. Due to the nonconvexity of the second-stage feasible sets, standard decomposition approaches cannot be applied. We develop a provably convergent branch-and-cut scheme that iteratively generates valid inequalities for the convex hull of the second-stage feasible … Read more

    An exact algorithm for robust influence maximization

  • Giacomo Nannicini
  • Roberto Wolfler Calvo
  • Giorgio Sartor
  • Emiliano Traversi
    • Categories Branch and Cut Algorithms, Robust Optimization Tags , ,

    We propose a Branch-and-Cut algorithm for the robust influence maximization problem. The influence maximization problem aims to identify, in a social network, a set of given cardinality comprising actors that are able to influence the maximum number of other actors. We assume that the social network is given in the form of a graph with … Read more

    Toward breaking the curse of dimensionality: an FPTAS for stochastic dynamic programs with multidimensional action and scalar state

  • Nir Halman
  • Giacomo Nannicini
    • Categories Approximation Algorithms, Dynamic Programming, Supply Chain Management Tags , , , ,

    We propose a Fully Polynomial-Time Approximation Scheme (FPTAS) for stochastic dynamic programs with multidimensional action, scalar state, convex costs and linear state transition function. The action spaces are polyhedral and described by parametric linear programs. This type of problems finds applications in the area of optimal planning under uncertainty, and can be thought of as … Read more

    A Benders squared (B2) framework for infinite-horizon stochastic linear programs

  • Giacomo Nannicini
  • Roberto Wolfler Calvo
  • Emiliano Traversi
    • Categories Cutting Plane Approaches, Linear Programming, Stochastic Programming

    We propose a nested decomposition scheme for infinite-horizon stochastic linear programs. Our approach can be seen as a provably convergent extension of stochastic dual dynamic programming to the infinite-horizon setting: we explore a sequence of finite-horizon problems of increasing length until we can prove convergence with a given confidence level. The methodology alternates between a … Read more

    Fully Polynomial Time (Sigma,Pi)-Approximation Schemes for Continuous Nonlinear Newsvendor and Continuous Stochastic Dynamic Programs

  • Nir Halman
  • Giacomo Nannicini
    • Categories Approximation Algorithms, Dynamic Programming Tags , , , , ,

    We study the continuous newsvendor problem (i.e. a newsvendor problem concerning goods of a non-discrete nature, such as fresh fruit juice) and a class of stochastic dynamic programs with several application areas, such as inventory control of a continuous good, economics, and supply chain management. The class is characterized by continuous state and action spaces, … Read more

    Fully Polynomial Time hBcApproximation Schemes for Continuous Stochastic Convex Dynamic Programs

  • Nir Halman
  • Giacomo Nannicini
    • Categories Approximation Algorithms, Dynamic Programming Tags , ,

    We develop fully polynomial time $(\Sigma,\Pi)$-approximation schemes for stochastic dynamic programs with continuous state and action spaces, when the single-period cost functions are convex Lipschitz-continuous functions that are accessed via value oracle calls. That is, for every given additive error parameter $\Sigma>0$ and multiplicative error factor $\Pi=1+\epsilon>1$, the scheme returns a feasible solution whose value … Read more

    RBFOpt: an open-source library for black-box optimization with costly function evaluations

  • Alberto Costa
  • Giacomo Nannicini
    • Categories Bound-constrained Optimization, Global Optimization, Optimization Software and Modeling Systems

    We consider the problem of optimizing an unknown function given as an oracle over a mixed-integer box-constrained set. We assume that the oracle is expensive to evaluate, so that estimating partial derivatives by finite differences is impractical. In the literature, this is typically called a black-box optimization problem with costly evaluation. This paper describes the … Read more

    How tight is the corner relaxation? Insights gained from the stable set problem

  • Gérard Cornuéjols
  • Carla Michini
  • Giacomo Nannicini
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Polyhedra Tags , ,

    The corner relaxation of a mixed-integer linear program is a central concept in cutting plane theory. In a recent paper Fischetti and Monaci provide an empirical assessment of the strength of the corner and other related relaxations on benchmark problems. In this paper we give a precise characterization of the bounds given by these relaxations … Read more

    A Probing Algorithm for MINLP with Failure Prediction by SVM

  • Pietro Belotti
  • Jon Lee
  • Jeff Linderoth
  • Giacomo Nannicini
  • François Margot
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization

    Bound tightening is an important component of algorithms for solving nonconvex Mixed Integer Nonlinear Programs. A {\em probing} algorithm is a bound-tightening procedure that explores the consequences of restricting a variable to a subinterval with the goal of tightening its bounds. We propose a variant of probing where exploration is based on iteratively applying a … Read more

    Core Routing on Dynamic Time-Dependent Road Networks

  • Daniel Delling
  • Giacomo Nannicini
    • Categories Network Optimization Tags , , ,

    Route planning in large scale time-dependent road networks is an important practical application of the shortest paths problem that greatly benefits from speedup techniques. In this paper we extend a two-levels hierarchical approach for point-to-point shortest paths computations to the time-dependent case. This method, also known as core routing in the literature for static graphs, … Read more