benders decomposition

Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework

  • Stephen J. Maher
    • Categories Integer Programming, Optimization Software and Modeling Systems Tags , , , ,

    Benders’ decomposition is a popular mathematical and constraint programming algorithm that is widely applied to exploit problem structure arising from real-world applications. While useful for exploiting structure in mathematical and constraint programs, the use of Benders’ decomposition typically requires significant implementation effort to achieve an effective solution algorithm. Traditionally, Benders’ decomposition has been viewed as … Read more

    A Computationally Efficient Algorithm for Computing Convex Hull Prices

  • Anya Castillo
  • Bernard Knueven
  • James Ostrowski
  • Jean-Paul Watson
    • Categories Applications - OR and Management Sciences Tags , , , ,

    Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource’s capabilities, they create challenges for market clearing processes. For example, system operators may be required to execute side payments to participants whose costs are not covered through energy sales as determined via traditional locational marginal pricing … Read more

    Benders Decomposition with Adaptive Oracles for Large Scale Optimization

  • Andreas Grothey
  • Kenneth McKinnon
  • Nicolò Mazzi
  • Nagisa Sugishita
    • Categories Applications - OR and Management Sciences Tags , , ,

    This paper proposes an algorithm to efficiently solve large optimization problems which exhibit a column bounded block-diagonal structure, where subproblems differ in right-hand side and cost coefficients. Similar problems are often tackled using cutting-plane algorithms, which allow for an iterative and decomposed solution of the problem. When solving subproblems is computationally expensive and the set … Read more

    Benders Cut Classification via Support Vector Machines for Solving Two-stage Stochastic Programs

  • Huiwen Jia
  • Siqian Shen
    • Categories Cutting Plane Approaches, Stochastic Programming Tags , , ,

    We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. We define the Benders cuts binding at the final optimal solution or the ones significantly improving bounds over iterations as valuable cuts. We propose a learning-enhanced Benders decomposition (LearnBD) algorithm, which adds a cut classification … Read more

    Avoiding redundant columns by adding classical Benders cuts to column generation subproblems

  • Marco E. Lübbecke
  • Stephen J. Maher
  • Jonas T. Witt
    • Categories (Mixed) Integer Linear Programming Tags , , ,

    When solving the linear programming (LP) relaxation of a mixed-integer program (MIP) with column generation, columns might be generated that are not needed to express any integer optimal solution of the MIP. Such columns are called strongly redundant and the dual bound obtained by solving the LP relaxation is potentially stronger if these columns are … Read more

    Large-scale Influence Maximization via Maximal Covering Location

  • Evren Güney
  • Markus Leitner
  • Mario Ruthmair
  • Markus Sinnl
    • Categories Applications - OR and Management Sciences, Integer Programming, Stochastic Programming Tags , , ,

    Influence maximization aims at identifying a limited set of key individuals in a (social) network which spreads information based on some propagation model and maximizes the number of individuals reached. We show that influence maximization based on the probabilistic independent cascade model can be modeled as a stochastic maximal covering location problem. A reformulation based … Read more

    Enhancing large neighbourhood search heuristics for Benders’ decomposition

  • Stephen J. Maher
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , ,

    A general enhancement of the Benders’ decomposition (BD) algorithm can be achieved through the improved use of large neighbourhood search heuristics within mixed-integer programming solvers. While mixed-integer programming solvers are endowed with an array of large neighbourhood search heuristics, few, if any, have been designed for BD. Further, typically the use of large neighbourhood search … Read more

    The SCIP Optimization Suite 6.0

  • Michael Bastubbe
  • Leon Eifler
  • Tristan Gally
  • Gerald Gamrath
  • Ambros Gleixner
  • Robert Lion Gottwald
  • Gregor Hendel
  • Christopher Hojny
  • Thorsten Koch
  • Marco E. Lübbecke
  • Stephen J. Maher
  • Matthias Miltenberger
  • Marc E. Pfetsch
  • Felipe Serrano
  • Matthias Walter
  • Jakob Witzig
  • Benjamin Müller
  • Christian Puchert
  • Daniel Rehfeldt
  • Franziska Schlösser
  • Christoph Schubert
  • Yuji Shinano
  • Merlin Viernickel
  • Fabian Wegscheider
  • Jonas T. Witt
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , , , , , , , , , ,

    The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion … Read more

    Benders Decomposition for Very Large Scale Partial Set Covering and Maximal Covering Problems

  • Jean-François Cordeau
  • Fabio Furini
  • Ivana Ljubić
    • Categories Branch and Cut Algorithms, Combinatorial Optimization Tags , , , ,

    Covering problems constitute an important family of facility location problems. This paper intro- duces a new exact algorithm for two important members of this family: i) the maximal covering location problem, which requires finding a subset of facilities that maximizes the amount of demand covered while respecting a budget constraint on the cost of the … Read more

    Exact and heuristic algorithms for finding envy-free allocations in food rescue pickup and delivery logistics

  • Khaled Almi'ani
  • Divya J Nair
  • David Rey
    • Categories Branch and Cut Algorithms, Production and Logistics, Transportation Tags , , ,

    Food rescue organizations collect and re-distribute surplus perishable food for hunger relief. We propose novel approaches to address this humanitarian logistics challenge and find envy-free allocations of the rescued food together with least travel cost routes. We show that this food rescue and delivery problem is NP-hard and we present a cutting-plane algorithm based on … Read more