benders decomposition

A two-level SDDP Solving Strategy with Risk-Averse multivariate reservoir Storage Levels for Long Term power Generation Planning

  • Andre Diniz
  • Maria Elvira P. Maceira
  • D.D. Penna
  • C. L. Vasconcellos
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , ,

    Power generation planning in large-scale hydrothermal systems is a complex optimization task, specially due to the high uncertainty in the inflows to hydro plants. Since it is impossible to traverse the huge scenario tree of the multi-stage problem, stochastic dual dynamic programming (SDDP) is the leading optimization technique to solve it, originally from an expected-cost … Read more

    Efficient approaches for the robust network loading problem

  • Sara Mattia
  • Michael Poss
    • Categories (Mixed) Integer Linear Programming, Network Optimization, Robust Optimization Tags , , , ,

    We consider the Robust Network Loading problem with splittable flows and demands that belong to the budgeted uncertainty set. We compare the optimal solution cost and computational cost of the problem when using static routing, volume routing, affine routing, and dynamic routing. For the first three routing types, we compare the compact formulation with a … Read more

    A Generalization of Benders’ Algorithm for Two-Stage Stochastic Optimization Problems With Mixed Integer Recourse

  • Anahita Hassanzadeh
  • Ted K. Ralphs
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags ,

    We describe a generalization of Benders’ method for solving two-stage stochastic linear optimization problems in which there are both continuous and integer variables in the first and second stages. Benders’ method relies on finding effective lower approximations for the value function of the second-stage problem. In this setting, the value function is a discontinuous, non-convex, … Read more

    The unrooted set covering connected subgraph problem differentiating between HIV envelope sequences

  • Stephen J. Maher
  • John M Murray
    • Categories (Mixed) Integer Linear Programming, Biomedical Applications Tags , , ,

    This paper presents a novel application of operations research techniques to the analysis of HIV env gene sequences, aiming to identify key features that are possible vaccine targets. These targets are identified as being critical to the transmission of HIV by being present in early transmitted (founder) sequences and absent in later chronic sequences. Identifying … Read more

    Chance-Constrained Multi-Terminal Network Design Problems

  • Yongjia Song
  • Minjiao Zhang
    • Categories Integer Programming, Network Optimization, Stochastic Programming Tags , , ,

    We consider a reliable network design problem under uncertain edge failures. Our goal is to select a minimum-cost subset of edges in the network to connect multiple terminals together with high probability. This problem can be seen as a stochastic variant of the Steiner tree problem. We propose a scenario-based Steiner cut formulation, and a … Read more

    Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition

  • Yu An
  • Bo Zeng
  • Ludwig Kuznia
    • Categories Integer Programming, Stochastic Programming Tags , , , , ,

    In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant … Read more

    Decomposition Algorithms for Two-Stage Chance-Constrained Programs

  • Simge Küçükyavuz
  • James R. Luedtke
  • Xiao Liu
    • Categories Branch and Cut Algorithms, Integer Programming, Stochastic Programming Tags , , ,

    We study a class of chance-constrained two-stage stochastic optimization problems where second-stage feasible recourse decisions incur additional cost. In addition, we propose a new model, where “recovery” decisions are made for the infeasible scenarios to obtain feasible solutions to a relaxed second-stage problem. We develop decomposition algorithms with specialized optimality and feasibility cuts to solve … Read more

    Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse

  • Merve Bodur
  • Sanjeeb Dash
  • Oktay Gunluk
  • James R. Luedtke
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Stochastic Programming Tags , ,

    With stochastic integer programming as the motivating application, we investigate techniques to use integrality constraints to obtain improved cuts within a Benders decomposition algorithm. We compare the effect of using cuts in two ways: (i) cut-and-project, where integrality constraints are used to derive cuts in the extended variable space, and Benders cuts are then used … Read more

    A Two-Stage Stochastic Integer Programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management

  • Kibaek Kim
  • Sanjay Mehrotra
    • Categories (Mixed) Integer Nonlinear Programming, Scheduling, Stochastic Programming Tags , , , , ,

    We study the problem of integrated staffing and scheduling under demand uncertainty. The problem is formulated as a two-stage stochastic integer program with mixed-integer recourse. The here-and-now decision is to find initial staffing levels and schedules, well ahead in time. The wait-and-see decision is to adjust these schedules at a time epoch closer to the … Read more

    Ancestral Benders’ Cuts and Multi-term Disjunctions for Mixed-Integer Recourse Decisions in Stochastic Programming

  • Yunwei Qi
  • Suvrajeet Sen
    • Categories Branch and Cut Algorithms, Stochastic Programming Tags , ,

    This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first stage approximation is solved using a branch-and-bound tree with nodes inheriting Benders’ cuts that are valid for their ancestor nodes. In addition, we develop two closely … Read more