ODTlearn: A Package for Learning Optimal Decision Trees for Prediction and Prescription

  • Patrick Vossler
  • Sina Aghaei
  • Nathan Justin
  • Nathanael Jo
  • Andrés Gómez
  • Phebe Vayanos
    • Categories (Mixed) Integer Linear Programming, Optimization Software and Modeling Systems Tags , , , , , ,

    ODTLearn is an open-source Python package that provides methods for learning optimal decision trees for high-stakes predictive and prescriptive tasks based on the mixed-integer optimization (MIO) framework proposed in Aghaei et al. (2019) and several of its extensions. The current version of the package provides implementations for learning optimal classification trees, optimal fair classification trees, … Read more

    Delay-Resistant Robust Vehicle Routing with Heterogeneous Time Windows

  • Lukas Schürmann
  • Tim Niemann
  • Petra Mutzel
  • Andreas M. Tillmann
  • Sebastian Stiller
    • Categories Combinatorial Optimization, Integer Programming, Transportation Tags , , ,

    We consider a robust variant of the vehicle routing problem with heterogeneous time windows (RVRP-HTW) with a focus on delay-resistant solutions. Here, customers have different availability time windows for every vehicle and must be provided with a preferably tight appointment window for the planned service. Different vehicles are a possibility to model different days on … Read more

    Stability of Markovian Stochastic Programming

  • David Wozabal
    • Categories Stochastic Programming Tags , , ,

    Multi-stage stochastic programming is notoriously hard, since solution methods suffer from the curse of dimensionality. Recently, stochastic dual dynamic programming has shown promising results for Markovian problems with many stages and a moderately large state space. In order to numerically solve these problems simple discrete representations of Markov processes are required but a convincing theoretical … Read more

    Dual Conflict Analysis for Mixed-Integer Semidefinite Programs

  • Marc E. Pfetsch
    • Categories (Mixed) Integer Linear Programming, Semi-definite Programming Tags ,

    Conflict analysis originally tried to exploit the knowledge that certain nodes in a relaxation-based branch-and-bound are infeasible. It has been extended to derive valid constraints also from feasible nodes. This paper adapts this approach to mixed-integer semidefinite programs. Using dual solutions, the primal constraints are aggregated and the resulting inequalities can be used at different … Read more

    Solution Path of Time-varying Markov Random Fields with Discrete Regularization

  • Salar Fattahi
  • Andrés Gómez
    • Categories Dynamic Programming, Integer Programming, Optimization in Data Science

    \(\) We study the problem of inferring sparse time-varying Markov random fields (MRFs) with different discrete and temporal regularizations on the parameters. Due to the intractability of discrete regularization, most approaches for solving this problem rely on the so-called maximum-likelihood estimation (MLE) with relaxed regularization, which neither results in ideal statistical properties nor scale to … Read more

    A Multicut Approach to Compute Upper Bounds for Risk-Averse SDDP

  • Joaquim Dias Garcia
  • Mario Pereira
    • Categories Dynamic Programming, Energy, Stochastic Programming Tags , , , ,

    Stochastic Dual Dynamic Programming (SDDP) is a widely used and fundamental algorithm for solving multistage stochastic optimization problems. Although SDDP has been frequently applied to solve risk-averse models with the Conditional Value-at-Risk (CVaR), it is known that the estimation of upper bounds is a methodological challenge, and many methods are computationally intensive. In practice, this … Read more

    A Tutorial on Solving Single-Leader-Multi-Follower Problems using SOS1 Reformulations

  • Didier Aussel
  • Cecile Egea
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities, Game Theory Tags , , ,

    In this tutorial we consider single-leader-multi-follower games in which the models of the lower-level players have polyhedral feasible sets and convex objective functions. This situation allows for classic KKT reformulations of the separate lower-level problems, which lead to challenging single-level reformulations of MPCC type. The main contribution of this tutorial is to present a ready-to-use … Read more

    Duality of upper bounds in stochastic dynamic programming

  • Bernardo Freitas Paulo da Costa
  • Vincent Leclère
    • Categories Convex Optimization, Dynamic Programming, Stochastic Programming Tags , , , ,

    For multistage stochastic programming problems with stagewise independent uncertainty, dynamic programming algorithms calculate polyhedral approximations for the value functions at each stage.  The SDDP algorithm provides piecewise linear lower bounds, in the spirit of the L-shaped algorithm, and corresponding upper bounds took a longer time to appear.  One strategy uses the primal dynamic programming recursion … Read more

    Modified Monotone Policy Iteration for Interpretable Policies in Markov Decision Processes and the Impact of State Ordering Rules

  • Sun Ju Lee
  • Xingyu Gong
  • Gian-Gabriel Garcia
    • Categories Dynamic Programming

    Optimizing interpretable policies for Markov Decision Processes (MDPs) can be computationally intractable for large-scale MDPs, e.g., for monotone policies, the optimal interpretable policy depends on the initial state distribution, precluding standard dynamic programming techniques. Previous work has proposed Monotone Policy Iteration (MPI) to produce a feasible solution for warm starting a Mixed Integer Linear Program … Read more

    A more efficient reformulation of complex SDP as real SDP

  • Jie Wang
    • Categories Global Optimization Theory, Semi-definite Programming Tags , , , ,

    This note proposes a new reformulation of complex semidefinite programs (SDPs) as real SDPs. As an application, we present an economical reformulation of complex SDP relaxations of complex polynomial optimization problems as real SDPs and derive some further reductions by exploiting inner structure of the complex SDP relaxations. Various numerical examples demonstrate that our new … Read more