Stochastic Programming

Integer Programming Approaches for Distributionally Robust Chance Constraints with Adjustable Risks

  • Yiling Zhang
    • Categories Integer Programming, Robust Optimization, Stochastic Programming

    We study distributionally robust chance-constrained programs (DRCCPs) with individual chance constraints under a Wasserstein ambiguity. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. The introduction of … Read more

    A Decomposition Algorithm for Distributionally Robust Chance-Constrained Programs with Polyhedral Ambiguity Set

  • Hamed Rahimian
    • Categories Stochastic Programming Tags , , ,

    In this paper, we study a distributionally robust optimization approach to chance-constrained stochastic programs to hedge against uncertainty in the distributions of the random parameters. We consider a general polyhedral ambiguity set under finite support and study Wasserstein ambiguity set, total variation distance ambiguity set, and moment-based ambiguity set as examples for our computations. We … Read more

    Contextual Stochastic Programs with Expected-Value Constraints

  • Hamed Rahimian
  • Bernardo K. Pagnoncelli
    • Categories Stochastic Programming Tags , , ,

    Expected-value-constrained programming (ECP) formulations are a broad class of stochastic programming problems including integrated chance constraints, risk models, and stochastic dominance formulations. Given the wide availability of data, it is common in applications to have independent contextual information associated with the target or dependent random variables of the problem. We show how to incorporate such … Read more

    Distributionally Robust Optimization with Decision-Dependent Polyhedral Ambiguity

  • Hamed Rahimian
  • Sanjay Mehrotra
    • Categories Stochastic Programming Tags , , ,

    We consider a two-stage stochastic program with continuous recourse, where the distribution of the random parameters depends on the decisions. Assuming a finite sample space, we study a distributionally robust approach to this problem, where the decision-dependent distributional ambiguity is modeled with a polyhedral ambiguity set. We consider cases where the recourse function and the … Read more

    BattOpt: Optimal Facility Planning for Electric Vehicle Battery Recycling

  • Matthew Brun
  • Xu Andy Sun
    • Categories Energy, Global Optimization Applications, Stochastic Programming Tags , , ,

    The electric vehicle (EV) battery supply chain will face challenges in sourcing scarce, expensive minerals required for manufacturing and in disposing of hazardous retired batteries. Integrating recycling technology into the supply chain has the potential to alleviate these issues; however, players in the battery market must design investment plans for recycling facilities. In this paper, … Read more

    Incorporating Service Reliability in Multi-depot Vehicle Scheduling: A Chance-Constrained Approach

  • Margarita P Castro
  • Merve Bodur
  • Amer Shalaby
    • Categories Cutting Plane Approaches, Stochastic Programming, Transportation Tags , , ,

    The multi-depot vehicle scheduling problem (MDVSP) is a critical planning challenge for transit agencies. We introduce a novel approach to MDVSP by incorporating service reliability through chance-constrained programming (CCP), targeting the pivotal issue of travel time uncertainty and its impact on transit service quality. Our model guarantees service reliability measured by on-time performance (OTP), a … Read more

    Benders decomposition with scaled cuts for multistage stochastic mixed-integer programs

  • Ward Romeijnders
  • Niels van der Laan
    • Categories Stochastic Programming Tags , ,

    We consider Benders decomposition algorithms for multistage stochastic mixed-integer programs (SMIPs) with general mixed-integer decision variables at every node in the scenario tree. We derive a hierarchy of convex polyhedral lower bounds for the value functions and expected cost to-go functions in multistage SMIPs using affine parametric cutting planes in extended spaces for the feasible … Read more

    MUSE-BB: A Decomposition Algorithm for Nonconvex Two-Stage Problems using Strong Multisection Branching

  • Marco Langiu
  • Manuel Dahmen
  • D. Bongartz
  • Alexander Mitsos
    • Categories Global Optimization, Parallel Algorithms, Stochastic Programming Tags , , , ,

    \(\) We present MUSE-BB, a branch-and-bound (B&B) based decomposition algorithm for the deterministic global solution of nonconvex two-stage stochastic programming problems. In contrast to three recent decomposition algorithms, which solve this type of problem in a projected form by nesting an inner B&B in an outer B&B on the first-stage variables, we branch on all … Read more

    Stackelberg Games with k-Submodular Function under Distributional Risk-Receptiveness and Robustness

  • Seonghun Park
  • Manish Bansal
    • Categories Game Theory, Robust Optimization, Stochastic Programming

    \(\) We study submodular optimization in adversarial context, applicable to machine learning problems such as feature selection using data susceptible to uncertainties and attacks. We focus on Stackelberg games between an attacker (or interdictor) and a defender where the attacker aims to minimize the defender’s objective of maximizing a k-submodular function. We allow uncertainties arising … Read more

    Exploiting Overlap Information in Chance-constrained Program with Random Right-hand Side

  • Wei Lv
  • Wei-Kun Chen
  • Yu-Hong Dai
  • Xiao-Jiao Tong
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    We consider the chance-constrained program (CCP) with random right-hand side under a finite discrete distribution. It is known that the standard mixed integer linear programming (MILP) reformulation of the CCP is generally difficult to solve by general-purpose solvers as the branch-and-cut search trees are enormously large, partly due to the weak linear programming relaxation. In … Read more