Robust Optimization

Managing Distributional Ambiguity in Stochastic Optimization through a Statistical Upper Bound Framework

  • Shixin Liu
  • Jian Hu
    • Categories Robust Optimization, Stochastic Programming

    Stochastic optimization is often hampered by distributional ambiguity, where critical probability distributions are poorly characterized or unknown. Addressing this challenge, we introduce a new framework that targets the minimization of a statistical upper bound for the expected value of uncertain objectives, facilitating more statistically robust decision-making. Central to our approach is the Average Percentile Upper … Read more

    Adjustable robust optimization for fleet sizing problem in closed-loop supply chains with simultaneous delivery and pickup

  • Ali Borumand
  • Ali Nookabadi
    • Categories (Mixed) Integer Linear Programming, Meta Heuristics, Robust Optimization Tags , , , ,

    The Fleet Sizing Problem (FSP) stands as a critical challenge within the realm of logistics and supply chain management, particularly in the context of Closed-Loop Supply Chains (CLSC). The significance of addressing the FSP lies in its direct impact on operational costs, resource utilization, and environmental sustainability. By effectively optimizing fleet size, organizations can streamline … Read more

    Fourth-order Marginal Moment Model: Reformulations and Applications

  • Mingyang FU
  • Xiaobo Li
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Robust Optimization Tags , , , , ,

    This paper investigates the bounds on the expectation of combinatorial optimization given moment information for each individual random variable. A popular approach to solving this problem, known as the marginal moment model (MMM), is to reformulate it as a semidefinite program (SDP). In this paper, we investigate the structure of MMM with up to fourth-order … Read more

    Quadratic Optimization Through the Lens of Adjustable Robust Optimization

  • Abbas Khademi
  • Ahmadreza Marandi
    • Categories Quadratic Programming, Robust Optimization Tags , , , ,

    Quadratic optimization (QO) has been studied extensively in the literature due to its applicability in many practical problems. While practical, it is known that QO problems are generally NP-hard. So, researchers developed many approximation methods to find good solutions. In this paper, we go beyond the norm and analyze QO problems using robust optimization techniques. … Read more

    Information Basis in Dynamic Robust Optimization

  • Ningji Wei
  • Peter Yun Zhang
    • Categories Robust Optimization Tags , , ,

    Dynamic robust optimization deals with sequential, multi-stage decisions in the face of uncertain, worst-case scenarios. To manage its complexity and the curse of dimensionality, decision rules simplify the search for an optimal policy. This paper explores a middle ground between two common decision rules: simple but imprecise constant policies, and accurate but less scalable affine … Read more

    Robust Mask-Based Appointment Scheduling in Primary Care Practices

  • Sabrina Schmitz
  • Martin Comis
  • Christina Büsing
    • Categories Applications - OR and Management Sciences, Robust Optimization, Scheduling Tags , , ,

    In most health care systems, a primary care physician (PCP) is both the first instance consulted by patients with medical concerns and the instance coordinating patients’ continued access to medical care. Due to the PCP’s pivotal role, we address challenges of a high-quality primary care service by interday appointment scheduling on a tactical decision level. Our … Read more

    libDIPS — Discretization-Based Semi-Infinite and Bilevel Programming Solvers

  • Aron Zingler
  • Alexander Mitsos
  • Daniel Jungen
  • Hatim Djelassi
    • Categories Optimization Software and Modeling Systems, Robust Optimization, Semi-infinite Programming Tags , , , , ,

    We consider several hierarchical optimization programs: (generalized) semi-infinite and existence-constrained semi-infinite programs, minmax, and bilevel programs. Multiple adaptive discretization-based algorithms have been published for these program classes in recent decades. However, rigorous numerical performance comparisons between these algorithms are lacking. Indeed, if numerical comparisons are provided at all, they usually compare a small selection of … Read more

    Robust Regression over Averaged Uncertainty

  • Dimitris Bertsimas
  • Yu Ma
    • Categories Robust Optimization Tags , , , ,

    We propose a new formulation of robust regression by integrating all realizations of the uncertainty set and taking an averaged approach to obtain the optimal solution for the ordinary least squares regression problem. We show that this formulation recovers ridge regression exactly and establishes the missing link between robust optimization and the mean squared error … Read more

    ROBIST: Robust Optimization by Iterative Scenario Sampling and Statistical Testing

  • Justin Starreveld
  • Dick den Hertog
  • Roger Laeven
  • Guanyu Jin
    • Categories Robust Optimization Tags , , ,

    In this paper, we propose ROBIST, a simple, yet effective, data-driven algorithm for optimization under parametric uncertainty. The algorithm first generates solutions in an iterative manner by sampling and optimizing over a relatively small set of scenarios. Then, using statistical testing, the robustness of the solutions is evaluated, which can be done with a much … Read more