Other Topics

Bilevel optimization with a multi-objective lower-level problem: Risk-neutral and risk-averse formulations

  • Tommaso Giovannelli
  • Griffin D. Kent
  • Luis Nunes Vicente
    • Categories Data-Mining, Multi-Criteria Optimization, Stochastic Programming Tags , , ,

    In this work, we propose different formulations and gradient-based algorithms for deterministic and stochastic bilevel problems with conflicting objectives in the lower level. Such problems have received little attention in the deterministic case and have never been studied from a stochastic approximation viewpoint despite the recent advances in stochastic methods for single-level, bilevel, and multi-objective … Read more

    Efficient Discovery of Cost-effective Policies in Sequential, Medical Decision-Making Problems

  • Narges Mohammadi
  • M Skandari
    • Categories Applications - OR and Management Sciences, Dynamic Programming Tags , , ,

    Cost-effectiveness analysis (CEA) is extensively employed by healthcare policymakers to guide funding decisions and inform optimal design of medical interventions. In the CEA literature, willingness to pay (WTP) serves as a common metric for converting health benefits into monetary value and defining the net monetary benefit of an intervention. However, there is no universally accepted … Read more

    Generating balanced workload allocations in hospitals

  • Pieter Smet
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , ,

    As pressure on healthcare systems continues to increase, it is becoming more and more important for hospitals to properly manage the high workload levels of their staff. Ensuring a balanced workload allocation between various groups of employees in a hospital has been shown to contribute considerably towards creating sustainable working conditions. However, allocating work to … Read more

    The min-Knapsack Problem with Compactness Constraints and Applications in Statistics

  • Alberto Santini
  • Enrico Malaguti
    • Categories Branch and Cut Algorithms, Dynamic Programming, Statistics Tags , ,

    In the min-Knapsack problem, one is given a set of items, each having a certain cost and weight. The objective is to select a subset with minimum cost, such that the sum of the weights is not smaller than a given constant. In this paper we introduce an extension of the min-Knapsack problem with additional … Read more

    Set-based Robust Optimization of Uncertain Multiobjective Problems via Epigraphical Reformulations

  • Gabriele Eichfelder
  • Ernest Quintana
    • Categories Multi-Criteria Optimization, Robust Optimization Tags , , ,

    In this paper, we study a method for finding robust solutions to multiobjective optimization problems under uncertainty. We follow the set-based minmax approach for handling the uncertainties which leads to a certain set optimization problem with the strict upper type set relation. We introduce, under some assumptions, a reformulation using instead the strict lower type … Read more

    Transportation and Inventory Planning in Serial Supply Chain with Heterogeneous Capacitated Vehicles

  • Kartik Kulkarni
  • Manish Bansal
    • Categories Applications - OR and Management Sciences, Dynamic Programming, Production and Logistics

    We study serial supply chain problems where a product is transported from a supplier to a warehouse (inbound transportation), and then from the warehouse (outbound transportation) to a retailer such that demand for a given planning horizon is satisfied. We consider heterogeneous vehicles of varying capacities for the transportation in each time period, and the … Read more

    A branch-and-bound algorithm for non-convex Nash equilibrium problems

  • Peter Kirst
  • Stefan Schwarze
  • Oliver Stein
    • Categories Game Theory Tags , , , ,

    This paper introduces a spatial branch-and-bound method for the approximate computation of the set of all epsilon-Nash equilibria of continuous box-constrained non-convex Nash equilibrium problems. We explain appropriate discarding and fathoming techniques, provide a termination proof for a prescribed approximation tolerance, and report our computational experience. ArticleDownload View PDF

    A Branch and Bound Algorithm for Biobjective Mixed Integer Quadratic Programs

  • Pubudu L.W. Jayasekara Merenchige
  • Margaret Wiecek
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Multi-Criteria Optimization Tags , , , , ,

    Multiobjective quadratic programs (MOQPs) are appealing since convex quadratic programs have elegant mathematical properties and model important applications. Adding mixed-integer variables extends their applicability while the resulting programs become global optimization problems. We design and implement a branch and bound (BB) algorithm for biobjective mixed-integer quadratic programs (BOMIQPs). In contrast to the existing algorithms in … Read more

    Decremental State-Space Relaxations for the Basic Traveling Salesman Problem with a Drone

  • Marcos Blufstein
  • Gonzalo Lera-Romero
  • Francisco J. Soulignac
    • Categories Dynamic Programming, Transportation Tags , , , , ,

    Truck-and-drone routing problems have become an important topic of research in the last decade due to their applications for last-mile deliveries. Despite the large number of publications in this area, the most efficient exact algorithms designed thus far struggle to solve the benchmark instances with 39 or more customers. This fact is true even for … Read more

    Data-driven Multistage Distributionally Robust Linear Optimization with Nested Distance

  • Rui Gao
    • Categories Dynamic Programming, Robust Optimization, Stochastic Programming Tags , , ,

    We study multistage distributionally robust linear optimization, where the uncertainty set is defined as a ball of distribution centered at a scenario tree using the nested distance. The resulting minimax problem is notoriously difficult to solve due to its inherent non-convexity. In this paper, we demonstrate that, under mild conditions, the robust risk evaluation of … Read more