Solving Mixed-Integer Nonlinear Optimization Problems using Simultaneous Convexification – a Case Study for Gas Networks

  • Frauke Liers
  • Maximilian Merkert
  • Alexander Martin
  • Nick Mertens
  • Dennis Michaels
    • Categories Applications - Science and Engineering, Global Optimization, Network Optimization Tags , , ,

    Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each … Read more

    On the propagation of quality requirements for mechanical assemblies in industrial manufacturing

  • Philipp Armbrust
  • Paul Alexandru Bucur
  • Philipp Hungerländer
    • Categories Mechanical Engineering Tags , , , ,

    A frequent challenge encountered by manufacturers of mechanical assemblies consists of the definition of quality criteria for the assembly lines of the subcomponents which are mounted into the final product. The rollout of Industry 4.0 standards paves the way for the usage of data-driven, intelligent approaches towards this goal. In this work, we investigate such … Read more

    Learning Generalized Strong Branching for Set Covering, Set Packing, and 0-1 Knapsack Problems

  • Yu Yang
  • Natashia Boland
  • Bistra Dilkina
  • Martin Savelsbergh
    • Categories (Mixed) Integer Linear Programming, Integer Programming Tags , ,

    Branching on a set of variables, rather than on a single variable, can give tighter bounds at the child nodes and can result in smaller search trees. However, selecting a good set of variables to branch on is even more challenging than selecting a good single variable to branch on. Generalized strong branching extends the … Read more

    Coordinate Descent Without Coordinates: Tangent Subspace Descent on Riemannian Manifolds

  • David H. Gutman
  • Nam Ho-Nguyen
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , ,

    We extend coordinate descent to manifold domains, and provide convergence analyses for geodesically convex and non-convex smooth objective functions. Our key insight is to draw an analogy between coordinate blocks in Euclidean space and tangent subspaces of a manifold. Hence, our method is called tangent subspace descent (TSD). The core principle behind ensuring convergence of … Read more

    Pump scheduling in drinking water distribution networks with an LP/NLP-based branch and bound

  • Gratien Bonvin
  • Andrea Lodi
  • Sophie Demassey
    • Categories Global Optimization Applications Tags , , ,

    This paper offers a novel approach for computing globally optimal solutions to the pump scheduling problem in drinking water distribution networks. A tight integer linear relaxation of the original non-convex formulation is devised and solved by branch and bound where integer nodes are investigated through non-linear programming to check the satisfaction of the non-convex constraints … Read more

    Random-Sampling Multipath Hypothesis Propagation for Cost Approximation in Long-Horizon Optimal Control

  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering, Control Applications Tags , , ,

    In this paper, we develop a Monte-Carlo based heuristic approach to approximate the objective function in long horizon optimal control problems. In this approach, we evolve the system state over multiple trajectories into the future while sampling the noise disturbances at each time-step, and find the weighted average of the costs along all the trajectories. … Read more

    Stochastic Last-mile Delivery with Crowd-shipping and Mobile Depots

  • Merve Bodur
  • Kianoush Mousavi
  • Matthew J. Roorda
    • Categories Stochastic Programming, Transportation Tags , , , , , ,

    This paper proposes a two-tier last-mile delivery model that optimally selects mobile depot locations in advance of full information about the availability of crowd-shippers, and then transfers packages to crowd-shippers for the final shipment to the customers. Uncertainty in crowd-shipper availability is incorporated by modeling the problem as a two-stage stochastic integer program. Enhanced decomposition … Read more

    Optimal Learning for Structured Bandits

  • Negin Golrezaei
  • Bart Paul Gerard Van Parys
    • Categories Convex Optimization, Semi-infinite Programming, Stochastic Programming Tags , ,

    We study structured multi-armed bandits, which is the problem of online decision-making under uncertainty in the presence of structural information. In this problem, the decision-maker needs to discover the best course of action despite observing only uncertain rewards over time. The decision- maker is aware of certain structural information regarding the reward distributions and would … Read more

    Two-Stage Facility Location Problems with Restricted Recourse

  • Esra Koca
  • Nilay Noyan
  • Hande Yaman
    • Categories Stochastic Programming

    We introduce a new class of two-stage stochastic uncapacitated facility location problems under system nervousness considerations. The location and allocation decisions are made under uncertainty, while the allocation decisions may be altered in response to the realizations of the uncertain parameters. A practical concern is that the uncertainty-adaptive second-stage allocation decisions might substantially deviate from … Read more