Other Topics

Application of a Gas Market Model with Linear Programming. The Influence of the Dollar Exchange Rate on the Wholesale Price of Natural Gas in Northwest Europe until 2040

  • Maik Günther
    • Categories Finance and Economics, Linear Programming, Optimization of Simulated Systems Tags , , , , , , , , ,

    The price of natural gas at wholesale markets in Northwest Europe is influenced by numerous parameters. The USD to EUR exchange rate is one of these parameters. Using the LP-based gas market model WEGA, this paper will examine the impact of USD exchange rates on wholesale natural gas prices in Northwest Europe from 2025 to … Read more

    Algorithms for Cameras View-Frame Placement Problems in the Presence of an Adversary and Distributional Ambiguity

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

    In this paper, we introduce cameras view-frame placement problem (denoted by CFP) in the presence an adversary whose objective is to minimize the maximum coverage by p cameras in response to input provided by n autonomous agents in a remote location. We allow uncertainty in the success of attacks, incomplete information of the probability distribution … Read more

    Multi-Stage Robust Mixed-Integer Programming

  • Krzysztof Postek
  • Ward Romeijnders
  • Wolfram Wiesemann
    • Categories (Mixed) Integer Linear Programming, Dynamic Programming, Robust Optimization Tags , ,

    Multi-stage robust optimization, in which decisions are taken sequentially as new information becomes available about the uncertain problem parameters, is a very versatile yet computationally challenging paradigm for decision-making under uncertainty. In this paper, we propose a new model and solution approach for multi-stage robust mixed-integer programs, which may contain both continuous and discrete decisions … Read more

    Test Instances for Multiobjective Mixed-Integer Nonlinear Optimization

  • Leo Warnow
  • Gabriele Eichfelder
  • Tobias Gerlach
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization, Nonlinear Optimization Tags , , ,

    A suitable set of test instances, also known as benchmark problems, is a key ingredient to systematically evaluate numerical solution algorithms for a given class of optimization problems. While in recent years several solution algorithms for the class of multiobjective mixed-integer nonlinear optimization problems have been proposed, there is a lack of a well-established set … Read more

    (ε-)Efficiency in Fractional Vector Optimization

  • Mounir El Maghri
    • Categories Convex and Nonsmooth Optimization, Global Optimization, Multi-Criteria Optimization Tags , , , ,

    The issue of characterizing completely efficient (Pareto) solutions to a fractional vector (multiobjective or multicriteria) minimization problem, where the involved functions are convex, has not been addressed previously. Thanks to an earlier characterization of weak efficiency in difference vector optimization by El Maghri, we get a vectorial necessary and sufficient condition given in terms of … Read more

    An Explicit Three-Term Polak-Ribière-Polyak Conjugate Gradient Method for Bicriteria Optimization

  • Mounir El Maghri
  • Youssef Elboulqe
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , , , ,

    We propose in this paper a Polak-Ribière-Polyak conjugate gradient type method for solving bicriteria optimization problems by avoiding scalarization techniques. Two particular advantages in this contribution are to be noted. First, the suggested descent direction common to both criteria may be directly computed by a given formula without solving any intermediate subproblem. Second, the descent … Read more

    On a Frank-Wolfe Approach for Abs-smooth Functions

  • Timo Kreimeier
  • Sebastian Pokutta
  • Andrea Walther
  • Zev Woodstock
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization, Other Topics Tags , , , ,

    We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as $\ell_1$ regularization, phase retrieval problems, or ReLU activation in machine learning. To handle the nonsmoothness in our problem, we propose … Read more

    Cooperative locker locations games

  • Fabio Mercurio
  • Loe Schlicher
  • S.U.K Rohmer
  • Tom Van Woensel
    • Categories Applications - OR and Management Sciences, Game Theory, Other Topics Tags , ,

    More and more people are ordering products online, having their parcels delivered to their homes. This leads to more congestion, which negatively impacts the environment as well as public health and safety. To reduce these negative impacts, carriers can use parcel lockers to consolidate and serve their customers. The implementation of a locker network can, … Read more

    An approximation algorithm for multi-objective mixed-integer convex optimization

  • Ina Lammel
  • Karl-Heinz Küfer
  • Philipp Süss
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , ,

    In this article we introduce an algorithm that approximates Pareto fronts of multiobjective mixed-integer convex optimization problems. The algorithm constructs an inner and outer approximation of the front exploiting the convexity of the patches and is applicable to problems with an arbitrary number of criteria. In the algorithm, the problem is decomposed into patches, which … Read more

    Column Elimination for Capacitated Vehicle Routing Problems

  • Anthony Karahalios
  • Willem-Jan van Hoeve
    • Categories (Mixed) Integer Linear Programming, Branch and Cut Algorithms, Dynamic Programming Tags , , ,

    We introduce a column elimination procedure for the capacitated vehicle routing problem. Our procedure maintains a decision diagram to represent a relaxation of the set of feasible routes, over which we define a constrained network flow. The optimal solution corresponds to a collection of paths in the decision diagram and yields a dual bound. The … Read more