Month: July 2021

Exact and Approximate Schemes for Robust Optimization Problems with Decision Dependent Information Discovery

  • Said Dabia
  • Angelos Georghiou
  • Rosario Paradiso
  • Denise Tönissen
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , , , ,

    Uncertain optimization problems with decision dependent information discovery allow the decision maker to control the timing of information discovery, in contrast to the classic multistage setting where uncertain parameters are revealed sequentially based on a prescribed filtration. This problem class is useful in a wide range of applications, however, its assimilation is partly limited by … Read more

    A solution algorithm for chance-constrained problems with integer second-stage recourse decisions

  • Andrea Lodi
  • Enrico Malaguti
  • Michele Monaci
  • Giacomo Nannicini
  • Paolo Paronuzzi
    • Categories (Mixed) Integer Nonlinear Programming, Stochastic Programming

    We study a class of chance-constrained two-stage stochastic optimization problems where the second-stage recourse decisions belong to mixed-integer convex sets. Due to the nonconvexity of the second-stage feasible sets, standard decomposition approaches cannot be applied. We develop a provably convergent branch-and-cut scheme that iteratively generates valid inequalities for the convex hull of the second-stage feasible … Read more

    Robust Integration of Electric Vehicles Charging Load in Smart Grid’s Capacity Expansion Planning

  • Sajad Aliakbari-Sani
  • Olivier Bahn
  • Erick Delage
  • Rinel Foguen Tchuendom
    • Categories Energy, Game Theory, Robust Optimization Tags , , ,

    Battery charging of electric vehicles (EVs) needs to be properly coordinated by electricity producers to maintain network reliability. In this paper, we propose a robust approach to model the interaction between a large fleet of EV users and utilities in a long-term generation expansion planning problem. In doing so, we employ a robust multi-period adjustable … Read more

    Dual SDDP for risk-averse multistage stochastic programs

  • Bernardo Freitas Paulo da Costa
  • Vincent Leclère
    • Categories Dynamic Programming, Stochastic Programming Tags , , , ,

    Risk-averse multistage stochastic programs appear in multiple areas and are challenging to solve. Stochastic Dual Dynamic Programming (SDDP) is a well-known tool to address such problems under time-independence assumptions. We show how to derive a dual formulation for these problems and apply an SDDP algorithm, leading to converging and deterministic upper bounds for risk-averse problems. … Read more

    Bishop-Phelps cones given by an equation in Banach spaces

  • Xuan Duc Ha Truong
  • Johannes Jahn
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization, Second-Order Cone Programming Tags , , , ,

    In this work, we study Bishop-Phelps cones (briefly, BP cones) given by an equation in Banach spaces. Due to the special form, these cones enjoy interesting properties. We show that nontrivial BP cones given by an equation form a “large family” in some sense in any Banach space and they can be used to characterize … Read more

    A primal heuristic to compute an upper bound set for multi-objective 0-1 linear optimisation problems

  • Xavier Gandibleux
  • Guillaume Gasnier
  • Said Hanafi
    • Categories Branch and Cut Algorithms, Integer Programming, Multi-Criteria Optimization

    This paper presents an algorithm aiming to compute an upper bound set for a multi-objective linear optimisation problem with binary variables (p-01LP). Inspired by the well known « Feasibility Pump » algorithm in single objective optimisation, it belongs to the class of primal heuristics. The proposed algorithm, named « Gravity Machine », aims to deal … Read more

    A Vectorization Scheme for Nonconvex Set Optimization Problems

  • Gabriele Eichfelder
  • Ernest Quintana
  • Stefan Rocktäschel
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization Tags , , , ,

    In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution … Read more

    A novel approach for bilevel programs based on Wolfe duality

  • Yuwei Li
  • Guihua Lin
  • Jin Zhang
  • Xide Zhu
    • Categories Constrained Nonlinear Optimization Tags , , , ,

    This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most popular approach is to replace the lower-level program by its KKT conditions and then the bilevel program can be transformed into a … Read more

    Battery Storage Formulation and Impact on Day Ahead Security Constrained Unit Commitment

  • Ross Baldick
  • Yonghong Chen
    • Categories Applications - OR and Management Sciences Tags , ,

    This paper discusses battery storage formulations and analyzes the impact of the constraints on the computational performance of security constrained unit commitment (SCUC). Binary variables are in general required due to mutual exclusiveness of charging and discharging modes. We use valid inequalities to improve the SOC constraints. Adding batteries to the MISO day ahead market … Read more

    Generating Cutting Inequalities Successively for Quadratic Optimization Problems in Binary Variables

  • Sunyoung Kim
  • Masakazu Kojima
    • Categories 0-1 Programming, Linear, Cone and Semidefinite Programming, Quadratic Programming Tags , , , , , , ,

    We propose a successive generation of cutting inequalities for binary quadratic optimization problems. Multiple cutting inequalities are successively generated for the convex hull of the set of the optimal solutions $\subset \{0, 1\}^n$, while the standard cutting inequalities are used for the convex hull of the feasible region. An arbitrary linear inequality with integer coefficients … Read more