multiobjective optimization

The Impact of Neighboring Markets on Renewable Locations, Transmission Expansion, and Generation Investment

  • Jonas Egerer
  • Veronika Grimm
  • Thomas Kleinert
  • Martin Schmidt
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , ,

    Many long-term investment planning models for liberalized electricity markets either optimize for the entire electricity system or focus on confined jurisdictions, abstracting from adjacent markets. In this paper, we provide models for analyzing the impact of the interdependencies between a core electricity market and its neighboring markets on key long-run decisions. This we do both … Read more

    On the use of polynomial models in multiobjective directional direct search

  • C. P. Brás
  • Ana Luisa Custódio
    • Categories Nonlinear Optimization Tags , , , ,

    Polynomial interpolation or regression models are an important tool in Derivative-free Optimization, acting as surrogates of the real function. In this work, we propose the use of these models in the multiobjective framework of directional direct search, namely the one of Direct Multisearch. Previously evaluated points are used to build quadratic polynomial models, which are … Read more

    Solving Multiobjective Mixed Integer Convex Optimization Problems

  • Marianna De Santis
  • Gabriele Eichfelder
  • Julia Niebling
  • Stefan Rocktäschel
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , ,

    Multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. We present a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, … Read more

    An Algorithmic Approach to Multiobjective Optimization with Decision Uncertainty

  • Gabriele Eichfelder
  • Julia Niebling
  • Stefan Rocktäschel
    • Categories Global Optimization, Multi-Criteria Optimization, Robust Optimization Tags , ,

    In real life applications optimization problems with more than one objective function are often of interest. Next to handling multiple objective functions, another challenge is to deal with uncertainties concerning the realization of the decision variables. One approach to handle these uncertainties is to consider the objectives as set-valued functions. Hence, the image of one … Read more

    Endogenous Price Zones and Investment Incentives in Electricity Markets: An Application of Multilevel Optimization with Graph Partitioning

  • Mirjam Ambrosius
  • Veronika Grimm
  • Thomas Kleinert
  • Frauke Liers
  • Martin Schmidt
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , ,

    In the course of the energy transition, load and supply centers are growing apart in electricity markets worldwide, rendering regional price signals even more important to provide adequate locational investment incentives. This paper focuses on electricity markets that operate under a zonal pricing market design. For a fixed number of zones, we endogenously derive the … Read more

    Nonmonotone line searches for unconstrained multiobjective optimization problems

  • Ellen H. Fukuda
  • Kanako Mita
  • Nobuo Yamashita
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , , ,

    In the last two decades, many descent methods for multiobjective optimization problems were proposed. In particular, the steepest descent and the Newton methods were studied for the unconstrained case. In both methods, the search directions are computed by solving convex subproblems, and the stepsizes are obtained by an Armijo-type line search. As a consequence, the … Read more

    Fast Multilevel Algorithms for Compressive Principle Component Pursuit

  • Vahan Hovhannisyan
  • Panos Parpas
  • Yannis Panagakis
  • Stefanos Zafeiriou
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , ,

    Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via principal component pursuit (PCP), recovers a low-rank matrix from sparse corruptions that are of unknown value and support by decomposing the observation matrix into two … Read more

    Complexity of gradient descent for multiobjective optimization

  • Jörg Fliege
  • A. Ismael F. Vaz
  • Luis Nunes Vicente
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , ,

    A number of first-order methods have been proposed for smooth multiobjective optimization for which some form of convergence to first order criticality has been proved. Such convergence is global in the sense of being independent of the starting point. In this paper we analyze the rate of convergence of gradient descent for smooth unconstrained multiobjective … Read more

    A barrier-type method for multiobjective optimization

  • Ellen H. Fukuda
  • L. M. Graña Drummond
  • Fernanda M. P. Raupp
    • Categories Multi-Criteria Optimization Tags , , ,

    For solving constrained multicriteria problems, we introduce the multiobjective barrier method (MBM), which extends the scalar-valued internal penalty method. This multiobjective version of the classical method also requires a penalty barrier for the feasible set and a sequence of nonnegative penalty parameters. Differently from the single-valued procedure, MBM is implemented by means of an auxiliary … Read more

    A Trust Region Algorithm for Heterogeneous Multiobjective Optimization

  • Gabriele Eichfelder
  • Jana Thomann
    • Categories Multi-Criteria Optimization Tags , , , ,

    This paper presents a new trust region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, for example given by a time-consuming simulation. For this function derivative information cannot be used and the computation of function values involves high computational effort. The other objective functions are given analytically … Read more