multi-objective optimization

Analysis and discussion of single and multi-objective IP formulations for the Truck-to-dock Door Assignment Problem

  • Xavier Gandibleux
  • Nicolas Forget
    • Categories Applications - OR and Management Sciences, Integer Programming, Multi-Criteria Optimization Tags , , , ,

    This paper is devoted to the Truck-to-dock Door Assignment Problem. Two integer programming formulations introduced after 2009 are examined. Our review of the literature takes note of the criticisms and limitations addressed to the seminal work of 2009. Although the published adjustments that followed present strong argument and technical background, we have identified several errors, … Read more

    An adaptive relaxation-refinement scheme for multi-objective mixed-integer nonconvex optimization

  • Gabriele Eichfelder
  • Moritz Link
  • Stefan Volkwein
  • Leo Warnow
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , , ,

    In this work, we present an algorithm for computing an enclosure for multi-objective mixed-integer nonconvex optimization problems. In contrast to existing solvers for this type of problem, this algorithm is not based on a branch-and-bound scheme but rather relies on a relax-and-refine approach. While this is an established technique in single-objective optimization, several adaptions to … Read more

    Properties of Two-Stage Stochastic Multi-Objective Linear Programs

  • Akshita Gupta
  • Susan R. Hunter
    • Categories Multi-Criteria Optimization, Other Topics, Stochastic Programming Tags , ,

    We consider a two-stage stochastic multi-objective linear program (TSSMOLP) which is a natural multi-objective generalization of the well-studied two-stage stochastic linear program. The second-stage recourse decision is governed by an uncertain multi-objective linear program whose solution maps to an uncertain second-stage nondominated set. The TSSMOLP then comprises the objective function, which is the Minkowsi sum … Read more

    Considering homeowner acceptance of retrofit measures within energy supply network optimization

  • Carl Eggen
  • Moritz Link
  • Stefan Volkwein
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , ,

    A key factor towards a low-carbon society is energy efficient heating of private houses. The choice of heating technology as well as the decision for certain energy-efficient house renovations are made mainly by individual homeowners. In contrast, municipal energy network planning heavily depends on and strongly affects these decisions. Further, there are different conflicting objectives … Read more

    Computing an approximation of the nondominated set of multi-objective mixed-integer nonlinear optimization problems

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

    In practical applications, one often has not only one, but several objectives that need to be optimized simultaneously. What is more, modeling such real world problems usually involves using both, continuous and integer variables. This then results in multi-objective mixed-integer optimization problems, which are in focus of this paper. We present an approximation concept, called … Read more

    Solving Hard Bi-objective Knapsack Problems Using Deep Reinforcement Learning

  • Sasan Mahmoudinazlou
  • Hadi Charkhgard
  • Ali Eshragh
    • Categories Approximation Algorithms, Integer Programming Tags , , ,

    We study a class of bi-objective integer programs known as bi-objective knapsack problems (BOKPs). Our research focuses on the development of innovative exact and approximate solution methods for BOKPs by synergizing algorithmic concepts from two distinct domains: multi-objective integer programming and (deep) reinforcement learning. While novel reinforcement learning techniques have been applied successfully to single-objective … Read more

    A Criterion Space Search Feasibility Pump Heuristic for Solving Maximum Multiplicative Programs

  • Ashim Khanal
  • Hadi Charkhgard
    • Categories Game Theory, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    We study a class of nonlinear optimization problems with diverse practical applications, particularly in cooperative game theory. These problems are referred to as Maximum Multiplicative Programs (MMPs), and can be conceived as instances of “Optimization Over the Frontier” in multiobjective optimization. To solve MMPs, we introduce a feasibility pump-based heuristic that is specifically designed to … Read more

    A novel UCB-based batch strategy for Bayesian optimization

  • Carmen-Ana Domínguez-Bravo
    • Categories Global Optimization, Multi-Criteria Optimization Tags , , ,

    The optimization of expensive black-box functions appears in many situations. Bayesian optimization methods have been successfully applied to solve these prob- lems using well-known single-point acquisition functions. Nowadays, the develop- ments in technology allow us to perform evaluations of some of these expensive function in parallel. Therefore, there is a need for batch infill criteria … 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

    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