Multi-Criteria Optimization

Universal nonmonotone line search method for nonconvex multiobjective optimization problems with convex constraints

  • Maria Eduarda Pinheiro
  • Geovani Nunes Grapiglia
    • Categories Multi-Criteria Optimization Tags

    In this work we propose a general nonmonotone line-search method for nonconvex multi-objective optimization problems with convex constraints. At the \(k\)th iteration, the degree of nonmonotonicity is controlled by a vector \(\nu_{k}\) with nonnegative components. Different choices for \(\nu_{k}\) lead to different nonmonotone step-size rules. Assuming that the sequence \(\left\{\nu_{k}\right\}_{k\geq 0}\) is summable, and that … Read more

    Scaled Proximal Gradient Methods for Multiobjective Optimization: Improved Linear Convergence and Nesterov’s Acceleration

  • Jian Chen
    • Categories Multi-Criteria Optimization Tags , , ,

    Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for multiobjective optimization converge slowly, even for well-conditioned problems, due to the objective imbalances. To address this limitation, we incorporate curvature information to scale each objective within … Read more

    On Subproblem Tradeoffs in Decomposition for Multiobjective Optimization

  • Philip de Castro
  • Margaret Wiecek
    • Categories Multi-Criteria Optimization Tags , ,

    Multiobjective optimization is widely used in applications for modeling and solving complex decision-making problems. To help resolve computational and cognitive difficulties associated with problems which have more than 3 or 4 objectives, we propose a decomposition and coordination methodology to support decision making for large multiobjective optimization problems (MOPs) with global, quasi-global, and local variables. … Read more

    Designing sustainable diet plans by solving triobjective integer programs

  • Marianna De Santis
  • Alberto De Santis
  • Daniele Patria
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , ,

    We present an algorithm for triobjective nonlinear integer programs that combines the epsilon-constrained method with available oracles for biobjective integer programs. We prove that our method is able to detect the nondominated set within a finite number of iterations. Specific strategies to avoid the detection of weakly nondominated points are devised. The method is then … Read more

    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

    Equity-promoting Integer Programming Approaches For Medical Resident Rotation Scheduling

  • Karmel S. Shehadeh
  • Shutian Li
  • Frank E. Curtis
  • Beth Hochman
    • Categories Applications - OR and Management Sciences, Integer Programming, Multi-Criteria Optimization Tags , , ,

    Motivated by our collaboration with a residency program at an academic health system, we propose new integer programming (IP) approaches for the resident-to-rotation assignment problem (RRAP). Given sets of residents, resident classes, and departments, as well as a block structure for each class, staffing needs, rotation requirements for each class, program rules, and resident vacation … 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

    Equity-Driven Workload Allocation for Crowdsourced Last-Mile Delivery

  • Abhay Sobhanan
  • Hadi Charkhgard
  • Iman Dayarian
    • Categories Meta Heuristics, Multi-Criteria Optimization, Transportation Tags , , , ,

    Crowdshipping, a rapidly growing approach in Last-Mile Delivery (LMD), relies on independent crowdworkers for delivery orders. Building a sustainable network of crowdshippers is essential for the survival and growth of such systems, while their participation is primarily motivated by fair pay. Additionally, the financial well-being of crowdworkers is sensitive to fair compensation, especially for those … Read more

    Strict efficiency in set optimization studied with the set approach

  • Xuan Duc Ha Truong
    • Categories Multi-Criteria Optimization Tags , , , , ,

    This paper is devoted to strict efficiency in set optimization studied with the set approach. Strict efficient solutions are defined with respect to the $l$-type less order relation and the possibly less order relation. Scalar characterization and necessary and/or sufficient conditions for such solutions are obtained. In particular, we establish some conditions expressed in terms … Read more