Philip de Castro

On Subproblem Tradeoffs in Decomposition and Coordination of Multiobjective Optimization Problems

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

    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 three or four 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

    On Bivariate Achievement Scalarizing Functions

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

    Achievement Scalarizing Functions (ASFs) are a class of scalarizing functions for multiobjective optimization problems that have been successfully implemented in many applications due to their mathematical elegance and decision making utility. However, no formal proofs of the fundamental properties of ASFs have been presented in the literature. Furthermore, developments of ASFs, including the construction of … Read more

    Pareto Leap: An Algorithm for Biobjective Mixed-Integer Programming

  • Philip de Castro
  • Margaret Wiecek
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Multi-Criteria Optimization Tags , , ,

    Many real-life optimization problems need to make decisions with discrete variables and multiple, conflicting objectives. Due to this need, the ability to solve such problems is an important and active area of research. We present a new algorithm, called Pareto Leap, for identifying the (weak) Pareto slices of biobjective mixed-integer programs (BOMIPs), even when Pareto … Read more