Pradyumn Kumar Shukla

Line-Prioritized Environmental Selection and Normalization Scheme for Many-Objective Optimization using Reference-Line-based Framework

  • Deepak Sharma
  • Pradyumn Kumar Shukla
    • Categories Multi-Criteria Optimization

    The Pareto-dominance-basedmulti-objective evolutionary algorithms (MOEAs) have been successful in solving many test problems and other engineering optimization problems. However, their performance gets affected when solving more than 3-objective optimization problems due to lack of sufficient selection pressure. Many attempts have been made by the researchers toward improving the environmental selection of those MOEAs. One such … Read more

    Approximations for Pareto and Proper Pareto solutions and their KKT conditions

  • Kalyanmoy Deb
  • Joydeep Dutta
  • Poonam Kesarwani
  • Pradyumn Kumar Shukla
    • Categories Multi-Criteria Optimization Tags , , ,

    There has been numerous amount of studies on proper Pareto points in multiobjective optimization theory. Geoffrion proper points are one of the most prevalent form of proper optimality. Due to some convergence issues a restricted version of these proper points, Geoffrion proper points with preset bounds has been introduced recently. Since solution of any algorithm … Read more

    On a Practical Notion of Geoffrion Proper Optimality in Multicriteria Optimization

  • Kalyanmoy Deb
  • Joydeep Dutta
  • Poonam Kesarwani
  • Pradyumn Kumar Shukla
    • Categories Multi-Criteria Optimization, Nonlinear Optimization

    Geoffrion proper optimality is a widely used optimality notion in multicriteria optimization that prevents exact solutions having unbounded trade-offs. As algorithms for multicriteria optimization usually give only approximate solutions, we analyze the notion of approximate Geoffrion proper optimality. We show that in the limit, approximate Geoffrion proper optimality may converge to solutions having unbounded trade-offs. … Read more

    On cone based decompositions of proper Pareto optimality

  • Marlon Braun
  • Hartmut Schmeck
  • Pradyumn Kumar Shukla
    • Categories Global Optimization, Multi-Criteria Optimization Tags , , ,

    In recent years, the research focus in multi-objective optimization has shifted from approximating the Pareto optimal front in its entirety to identifying solutions that are well-balanced among their objectives. Proper Pareto optimality is an established concept for eliminating Pareto optimal solutions that exhibit unbounded tradeo ffs. Imposing a strict tradeo ff bound allows specifying how many units … Read more

    A Theoretical and Algorithmic Characterization of Bulge Knees

  • Marlon Braun
  • Hartmut Schmeck
  • Pradyumn Kumar Shukla
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

    This paper deals with the problem of finding convex bulges on the Pareto-front of a multi-objective optimization problem. The point of maximum bulge is of particular interest as this point shows good trade-off properties and it is also close to the non-attainable utopia point. Our approach is to use a population based algorithm to simultaneously … Read more