Kimia Keshanian

A Binary Search-Based Criterion Space Algorithm for Solving Bi-Objective Integer Programs: The Quadtree Search Method

  • Lagnajita Basu
  • Aadya Bhattarai
  • Tapas Das
  • Kimia Keshanian
  • Hadi Charkhgard
    • Categories Integer Programming, Multi-Criteria Optimization Tags , , , ,

    We propose an exact binary search-based branch-and-bound algorithm, termed the Quadtree Search Method, for solving bi-objective integer programs. The existing literature on criterion space search methods for multi-objective optimization predominantly assumes that subproblems can be solved to optimality, an assumption that becomes computationally prohibitive for hard instances. In contrast, our approach departs from this assumption … Read more

    The Magic of Nash Social Welfare in Optimization: Do Not Sum, Just Multiply!

  • Hadi Charkhgard
  • Parisa Charkhgard
  • Rasul Esmaeilbeigi
  • Kimia Keshanian
    • Categories Game Theory, Global Optimization, Multi-Criteria Optimization Tags , , , ,

    In this paper, we explain some key challenges when dealing with a single/multi-objective optimization problem in practice. To overcome these challenges, we present a mathematical program that optimizes a Nash Social Welfare function. We refer to this mathematical program as the Nash Social Welfare Program (NSWP). An interesting property of the NSWP is that it … Read more