Bilevel Optimization-Based Decomposition for Solving Single and Multiobjective Optimization Problems

Ankur Sinha, Dhaval Pujara, Hemant Kumar Singh

Abstract: Real world optimization problems contain multiple complexities that are often not tractable if one completely relies on mathematical programming or metaheuristic approaches, as each approach has unique strengths and limitations in dealing with the complexities in optimization problems. For instance, metaheuristic methods have an edge in tackling non-regularities like discontinuity, non-convexity, and discreteness, given that problem has few decision variables (low dimensionality). Contrary to that, mathematical programming based classical methods can efficiently solve high dimensional problems if the problem encompasses regular functions as constraints and objective function. Thus, non-regular and high-dimensional optimization problems pose challenges to both approaches for getting solved using the method explicitly from any one approach. To excel in this situation, this study proposes a difficulties separation approach that enables to convert a single level optimization problem into bilevel optimization problem and solve the problem synergistically by applying methods from both complementary approaches. We demonstrate the benefits of proposed bilevel based decomposition approach on a wide range of single and multiobjective test problems.

External IDs:dblp:conf/emo/SinhaPS25