A Homotopy Framework for Constrained Multiobjective Optimization
This work provides a deterministic, structure-preserving method for multiobjective optimization, offering an alternative to stochastic evolutionary algorithms for practitioners needing reliable Pareto-stationary points.
The paper develops a homotopy-based framework for computing KKT points of constrained multiobjective optimization problems, achieving global convergence to Pareto-stationary solutions under mild assumptions. Numerical experiments show competitive efficiency and solution quality compared to scalarization methods and NSGA-II.
We develop a homotopy-based framework for computing Karush-Kuhn-Tucker (KKT) points of multiobjective optimization problems. The proposed homotopy map continuously deforms an easily solvable system into the KKT conditions associated with the multiobjective problem, yielding a deterministic and structure-preserving continuation path. Under mild regularity assumptions, we establish global convergence of the homotopy trajectory to a Pareto-stationary solution for any initial point chosen in the interior of the feasible region. In numerical experiments, the method exhibits robust convergence even when initialized from nonfeasible points, indicating stability beyond the theoretical guarantees. Efficient predictor-corrector continuation strategies are employed to trace the homotopy path. Numerical results on benchmark problems compare the proposed approach with classical scalarization methods and the evolutionary algorithm NSGA-II, demonstrating competitive computational efficiency and consistent solution quality. These results highlight the effectiveness of the homotopy framework for constrained multiobjective optimization and motivate extensions to more general problem settings and adaptive parameter strategies.