Multi-Objective Derivative-Free Optimization Based on Hessian-Aware Gaussian Smoothing Method

Most deterministic multi-objective optimization algorithms assume that the analytical objective functions and multi-objective gradients are available. However, there may be no available or explicit mathematical model for many real-world optimization problems. These problems are difficult to handle since the evaluations of gradients are inexact or even infeasible, which are termed derivative-free (or zeroth-order) optimization problems. To tackle the issues, a multi-objective derivative-free optimization based on Hessian-aware Gaussian smoothing method is proposed. We evaluate the multi-objective descent direction and produce new candidates for searching the Pareto front. Furthermore, we analyze the corresponding convergence rate of candidates produced by the Hessian-aware Gaussian smoothing method explicitly. Finally, we compared different multi-objective optimization algorithms and illustrated their performance on numerical benchmarks to show the proposed algorithm's effectiveness.