A Model-Search Multi-Objective Derivative-Free Optimization Algorithm with Sparse Modeling

Multi-objective derivative-free optimization has broad applications in engineering fields, with its main challenge being how to solve problems efficiently without gradient information. This article proposes a novel multi-objective derivative-free optimization algorithm that integrates sparse modeling techniques with a new non-dominated comparison function within a direct multisearch framework. To fully leverage information from historically evaluated points, the algorithm employs quadratic surrogate models constructed from these points to enhance the search step, with model coefficients determined through either linear programming or least-squares methods. Simultaneously, a Pareto dominance-based comparison function is introduced to improve the selection capability of candidate solutions. Experimental results on ZDT and WFG benchmark problems demonstrate that, through comparisons of hypervolume values and performance profiles, the proposed algorithm exhibits competitiveness and robustness under limited function evaluation budgets compared to existing state-of-the-art methods.