High-fidelity simulation models, which adhere to physical laws and social logic, offer a multidimensional projection of the real world. Within operations research, simulation has evolved from being solely an analytical tool to becoming an optimization evaluator. Today, simulation models are widely employed in various optimization problems and industrial cases. However, effectively and multidimensionally exploiting simulation performances in Multi-Objective Optimization (MOO) remains an underexplored territory, especially considering that simulation-optimization problems are inherently black-box or grey-box in nature. Traditionally, approaches to multi-objective simulation-optimization have relied on evolutionary algorithms (e.g., NSGA-II), which are notoriously challenged by high-dimensional and many-objective problems.

Motivated by these limitations, we introduced a novel framework—Multi-Objective Stochastic Approximation (MOSA)—that brings stochastic approximation theory into the MOO realm. First, we present the principal process of the MOSA algorithm along with its convergence properties. Next, a Gram–Schmidt orthogonalization process is incorporated to simplify the computation of the Common Descent Vector (CDV). Finally, leveraging the inherent characteristics of uniform descent across objectives in MOSA, we design an adaptive search step-size and direction scheme to achieve both rolling and navigational search along the Pareto front.

To demonstrate the efficiency of our method, we propose a MO-SPSA algorithm that utilizes a Simultaneous Perturbation Stochastic Approximation (SPSA) estimator for gradients. Comparisons of benchmark functions—including ZDT, DTLZ, and a large-scale MOSO instance—against mainstream multi-objective evolutionary algorithms show that MO-SPSA approximates the Pareto front in considerably shorter CPU time while enabling continuous and controllable navigation along the front. Notably, our approach yields superior quality solutions, especially in many-objective scenarios.

Li Yan is a PhD candidate in Industrial Systems Engineering and Management at the National University of Singapore, advised by Dr. Li Haobin and Prof. Chew Ek Peng. He received his bachelor’s and master’s degree from Southwest Jiaotong University, China, in 2019 and 2022, respectively. His research interests include simulation modelling, simulation-optimization, and multi-objective optimization.