A continuous m-objective optimization problem exhibits a regularity property under mild conditions, such that the Pareto set of the multiobjective optimization problem (MOP) forms an \((m-1)\) -dimensional piecewise continuous manifold. Leveraging this regularity in the design of multiobjective evolutionary algorithms can be advantageous. In this paper, we propose an online regularity learning-based evolutionary multiobjective optimization (OCEMO) algorithm. Given that the data generated by evolutionary algorithms are typically non-stationary and independent, OCEMO integrates an online clustering approach directly into the evolutionary process at the operator level. After each generation of evolution, a clustering iteration is performed to gradually uncover the regular structure of the Pareto set. The learned neighborhood relationships among solutions are then used to serve the mating selection and guide the search process within the algorithm. Experimental results demonstrate that OCEMO significantly outperforms several state-of-the-art multiobjective evolutionary algorithms on complex test suites and in a real-world application of aircraft trajectory planning.
