Evolutionary multi-objective high-order tetrahedral mesh optimization

High-order mesh optimization has many goals, such as improving smoothness, reducing approximation error, and improving mesh quality. The previous methods do not optimize these objectives together, resulting in suboptimal results. To this end, we propose a multi-objective optimization method for high-order meshes. Central to our algorithm is using the multi-objective genetic algorithm (MOGA) to adapt to the multiple optimization objectives. Specifically, we optimize each control point one by one, where the MOGA is applied. We demonstrate the feasibility and effectiveness of our method over various models. Compared to other state-of-the-art methods, our method achieves a favorable trade-off between multiple objectives. •We propose a multi-objective optimization method for high-order tetrahedral meshes.•Employ the multi-objective genetic algorithm to relocate control points to achieve a favorable trade-off among objectives.•Select the best individual via the weighted TOPSIS method, with weights determined by combining multi-objective problem.