Research on Evolutionary Level Set Method and Gaussian Mixture Model Based Target Shape Design Optimization Problem

Evolutionary algorithms (EAs) have been successfully used in solving many design optimization problems. However, it generally requires expensive computational resources to tune the EA hyper-parameters and validate the performance. Since a single simulation takes a long time and multiple iterations are required, using EAs to real-world design structure optimization is becoming extremely time-consuming. Therefore, the target shape design optimization problem (TSDOP) has been proposed as a miniature model to replace real-world complex problems. There are three major components in developing EAs for TSDOP, i.e., a shape representation, a fitness evaluation, and an evolutionary strategy. For the shape representation, spline-based methods are frequently used in the research community. However, as their flexibility is dramatically limited by the fixed topology, they have difficulty in representing discontinuous shapes without adding any adjustment strategies. In addition, the spline-based methods will easily generate self-intersection (loop) problem that always increases the search difficulty and reduces the convergence speed during the evolutionary iterations. Therefore, in this paper, we first propose a level-set method integrated with a Gaussian mixture model (GMMLSM) as a shape representation method to overcome the fixed topology and loop problem in the existing spline-based methods. We also propose an improved chaotic evolution for the GMMLSM shape representation, namely, GMMLSM-CE, which integrates the ergodicity from the chaotic system and the good robustness from differential evolution (DE). To evaluate the efficiency and performance of the proposed GMMLSM-CE, experiments on two target shapes with three different EAs are conducted. The empirical results show that: 1) GMMLSM has the ability to represent continuous and discontinuous shapes and can naturally avoid self-intersection (loop) problem; 2) CE has a good performance for parameter tuning, and; 3) GMMLSM-CE has a good representation accuracy and fast convergence speed in terms of solving the TSDOP.