Abstract
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.
Highlights
Optimization is one of the most critical problems in the creation of engineering design and has been an important area of research for many years [1]
In contrast to topology optimization (TO), shape optimization (SO) requires a close-to-optimal target shape, so we propose a new shape optimization method based on the level set method associated with shape representation of mixture Gaussian functions, namely Gaussian mixture model level set method (GMMLSM)
SHAPE REPRESENTATION: GMMLSM we explain the underlying fundamentals of the proposed method GMMLSM in subsection II-A.1; we describe the specific technology of GMMLSM in subsection II-A.2
Summary
Optimization (size, shape, and topology) is one of the most critical problems in the creation of engineering design and has been an important area of research for many years [1]. Target Shape Design Optimization Problem (TSDOP) was first proposed in 2001 [4] as a miniature model, and further developed in ([5]–[7]). Many researchers have proposed to add some adjusted strategies to deal with the loop problem with spline-based methods such as the penalty functions [6], antipodal flipping [12], distance maps [11] and center control points [5]. Compared with the traditional spline-based shape optimization methods, the proposed GMMLSM has more topology flexibility, which can represent discontinuous shapes and large curvature shapes, and it can naturally avoid the local or global selfintersections (loop) problems. GAUSSIAN MIXTURE MODEL BASED LEVEL SET METHOD (GMMLSM) AND FITNESS EVALUATION As indicated, TSDOP consists of three main components: shape representation, fitness evaluation, and the evolutionary algorithm. In the following two subsections, a shape representation method (GMMLSM) and a shape similarity measurement (H-distance) used as the fitness evaluation are presented, respectively
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
