Abstract
Topology optimization by optimally distributing materials in a given domain requires non-gradient optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN’s prediction of the optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. The optimum predicted by the DNN is proved to converge to the true global optimum through iterations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.
Highlights
Topology optimization by optimally distributing materials in a given domain requires nongradient optimizers to solve highly complicated problems
Our algorithm reduces the computational cost by at least two orders of magnitude compared with directly applying heuristic methods including Generalized Simulated Annealing (GSA), Binary Bat Algorithm (BBA), and Bat Algorithm (BA)
We proposed an approach of self-directed online learning optimization (SOLO) to dramatically accelerate the optimization process and make solving complex optimization problems possible
Summary
Topology optimization by optimally distributing materials in a given domain requires nongradient optimizers to solve highly complicated problems. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. Because of the intrinsic limitation of gradient-based algorithms, the majority of existing approaches have only been applied to simple problems, since they would fail as soon as the problem becomes complicated such as involving varying signs on gradients or non-linear constraints[4] To address these difficulties, non-gradient methods have been developed which play a significant role in overcoming the tendency to be trapped in a local minimum[5]. Pattern search has been applied[13,14] which is a non-heuristic method with a smaller searching space but is more likely to be trapped in local minima
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