Fu-Yao Ko

Fu-Yao Ko, Katsuyuki Suzuki, Kazuo Yonekura

This paper proposes a novel reinforcement learning (RL) algorithm using improved Monte Carlo tree search (IMCTS) formulation for discrete optimum design of truss structures. IMCTS with multiple root nodes includes update process, the best reward, accelerating technique, and terminal condition. Update process means that once a final solution is found, it is used as the initial solution for next search tree. The best reward is used in the backpropagation step. Accelerating technique is introduced by decreasing the width of search tree and reducing maximum number of iterations. The agent is trained to minimize the total structural weight under various constraints until the terminal condition is satisfied. Then, optimal solution is the minimum value of all solutions found by search trees. These numerical examples show that the agent can find optimal solution with low computational cost, stably produces an optimal design, and is suitable for multi-objective structural optimization and large-scale structures.

Fu-Yao Ko, Katsuyuki Suzuki, Kazuo Yonekura

A novel method called mixed variable system Monte Carlo tree search (MVSMCTS) formulation is presented for optimization problems considering various types of variables with single and mixed continuous-discrete system. This method utilizes a reinforcement learning algorithm with improved Monte Carlo tree search (IMCTS) formulation. For sizing and shape optimization of truss structures, the design variables are the cross-sectional areas of the members and the nodal coordinates of the joints. MVSMCTS incorporates update process and accelerating technique for continuous variable and combined scheme for single and mixed system. Update process indicates that once a solution is determined by MCTS with automatic mesh generation in continuous space, it is used as the initial solution for next search tree. The search region should be expanded from the mid-point, which is the design variable for initial state. Accelerating technique is developed by decreasing the range of search region and the width of search tree based on the number of meshes during update process. Combined scheme means that various types of variables are coupled in only one search tree. Through several examples, it is demonstrated that this framework is suitable for mixed variable structural optimization. Moreover, the agent can find optimal solution in a reasonable time, stably generates an optimal design, and is applicable for practical engineering problems.