Truss layout optimization under complex constraints has been a hot and challenging problem for decades that aims to find the optimal node locations, connection topology between nodes, and cross-sectional areas of connecting bars. Monte Carlo Tree Search (MCTS) is a reinforcement learning search technique that is competent to solve decision-making problems. Inspired by the success of AlphaGo using MCTS, the truss layout problem is formulated as a Markov Decision Process (MDP) model, and a 2-stage MCTS-based algorithm, AlphaTruss, is proposed for generating optimal truss layout considering topology, geometry, and bar size. In this MDP model, three sequential action sets of adding nodes, adding bars, and selecting sectional areas greatly expand the solution space and the reward function gives feedback to actions according to both geometric stability and structural simulation. To find the optimal sequential actions, AlphaTruss solves the MDP model and gives the best decision in each design step by searching and learning through MCTS. Compared with existing results from the literature, AlphaTruss exhibits better performance in finding the truss layout with the minimum weight under stress, displacement, and buckling constraints, which verifies the validity and efficiency of the established algorithm.

Structural design is a complicated decision-making process involving multiple qualitative and quantitative factors. Currently, most automated design methods consider only quantitative objectives and constraints, ignoring the qualitative design information that is difficult define mathematically, such as the user preference for structural shapes. This limits the functionality and efficiency of such design methods. In this study, a design method named STSA-P is proposed for plane trusses to incorporate user preference into the automatic design process. Two main problems are addressed, i.e., how to quantify user preference information and how to coordinate it with other quantitative design objectives. A prediction model of user preference is developed for the first problem by generating the data set and selecting an appropriate machine learning (ML) algorithm. Specifically, a set of truss features quantitatively representing the structural shapes are identified for the truss sample population. Furthermore, an interactive system is developed for collecting user evaluation information as data labels. Strategies for reducing user fatigue are also considered during the evaluation process. A set of numerical experiments are conducted to select the suitable ML algorithm. Regarding the second problem, the physical programming method is modified to construct a new aggregate function which effectively coordinates user preference with other design objectives. A cost function is designed by considering the design constraints. On this basis, the prediction model is incorporated into the Structural Topology and Shape Annealing (STSA) method to form the STSA-P method. Two students are invited to perform a design case using the STSA-P method. It is demonstrated that the results verify the practicality and validity of the proposed method.

Structural reanalysis methods have been proposed to improve the efficiency of structural analysis. However, the methods are typically only applicable to their specific type of structural modification. Since the optimization process often involves multiple types of modifications, it is necessary to establish a criterion for selecting the most suitable reanalysis method for each type of modification, aiming to accelerate the optimization process. In this study, the effects of different types of structural modifications are first analyzed. A qualitative correspondence is established between different types of structural modifications and the mainstream of the reanalysis methods. Secondly, the most suitable reanalysis method for different types of structural modifications is quantitatively analyzed from the aspects of selecting efficiency indicators and clarifying accuracy requirements. Finally, in conjunction with the Structural Topology and Shape Annealing (STSA) algorithm, a criterion for selecting reanalysis methods, which are applicable to the optimization process of plane trusses, is established. To verify the validity of the selection criterion, two types of numerical examples are conducted. The results show that the proposed criterion can effectively improve the efficiency of structural computations.

Truss layout design aims to find the optimal layout, considering node locations, connection topology between nodes, and cross-sectional areas of connecting bars. The design process of trusses can be represented as a reinforcement learning problem by formulating the optimization task into a Markov Decision Process (MDP). The optimization variables such as node positions need to be transformed into discrete actions in this MDP; however, the common method is to uniformly discretize the design domain by generating a set of candidate actions, which brings dimension explosion problems in spatial truss design. In this paper, a reinforcement learning algorithm is proposed to deal with continuous action spaces in truss layout design problems by using kernel regression. It is a nonparametric regression way to sample the continuous action space and generalize the information about action value between sampled actions and unexplored parts of the action space. As the number of searches increases, the algorithm can gradually increase the candidate action set by appending actions of high confidence value from the continuous action space. The value correlation between actions is mapped by the Gaussian function and Euclidean distance. In this sampling strategy, a modified Confidence Upper Bound formula is proposed to evaluate the heuristics of sampled actions, including both 2D and 3D cases. The proposed algorithm was tested in various layout design problems of planar and spatial trusses. The results indicate that the proposed algorithm has a good performance in finding the truss layout with minimum weight. This implies the validity and efficiency of the established algorithm.