Computational tools such as finite element analysis and simulation are widely used in engineering, but they are mostly used for design analysis and validation. If these tools can be integrated for design optimization, it will undoubtedly enhance a manufacturer’s competitiveness. Such integration, however, faces three main challenges: (1) high computational expense of simulation, (2) the simulation process being a black-box function, and (3) design problems being high dimensional. In the past two decades, metamodeling has been intensively developed to deal with expensive black-box functions, and has achieved success for low dimensional design problems. But when high dimensionality is also present in design, which is often found in practice, there lacks of a practical method to deal with the so-called high dimensional, expensive, and black-box (HEB) problems. This paper proposes the first metamodel of its kind to tackle the HEB problem. This paper integrates the radial basis function with high dimensional model representation into a new model, RBF-HDMR. The developed RBF-HDMR model offers an explicit function expression, and can reveal (1) the contribution of each design variable, (2) inherent linearity/nonlinearity with respect to input variables, and (3) correlation relationships among input variables. An accompanying algorithm to construct the RBF-HDMR has also been developed. The model and the algorithm fundamentally change the exponentially growing computation cost to be polynomial. Testing and comparison confirm the efficiency and capability of RBF-HDMR for HEB problems.

Additive manufacturing (AM) continues to rise in popularity due to its various advantages over traditional manufacturing processes. AM interests industry, but achieving repeatable production quality remains problematic for many AM technologies. Thus, modeling different process variables in AM using machine learning can be highly beneficial in creating useful knowledge of the process. Such developed artificial neural network (ANN) models would aid designers and manufacturers to make informed decisions about their products and processes. However, it is challenging to define an appropriate ANN topology that captures the AM system behavior. Toward that goal, an approach combining dimensional analysis conceptual modeling (DACM) and classical ANNs is proposed to create a new type of knowledge-based ANN (KB-ANN). This approach integrates existing literature and expert knowledge of the AM process to define a topology for the KB-ANN model. The proposed KB-ANN is a hybrid learning network that encompasses topological zones derived from knowledge of the process and other zones where missing knowledge is modeled using classical ANNs. The usefulness of the method is demonstrated using a case study to model wall thickness, part height, and total part mass in a fused deposition modeling (FDM) process. The KB-ANN-based model for FDM has the same performance with better generalization capabilities using fewer weights trained, when compared to a classical ANN.

Mode pursuing sampling (MPS) was developed as a global optimization algorithm for design optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for design problems of low dimensionality, i.e., the number of design variables is less than 10. This work integrates the concept of trust regions into the MPS framework to create a new algorithm, trust region based mode pursuing sampling (TRMPS2), with the aim of dramatically improving performance and efficiency for high dimensional problems. TRMPS2 is benchmarked against genetic algorithm (GA), dividing rectangles (DIRECT), efficient global optimization (EGO), and MPS using a suite of standard test problems and an engineering design problem. The results show that TRMPS2 performs better on average than GA, DIRECT, EGO, and MPS for high dimensional, expensive, and black box (HEB) problems.

Particle swarm optimization (PSO) is a well-known optimization algorithm that shows good performance in solving different optimization problems. However, PSO usually suffers from slow convergence. In this article, a reinforcement learning strategy is developed to enhance PSO in convergence by replacing the uniformly distributed random number in the updating function with a random number generated from a selected normal distribution. In the proposed method, the mean and standard deviation of the normal distribution are estimated from the current state of each individual through a policy net. The historic behaviour of the swarm group is used to update the policy net and guide the selection of parameters of the normal distribution. The proposed method is integrated into the original PSO and a state-of-the-art PSO, called the self-adaptive dynamic multi-swarm PSO (sDMS-PSO), and tested with numerical functions and engineering problems. The test results show that the convergence rate of PSO methods can be improved with the proposed reinforcement learning strategy.