A New Topology Optimization Methodology Based on Constraint Maximum-Weight Connected Graph Theorem

To eliminate the checkerboard pattern in topology optimizations (TOs), a new TO methodology based on the constrained maximum-weight connected graph (CMWG) theorem and algorithm is proposed. The underlying principle to extend the CMWG to TO is to convert the topology pattern into a network, and to employ a dynamic programming method to search the optimal solution. Also, a kriging model based on the support vector machine for predicting the sensitivity is introduced to reduce the overwhelmingly heavy computational burden as required in a topology optimizer. According to the numerical results as reported, the proposed methodology is able to avoid the checkerboard pattern, and can improve significantly the final solutions with a significantly reduced computation cost.