The title study is performed on the massively parallel processing (MPP) environment of Connection Machine (CM) computers using truss structural sizing design problems as example design problems. In this design optimization procedure, only the displacement solution is replaced by that based on neural net technology (under a given set of cross-sectional size parameters (e.g., areas) in the MPP finite element structural reanalysis). This structural reanalysis procedure, together with a vastly improved and parallelized version of the integral global optimization (IGO) stochastic algorithm, IIGO, forms the present MPP structural design methodology. In addition, a procedure to correct the final optimal design for constraint violation or too-conservatively satisfied constraint condition caused by inaccuracy of the NN (neural network) analysis model is also formulated. Evaluation of the numerical performance of the developed computational algorithm set, capability, and strategy is made, primarily on the Connection Machine CM-2 model computer by performing three neural-network-based truss structural reanalysis/minimum weight design problems.