The surrogate model-based optimization method provided an effective technical approach for the application of high-precision simulation models in optimal design due to its efficient search capability. To address the problem of time-consuming black-box constraint processing for optimization problems, a multi-constraint adaptive sampling method based on improved feasible rules was proposed, an elite archive-driven inexact search method and an ε-constraint-preserving pseudo-feasible domain construction method were established, and the algorithm's ability to explore the boundaries of the feasible domain was enhanced by dynamically scaling the feasible domain to accept high-quality nonfeasible samples during the iterative process, which improved the surrogate model-based optimization search ability. The algorithm's ability to explore the feasible domain boundaries was enhanced by dynamically scaling the feasible domain to accept high-quality nonfeasible samples during the iterative process. Simulation results of the Congress on Evolutionary Computation constraint optimization standard function indicated that the ε-constraint maintenance optimization method is effective in solving the multi-constraint surrogate model optimization problem compared with the existing methods. The results for the solid rocket motor rear wing pillar charge design show that the algorithm had the potential to be applied to complex engineering problems.