Abstract: Objectives To overcome the monopoly of foreign patent technologies and to ensure that the pump-tower structure of LNG（Liquefied Natural Gas）carrier cargo tanks simultaneously satisfies structural strength, fatigue life, and lightweight design requirements under combined loading, this study performs optimization of the pump tower’s primary geometric dimensions and sectional size variables. Methods Surrogate modeling is integrated with heuristic optimization. A mathematical model of the pump-tower optimization problem is first formulated, followed by parametric modeling, multi-physics loading, and initial sample selection via optimal Latin hypercube sampling. An XGBoost-based surrogate is then constructed, and an inexact adaptive sampling strategy is proposed to enhance model accuracy. Finally, the surrogate is coupled with four heuristic algorithms—NSGA-II, MOPSO, MOAHA, and NSWOA—to obtain the Pareto front. The TOPSIS method is used to compare Pareto solution sets and identify a relatively optimal design, which is validated through direct finite-element analyses. Results The XGBoost-NSWOA scheme yields the relatively optimal design; relative to the baseline, the structural weight is reduced by 19.63% and the fatigue life is increased by a factor of 1.503. Conclusions A complete and effective multi-objective optimization workflow is established for the mixed-variable optimization of the LNG cargo-tank pump-tower structure based on surrogate models, improving design efficiency and providing a reference for optimization under combined loads.