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A multi-objective heuristic particle swarm optimiser (MOHPSO) based on Pareto multi-objective theory is proposed to solve multi-objective optimality problems. The optimality objectives are the roof displacement and structure weight. Two types of structure are analysed in this paper, a truss structure and a framework structure. Performance-based seismic analysis, such as classical and modal pushover analysis, is carried out for the structures. Four optimality algorithms, namely, NSGA-II, MOPSO, MGSO, and MOHPSO, were used for structural optimisation to compare the effectiveness of the algorithms. The calculation results indicate that MOHPSO outperformed the other algorithms in terms of solution stability, universality, and consistency of the distribution of the Pareto front and the ability to consider constraints. The population can converge to the true Pareto front in the latter generations, which indicates that MOHPSO is effective for engineering multi-objective optimality problems.