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Natural cellular materials, such as honeycombs, woods, foams, trabecular bones, plant parenchyma, and sponges, may benefit from the disorderliness within their internal microstructures to achieve damage tolerant behaviours. Inspired by this, we have created quasi-disordered truss metamaterials (QTMs) via introducing spatial coordinate perturbations or strut thickness variations to the perfect, periodic truss lattices. Numerical studies have suggested that the QTMs can exhibit either ductile, damage tolerant behaviours or sudden, catastrophic failure mode, depending on the distribution of the introduced disorderliness. A data-driven approach has been developed, combining deep-learning and global optimization algorithms, to tune the distribution of the disorderliness to achieve the damage tolerant QTM designs. A case study on the QTMs created from a periodic Face Centred Cubic (FCC) lattice has demonstrated that the optimised QTMs can achieve up to 100% increase in ductility at the expense of less than 5% stiffness and less than 10% tensile strength. Our results suggest a novel design pathway for architected materials to improve damage tolerance.