The unique structure and properties of lattice-based cryptography make it a prominent candidate for post-quantum secure cryptographic schemes. The security of current lattice-based cryptographic schemes heavily depends on lattice problems, such as the Shortest Vector Problem (SVP) and the Closest Vector Problem (CVP). Analysing the complexity of these problems contributes significantly to the evaluation of the security of lattice-based cryptographic schemes. The Lenstra-Lenstra-Lovász (LLL) algorithm is a classical method for approximating the SVP. It takes a set of linearly independent lattice bases, produces a reduced vector set by reduction, and the first vector in the output is the approximately shortest vector determined by the LLL algorithm. Since the LLL algorithm does not emphasise on the input order of the lattice bases, in this paper, we investigate the effect of lattice order on the results of the LLL algorithm and propose that there may exist an optimal order for the LLL algorithm for a given set of lattice bases. In addition, we present a Particle Swarm Optimization (PSO)-based approach to discover this approximately optimal order. Experimental results show that, given sufficient computation time, the discovered approximately optimal order can result in the shorter shortest vectors after applying the LLL algorithm compared to un-sorted lattice bases, which improves the solustion of SVP.