The increasing dependency on network connectivity necessitates superior network performance, characterized by continuous availability and high reliability. Multiprotocol Label Switching (MPLS) networks have emerged as a robust solution to the limitations of traditional IP networks. However, determining optimal Label Switched Paths (LSPs) across multiple domains becomes a complex optimisation problem when considering multiple objectives. This paper addresses this challenge by transforming the path computation into an optimisation task. The Bat Algorithm, a popular meta-heuristic approach, is frequently employed for solving such optimisation problems. Despite its effectiveness, the Bat Algorithm is prone to premature convergence and the local optima problem, leading to sub-optimal solutions. This study explores the influence of the algorithm's loudness parameter and introduces a novel Adjustable Bat Algorithm (ABAT) that dynamically optimizes this parameter. The ABAT is integrated with a Pareto-based approach to enhance the discovery of non-dominant solutions. The proposed method effectively computes optimal paths while identifying the Pareto front of solutions, providing a balanced trade-off among competing objectives. The performance of the proposed algorithm was evaluated on networks of varying scales and compared against the standard Bat Algorithm and other meta-heuristic methods. The evaluation focused on convergence rate and computational complexity, demonstrating that the proposed Adjustable Bat Algorithm outperforms existing methods in both metrics, offering a more robust and efficient solution for multi-objective path optimisation in MPLS networks. Experimental results indicate that the proposed Adjustable Bat Algorithm (ABAT) outperformed the regular Bat Algorithm in terms of convergence rate by up to 35% and reduced load balancing expenses and routing latency by 15% to 20% at various MPLS network scales.