Routing in Mobile Ad-hoc NETwork (MANET) is a contemporary graph problem that is solved using various shortest path search techniques. The routing algorithms employed in modern routers use deterministic algorithms that extract an exact non-dominated set of solutions from the search space. The search efficiency of these algorithms is found to have an exponential time complexity in the worst case. Moreover this problem is a multi-objective optimization problem in nature for MANET and it is required to consider changing topology layout. This study attempts to employ a formulation incorporating objectives viz., delay, hop-distance, load, cost and reliability that has significant impact on network performance. Simulation with different random topologies has been carried out to illustrate the implementation of an exhaustive search algorithm and it is observed that the algorithm could handle small-scale networks limited to 15 nodes. A random search meta-heuristic that adopts the nature of firefly swarm has been proposed for larger networks to yield an approximated non-dominated path set. Firefly Algorithm is found to perform better than the exact algorithm in terms of scalability and computational time.