In the present work, application of evolutionary algorithm and gradient-based optimisation techniques are extended towards obtaining minimum drag axisymmetric bodies in hypersonic flows. An attempt has been made to study the comparative performance of greedy and heuristic algorithm-based optimisation algorithm of interest with its application towards generating optimal shape configurations. We compare the performance of memetic meta-heuristic-based shuffled frog-leaping algorithm (SFLA), biological evolution-based genetic algorithm (GA), stochastic method-based simulated annealing (SA) and gradient-based steepest descent (SD) method. The suitability of each optimisation algorithm is analysed for a common test case of minimum drag axisymmetric body with the use of theoretical correlation as its flow solver. This is then followed by the implementation of a computationally expensive but accurate in-house Euler flow solver based on Immersed Boundary (IB) method, which results in a discrete solution space. This naturally results in greater computational cost per function evaluation. Results indicate that evolutionary algorithm-based optimisation technique requires much greater number of function evaluations as compared to gradient-based optimisation technique. Moreover, for a uni-modal problem considered in this work, the choice of gradient-based optimisation method proves to be quite robust and computationally efficient.