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The problem of soft landing on Moon is formulated and solved using different solution schemes. The solution scheme consists of one of the two approaches i) direct ii) indirect and one of different optimization techniques (viz. gradient based and gradient free techniques). Gradient free (Particle Swarm optimization and Differential Evolution) and gradient based optimization techniques are explored to solve the problem for direct and indirect approaches. In indirect approach, the optimal control problem is transformed into a two point boundary value problem (TPBVP) using Pontryagin’s minimum principle and the appropriate initial costates are selected using different optimization techniques. The performances of these optimization techniques are evaluated for the indirect approach for soft landing trajectory design problem. In direct approach, it is transformed into a non linear programming (NLP) problem and is solved by using an optimizer. The performance of the direct schemes is compared with indirect schemes. A scheme based on the indirect approach and differential evolution technique is evaluated superior to other options for the soft landing trajectory problem. Also the trajectory design is carried out with different constant thrust levels and their sensitivities are analyzed.