This paper presents energy and stability functions, integrating the stability parameters of the Zero Moment Point (ZMP) classed bipeds where stability parameters are the positions of Center of Mass (CoM) and ZMP respectively. The Energy function is derived using the concept of Orbital Energy and is optimized using Real Coded Genetic Algorithm to produce an optimum set of walk parameters, which consumes minimum energy, during walking. A Stability function is also proposed, which is obtained by modifying the pre-existing ZMP trajectory. The ZMP trajectory is modified in such a manner, that it remains at the center of the convex hull, not only during the single support phase, but also during the transition of the robot from the Double Support Phase (DSP) to Single Support Phase (SSP) and vice-versa. The analytical results show that, when the energy function is optimized, the stability of the robot decreases. Similarly, if the stability function is optimized, the energy consumed by the robot increases. Thus, there is a clear trade-off between the stability and energy functions