The approximate computing paradigm provides methods to optimize algorithms while considering both application quality of service and computational complexity. Approximate computing can be applied at different levels of abstraction, from algorithm level to application level. Approximate computing at algorithm level reduces the computational complexity by approximating or skipping computational blocks. A number of applications in the signal and image processing domain integrate algorithms based on discrete optimization techniques. These techniques minimize a cost function by exploring an application parameter search space. In this paper, a new methodology is proposed that exploits the computation-skipping approximate computing concept. The methodology, named Smart Search Space Reduction (Sssr), explores at design time the Pareto relationship between computational complexity and application quality. At run time, an approximation manager can then early select a good candidate configuration. Sssr reduces the run time search space and, in turn, reduces computational complexity. An efficient Sssr technique adjusts at design time the configuration selectivity while selecting at run time the most suitable functions to skip. The real time High Efficiency Video Coding (Hevc) encoder in All Intra (AI) profile is used as a case study to illustrate the benefits of Sssr. In this application, two discrete optimizations are performed. They explore different coding parameters and select the values leading to the minimal cost in terms of a tradeoff between bitrate, quality and computational energy by acting on both the Hevc coding-tree partitioning and the intra-modes. Combining two Sssrs iterations on this use case, the energy consumption is reduced by up to 77%. Moreover, the combination of the two Sssrs iterations in comparison to using only one reduces the BD-BR bitrate/quality metric by 4% for the same energy consumption.