Trying to implement survival of the fittest is like trying to implement a sunrise. It just happens, natural selection is not something that can be or should be implemented. Survival of the fittest is simply a description of how species came to survive and/or thrive.
"Natural selection will modify the structure of the young in relation to the parent, and of the parent in relation to the young. In social animals it will adapt the structure of each individual for the benefit of the whole community, if the community profits by the selected change." ― Charles Darwin
Survival of the fittest does not and was not intended by Darwin to refer to the survival of the fittest individual. Survival of the fittest refers to the survival of the fittest communities of individuals within their environment. When discussing survival, it is impossible to separate a species from it's environment, for it is necessary to describe why some advantage is advantageous -- for instance, it is advantageous for fish to have gills... because they need to breath water. The survival of an individual is due to the survival of the group. When an individual thrives at the expense of the group, the individual is likely hurting their species as a whole. There is always a small percentage of humans known to do this (hurt the species as a whole in order to enrich the individual [himself or herself]).
“Besides love and sympathy, animals exhibit other qualities connected with the social instincts which in us would be called moral.” ― Charles Darwin
Like the other animals, human beings have morals. Morals are social instincts to benefit the community above the individual. Most human beings exhibit moral behavior, just like other species.