Search strategies for multiple roads by the graffiti

On the entrance of the program comes a graph that is assigned using a pair of heights, for example: 1 2 ; 1 3 ; 1 4 ; 2 3. The number of the initial and final top. With the help of a pair of heights formed triades, for example, a triade is a set of pairs 1 3 - 3 4.
Part of the program was the search for all the possible routes from the initial to the final top of the county. After we found all the possible paths, we had to make a lot of paths that would cover all the existing triades. The search for such masses was to be achieved through three different strategies: thirsty, genetic, and myrtle. In addition, each strategy had two priority settings: priority to the use of the shortest routes; priority to the use of the longest routes.