League of Legends Builds via Meta-heuristic search. So most League of Legends Builds sites either scrape the statistics from Riot Games or just allow players to upload their own builds. LoLSolved on the other hand calculates the builds from scratch using maths.
Similar to Evolution chamber for Starcraft 2, which found the famous 7 roach rush build. Very few site allow you do this because it's really really difficult to do the maths for generating League of Legends Builds. So currently the vast majority of builds played on League of Legends are either made up by random players or alternatively are scrapped from the Riot API and are in fact just builds that were made up by random players that performed well. Obviously, the ideal state of the world is that the builds are all generated from the maths and are near perfect rather than the random mess that exists today.
There are far more possible League of Legends builds then people realize. Even selecting 6 completed items from the 94 possible completed items in League of Legends results in 586,236,072,240 possible builds, which is far more then people typically expect. This is without including the extra combinations from runes and the sub item order. The same way that Evolution Chamber works, LoLSolved employs the use of a Genetic Algorithm to explore these build combinations in an semi intelligent manner to make the calculation of near optimal builds plausible. Genetic algorithms will do most of the human like changes automatically for example removing items that are completely irrelevant to the champion. They also do not suffer from human biases and so can create novel builds that human theorycrafters would not consider because they go against conventional wisdom.