Laurent_R has the key I think. When brute force takes a few seconds, or some tolerable time, thinking over the method may not be worth it, but when brute force makes you wait too long, it needs to be at least helped along, if not abandoned for a better method. In this case, not knowing how you constructed your player value function, can you think of a way to prune out the players that you can't conceive of being in a winning team? If not obvious up front, you could get your code to do something like:

• calculate the best possible team score, and discard players that can't deliver at least a substantial fraction of that total
• tag players that are consistently below their team and/or position average (or higher percentile), and favour them less in subsequent selections
• start by building sub teams and sort them by costs and values, then you can try assembling them in a second stage
• if your value function incorporates combinations of players (i.e. some players with some characteristics play better/worse when on a team with other players with other certain characteristics) genetics may be your best option to arrive at a good solution, if not provably optimal, in a satisfactory time

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