Total Unduplicated Reach and Frequency (TURF) is a common optimization procedure in the market research industry. It is used for optimizing a portfolio of items/flavors, or selecting the right mix of magazines to advertise within to reach the maximum number of potential customers.
One of the challenges with TURF is dealing with truly large spaces of potential portfolio combinations. For example, choosing the optimal 12 flavors out of 70 involves examining over 10 trillion possible 12-flavor combinations (if using an exhaustive algorithm which examines each possible one.) Such problems are hard to solve within reasonable time limits if using exhaustive search. Researchers often rely on heuristic search algorithms that can find nearly-optimal solutions in a fraction of the time required to exhaustively search for the globally optimal solution.
Until recently, our TURF routine had been limited to exhaustive search. Lately, we implemented a fast search procedure that involves stepwise TURF plus additional "swaps." Stepwise TURF searches for the optimzal portfolio in incremental steps, taking the best result from the previous step forward to the next step. To further improve upon the stepwise procedure, we take a few more seconds to examine hundreds of potential item swaps that could lead to better reach. We take the top several dozen portfolios found in the stepwise routine, and we try swapping non-included flavors for included flavors one at a time, looking for new portfolio definitions that increase the reach. It turns out that these last few seconds spent in swapping can improve the results quite dramatically.
Our TURF routine is available within our MaxDiff Analyzer software service, and can be used for MaxDiff or general data (such as Likert scales).