My preferred method for searching, assuming you are flexible:
1. Open Google Flights and search a random, but specific route with specific dates.
2. Add carrier filters for your preferred airlines.
3. Change the destination to a much broader one (e.g., "Asia").
4. Change dates from "Specific dates" to "Flexible dates."
This will transition GF to map view and show the best prices for all routes in the time-frame you've specified.
It's not perfect, but it gives a general sense of where you can go for what price, and it's pretty easy to discern routes that will earn a lot of miles.
If you have more specific criteria (e.g., same-day turn, can only fly certain days, etc), then Matrix is a better option.