There are a lot of ways to reduce weight without compromising strength, but as others are saying it really comes down to what solutions you are able to incorporate with your current conditions and structure restrictions.
Here are a couple of examples:
1. If you are restricted to a certain depth, for instance to ensure a specific clear height below the beam, then you can't go the route of increasing depth and reducing weight. A common option here would be to try and resist the top chord from buckling, and reduce your effecive length. If you cannot effectively brace the top flange, than the solution will become more complicated.
2. If you have multi-span conditions, adding a few double or single cantilevered beams with drop-in beams will lower your positive bending, and allow you to reduce your shape. But by doing this you have to be careful on how you are handling the negative bending.
3. If saving as much weight as possible is the focus, relaxing the deflection requirements can help you get there (you can do this for certain types of buildings, usually warehouses or low occupancy structures where deflection is of little concern).
In short, it really depends on the situation; there is no clear cut catch-all answer since there are several different failure modes of beams. With experience you'll get comfortable on a sort of "order" that you could start considering the solutions, and start with the easiest to implement and work your way down.
