Political scientists don't make decisions, so political science can't "solve" anything. That's up to politicians.
But political science can tell us what the likely consequences of political decisions will be. Some examples:
Economic interdependence tends to be correlated with peace, so if you pursue a project of global economic interdependence (through a liberal trade regime, for example), the consequence will be a more peaceful int'l system.
Int'l institutions tend to reduce uncertainty about the intentions of other states, so more institutions means more stability and less likelihood of war.
Most of the value of political science comes from debunking common wisdom or myths about the consequences of different policies.