For searching there's basically three things you need to do. Scan left and right, scan up and down (to maximum ranges sometimes, especially if you think the bandit is close) and change PRF (pulse repetition frequency). The latter is your sensitivity to bandits flying towards you (high PRF) or away from you (medium PRF). ILV PRF is interleaved where it switches between high and low.
TWS does not have benefits like the F-15C does where you can launch a missile without giving the target the launch warning, but TWS is certainly handy to get aspect information of multiple bandits at the same time, without the need to lock each one of them up.
Also don't forget to do occasional scans with EOS.
If you detect him early enough, use the range advantage of your R-27ER's. Launch from high, then descend and crank to minimize closure and increase ground clutter for the F-15. Try to keep him at a distance. There is no fool proof way of winning this battle, but there are many foolish ways of losing it.
Besides that, use teamwork! Check out the 51st PVO Regiment. We fly the Su-27 almost solely and use superior teamwork to win our battles.