Splitted Power supply oscillating
@brhans Thank you for your valuable hint. I separate the input paths of the LM675. When there is no load at the output, U114 acts exactly as expected, giving me a 15V. However, whenever I connect the output with the load, it starts to oscillate. 

Then I notice that both input signals are oscillating too. So I tried adding a 1uF cap to each of the input signal and BINGO! the output becomes really stable. So the schematic looks like this now. 


I don't have enough knowledge to explain this. The noise may come from the -15V connection to all the current source ICs. But they are all turned off at time of testing.