So you are using MinGW as your compiler and Visual Studio compiled binaries for Qt:
-IC:\Qt\5.5\msvc2013_64\include
Do you have a reasoning for that?
From what I see from your build log:
-IO:\developement\CPP\boost-1.30.1\boost-1.30.1\include
-IC:\MinGW\MinGW\include\boost
you should have the file:
O:\developement\CPP\boost-1.30.1\boost-1.30.1\include\boost\asio.hpp
or
C:\MinGW\MinGW\include\boost\boost\asio.hpp
Do you have either one of these files? If not, then you're not including the correct paths.
If your compiler includes boost why are you using a separate boost installation?
Also please don't ask boost (or any other library) related questions here. None of those are supported nor allowed unless it's a CodeBlocks related problem.
Btw current boost version is 1.58 or something, why do you use such old boost versions (1.30, 1.46)?