No, the 2050 Calculator is a user driven model. The user specifies energy supply and demand across the economy by selecting effort levels for around 40 sectors.
In this respect, the Calculator is fundamentally different from cost optimisation models such as MARKAL. Models such as MARKAL examine the costs of different technologies and work out the least cost pathway to achieving an emissions reduction target.
It is possible to identify low cost pathways using the Calculator, but the user has to do this manually through an iterative process. An example of a very low cost pathway is the Analogous to MARKAL pathway (this is a representation of a least cost pathway from MARKAL).
However, if you wish to use the 2050 calculator as an optimisation model, you can. You need to use the code from here: https://github.com/decc/decc_2050_optimizer