Identification of the thermal conductivity of a functionally graded material (FGM) is considered as an inverse heat conduction problem. ‎In this investigation, the measurements of the temperatures on the portion of the 2D body where heat flux is specified as the boundary ‎condition and/or the heat flux on the portion of the boundary where temperature is specified as the boundary condition are used as ‎additional data needed to identify the thermal conductivity of the FGM domain in an inverse procedure. The thermal conductivity is ‎approximated as a quadratic function of only one direction, and therefore three constant coefficients should be estimated simultaneously.‎‏ ‏The solution of the direct heat conduction problem for‏ ‏FGM domain is obtained using the boundary elements method (BEM).‎‏ ‏The ‎imperialist competitive algorithm (ICA) which is an evolutionary and meta-heuristic global optimization is used to identify the constants ‎in the thermal conductivity function of the quadratic FGM. An inverse computer code is developed which employs the boundary ‎temperature and heat flux measurements data obtained by solving the direct boundary elements code with known thermal conductivity. ‎To show the feasibility and effectiveness of the developed inverse code, a number of example problems are solved and results are ‎verified.‎