The generalized replica exchange method (gREM) is applied to simulate a solid-liquid phase change in an adapted Dzugutov model system. The idea of gREM is to incorporate the merit of sampling from a generalized ensemble into the replica exchange paradigm. The generalized ensemble weights are determined from effective temperatures tailored for this system, through an inverse mapping strategy. The ordered and disordered phases are smoothly joined together through a succession of unimodal energy distributions, providing a continuous transformation from an isotropic liquid into an amorphous solid phase under the given condition. The phase change temperature is determined by evaluation of various thermodynamic and structural order parameters The increasing tendency for icosahedral local order under cooling is quantified using bond order parameters. The ergodic measure is used to demonstrate the advantage of gREM over the traditional temperature-based REM in sampling the phase change region.