A new optimization technique, called the Genetic Annealing Algorithm (GAA), is proposed in this paper to solve the task matching and scheduling problem in a heterogeneous computing system (HCS). Simple in design and easy to implement, the GAA employs only a stir operation, a novel idea based on the annealing concept, to locate optimal solutions for the problem. Extensive simulation runs have been conducted to evaluate and compare the performance of the proposed GAA with that of other optimization techniques, such as the Genetic Algorithm, Simulated Annealing, and Guided Evolutionary Simulated Annealing approaches. The GAA is shown to consistently perform better than the other techniques in terms of speedup, running time, cost, and complexity.