In this thesis, the combinatorial optimization algorithm known as simulated annealing (SA) is applied to the solution of the next-state map design problem of data compression systems based on finite-state machine decoders. These data compression systems which include finite-state vector ciuantization (FSVQ), trellis waveform coding (TWC), predictive trellis waveform coding (PTWC), and trellis coded quantization (TCQ) are studied in depth. Incorporating generalized Lloyd algorithm for the optimization of output map to SA, a finite-state machine decoder design algorithm for the joint optimization of output map and next-state map is constructed. Simulation results on several discrete-time sources for FSVQ, TWC and PTWC show that decoders with higher performance are obtained by the SA-I-CLA algorithm, when compared to other related work in the literature. In TCQ, simulation results are obtained for sources with memory and new observations are made.