Optimal power flow (OPF) is a large dimension nonlinear, nonconvex and highly constrained optimization problem that has been used widely for power system planning and operation. The solution of the OPF problem provides the optimal settings of generator active power outputs and voltages, shun capacitors/reactors, transformer tap-settings and other control variables to minimize the fuel cost while the load bus voltages, generator reactive power outputs, network power flows and all other state variables in their operational and secure limits. Conventional gradient based optimization techniques, e.g. linear programming, nonlinear programming, or interior point method have been applied to solve the OPF problems. However, the drawback of such methods usually converges to sub-optimal solution when nonconvex characteristics of fuel cost function are considered. Heuristic algorithms, e.g. genetic algorithm (GA), evolutionary programming (EP), and differential evolution (DE), have the ability to avoid the entrapment in local optima. This dissertation proposes an enhanced version of differential evolution (DE) called self-adaptive differential evolution with augmented lagrange multiplier method (SADE_ALM) for solving the OPF problems with different nonconvex and discrete fuel cost characteristics. In addition, the parallel version of the SADE_ALM is also applied for this implementation to increase the search capability of the SADE_ALM. Numerical results show that the proposed algorithms are successfully and effectively implemented to find the best total generation fuel cost without violating any constraints.