The aim of this thesis is to look for the optimal solution of short-term hydrothermal generation scheduling problem (HGSP)or otherwise known as hydrothermal coordination (HTC) by Lagrangian Relaxation (LR) technique and Evolutionary Particle Swarm Optimization (EPSO). Lambda-iteration methodhas been used to relax/solve LR multipliers. The HGSP problem will be decomposed into thermal and hydro sub-problem where the thermal power demand will be solved by LR technique and later the data will be used to solve the demand for hydro power generation using EPSO together with minimizing the overall cost. Besides that several constraints such as restrictions of volume and discharges of water, spinning reserve and losses are also considered too.