In deregulated electricity markets, individual generation companies (GENCOs) carry out independent unit commitment based on predicted energy and revenue prices. The GENCOs unit commitment strategies are developed with the aim of maximizing profitbased on the cost characteristics of their generators and revenues from predicted prices of energy and reserve subject to all prevailing constraints in what is known as Profit Based Unit Commitment (PBUC). A tool for carrying out PBUC is an important need for the GENCOs. This paper demonstrates the development of a solution methodology for the PBUC optimization problem in deregulated electricity markets. A hybrid of the Lagrangian Relaxation (LR) and Particle Swarm Optimization (PSO) algorithms is used to determine an optimal UC schedule in a day-ahead market using the expected energy and reserve prices taking advantage of the strengths of both Algorithms. The PSO algorithm is used to update the Lagrange multipliers giving a better quality solution. An analysis of the PSO algorithm parameters is carried out to determine the parameters that give the best solution. The algorithm is implemented in MATLAB software and tested for a GENCO with 54 thermal units adapted from the standard IEEE 118-bus test system. .