The Portfolio Optimization problem is an example of a resource allocation problem with money as the resource to be allocated to assets. We first have to select the assets from a pool of them available in the market and then assign proper weights to them to maximize the return and minimize the risk associated with the Portfolio. In our work, we have introduced a new "greedy coordinate ascent mutation operator" and we have also included the trading volumes concept. We performed simulations with the past data of NASDAQ100 and DowJones30, concentrating mainly on the 2008 recession period. We also compared our results with the indices and the simple Genetic Algorithms approach