Portfolio optimization by GA is a problem that has recently received a lot of attention. However, most works in this area have so far ignored the effects of cost on Portfolio Optimization, and haven't directly addressed the problem of portfolio management (continuous optimization of a portfolio over time). In this work, we use the Euclidean Distance between the portfolio selection in two consecutive time periods as measure of cost, and the objective sharing method to balance the goals of maximizing returns and minimizing distance over time. We also improve the GA method by adding genetic material from previous runs into the new population (seeding). We experiment our method on historical monthly data from the NASDAQ and NIKKEI indexes, and obtain a better result than pure GA, defeating the index under non-bubble market conditions.