A variety of technical analyses techniques and fundamental indicators have been used to form trading strategies and modeled to determine the appropriate trading decisions for when to sell or buy stocks at unstable challenging financial market. A group trading strategy optimization portfolio algorithm was presented in the literature to find out an optimal group trading strategy portfolio to make trading decisions, and it belongs to the single objective optimization problem. However, in the real situation, traders have confronted to make decision by considering multiobjective goals. Hence, this thesis proposes a MOGA-based algorithm to find a set of Pareto solutions for investors to make more useful trading plans, and each solution is a group trading strategy portfolio. To optimize a GTSP, the candidate trading strategies are first produced according to the chosen technical indices. Then, a subset of the candidate trading strategies is selected using the determined ranking functions. Based on the subset of the trading strategies, the population is initialized as determined chromosome, and non-dominated set is initialized as empty. In the encoding scheme, the grouping, weighting and trading strategy parts are utilized to represent a possible GTSP. The two objective functions are used to evaluate the fitness values of chromosomes to discover non-dominated solutions. The first objective function is used to evaluate the return and risk of a GTSP in the chromosome. The second objective function is utilized to reveals the grouping and weight balances of the trading strategy groups. The genetic operators, including crossover, mutation, and inversion are executed on the population to generate new offspring. In the experiment, the proposed algorithm is evaluated on three datasets with different trends, namely uptrend, sideway trend and downtrend, to show the effectiveness of the proposed approach.