Because the manipulability index based on conventional Jacobian matrix of Gough-Stewart platform (GSP) is with no physical meaning and variant with the change of units, a new invariant manipulability index of GSP is established based on a dimensionless Jacobian matrix. A multimodal evolutionary algorithm, AEGA, is proposed to search the optimal solutions for the optimal design of GSP with only one objective function, and then many solutions are found as the candidates for the designer. To solve the problem with two or more objective functions needed to optimize simultaneously, one of the multi-objective evolutionary algorithms, Elitist Non-Dominated Sorting Genetic Algorithm version II (NSGA-II), is applied to the optimal design process of GSP, then many sets of trade-off solutions, namely, the Pareto optimal set parameters, are found. To illustrate the proposed methodology, a practical GSP as a motion simulator is optimized. The results validate the usefulness to solve the mentioned problems by using the applied optimal algorithms which could meet more engineering demands in practice than using the conventional optimal design method in single objective function.