Optimization is the art of finding the best answer among existing conditions and is used to design and maintain many engineering, economic, industrial and even social systems in order to minimize costs or maximize profits. In order to solve such problems, optimization algorithms are used. In recent decades, algorithms inspired by nature have shown significant success as smart optimization methods alongside classical methods. In this research study, a new multi-objective optimization method is applied to obtain the Pareto frontiers of some non-commensurable objective functions in the design of linear state feedback controllers for a ball-beam system. In the process of solving the problem, the control gains are included as the design variable and the normalized sum of the sitting time and overshoot as the objective function. The obtained results and analysis show that the multi-objective optimization algorithm presented in this article works very well in terms of convergence speed, global optimality, solution accuracy and reliability.