To solve the problems of local optimization and slow convergence in the process of optimization and iteration, the paper proposes an improved optimization algorithm for the equilibrium optimizer, introduces the Tent chaotic map to initialize the population to improve the convergence speed in the early stage of the iteration, and uses the lens imaging learning strategy to avoid falling into the local optimum in the later stage of the iteration. Twelve general standard test functions are selected for simulation experiments to compare with multiple intelligent group optimization algorithms. The experimental results verify the superiority of the improved algorithm in optimization performance. Finally, the improved algorithm is applied to the path planning task of mobile robots. Compared with the equilibrium optimizer algorithm, the improved algorithm not only has high search efficiency, but also can search shorter secure paths.