With the continuous development of high technology and the continuous progress of intelligent industry, mobile robots are gradually widely used in various fields. In the field of mobile robot research, path planning is crucial. However, the current ant colony optimization algorithm applied to mobile robot path planning still has some limitations, such as early blind search, slower convergence speed, and lower path smoothness. To overcome these problems, this paper proposes an ant colony optimization algorithm based on farthest point optimization and multi-objective strategy. The algorithm introduces new heuristic information such as the normal distribution model, triangle inequality principle, smoothness function, safety value function, etc. It adopts multi-objective comprehensive evaluation indexes to judge the quality of paths. For the high-quality and poor-quality paths, the algorithm takes additional pheromone increments and decrements in pheromone concentration to speed up the algorithm's convergence. Besides, the farthest point optimization strategy is used to improve the quality of the paths further. Finally, to verify the algorithm's effectiveness, the algorithm is compared with 20 existing methods for solving the robot path planning problem, and the experimental results show that the algorithm exhibits better results in terms of convergence, optimal path length, and smoothness. Specifically, the algorithm can produce the shortest path in four different environments while realizing the least number of turns with faster convergence, further proving the effectiveness of the improved algorithm in this paper.