The basic salp swarm algorithm (SSA) may suffer from the drawbacks of slow convergence and low accuracy of high-dimensional solutions. To solve these limitations, we proposed an improved SSA algorithm (OOSSA) which integrates orthogonal refracted opposition-based learning strategy and self-adaptive inertia weight strategy into SSA. In orthogonal refracted learning strategy, the refracted opposition-based learning based on the optical lens imaging principle was employed to enhance the exploration scope of the inverse solution space, which greatly reduced the probability of the algorithm falling into the local optimum. The orthogonal experimental design was used to construct several partial opposite solutions that take the refracted-based inverse values in part of the dimension, so as to deeply mine and preserve the dominant dimensional information of the current individual and the refracted-based opposite individual. In addition, an adaptive inertia weight was introduced in the follower position update phase to effectively improve the follower search pattern and enhance the local exploitation ability of the algorithm. The CEC2017 benchmark functions were employed for simulation experiments. Also, Wilcoxon’s rank-sum test and Friedman test were performed to verify the superiority of the proposed method. Experimental results show that the proposed OOSSA outperformed the basic SSA, eight improved SSA variants, and nine cutting-edge swarm-based intelligence algorithms. Moreover, the algorithm was applied to an engineering design problem, and results show that the algorithm had better performance than other algorithms in engineering optimization. Finally, an OOSSA-based robot path planning approach was developed for solving the path planning problem in autonomous mobile robots. The proposed algorithm was simulated in three environment settings and compared with other algorithms including particle swarm optimization (PSO), artificial bee colony (ABC), grey wolf optimizer (GWO), firefly algorithm (FA), and SSA. Simulation results show that the proposed algorithm could plan the optimal collision-free paths compared with its competitors. The systematic experiments indicate that the OOSSA algorithm can be an effective tool for problem optimization.