Salp swarm algorithm (SSA) is one of the recently developed meta-heuristic optimization algorithms. Since SSA outperforms other swarm-based algorithms, it has recently been employed in various applications, including feature selection, neural network training and renewable energy systems. In this paper, an improved salp swarm algorithm based on a Gaussian random walk is proposed, which enhances the algorithm’s performance particularly for multidimensional constrained global optimization problems. The integration of a Gaussian random walk into the algorithm balances between its exploration and exploitation capabilities. Furthermore, the proposed algorithm introduces a new re-dispersion strategy in the case of stagnation at local optimum points, which considerably enhances exploration. The performance of the proposed algorithm is evaluated using a set of twenty-three benchmark test functions and is compared to the performance of prevalent metaheuristic algorithms. Statistical analysis is performed using Wilcoxon signed-rank test, and the results reveal considerable improvement over the competing algorithms. Then, 21 real-world optimization problems are used to further evaluate the efficacy of the proposed algorithm. The winners of the CEC2020 Competition on Real-World Single Objective Constrained Optimization, SASS, sCMAgES, EnMODE, and COLSHADE algorithms, are used as four comparable algorithms in the real-world optimization problems. The convergence curves and simulations provide very competitive performance compared to the comparative algorithms. The proposed algorithm is used to address one of the most challenging real-world constrained problems in power system applications, namely, determining the optimal charging schedule for electric vehicles at charging stations. The results reveal that the proposed algorithm outperforms other existing algorithms in terms of increasing the charging revenues and achieving maximum power grid stability.