Salp swarm algorithm (SSA) is a newly developed meta-heuristic algorithm, which is mainly developed based on the swarming behavior of salps sailing and foraging in the ocean. An improved salp swarm-based optimizer is proposed in this paper to overcome the potential shortcomings of original SSA, including being easily trapped in local or deceptive optima and its slow convergence rates in dealing with some high-dimensional and multimodal landscapes. The designed variant is called CMSSA that combines two strategies simultaneously. First, a chaotic exploitative mechanism with ''shrinking'' mode is introduced into the basic SSA to improve the exploitative tendencies of the algorithm. Then, a combined mutation scheme is adapted to make full use of the strong intensification capabilities of Gaussian mutation and the strong exploratory leanings of Cauchy mutation. In addition, the embedded strategies can achieve a more stable equilibrium between the core searching patterns of the SSA, which are diversification and intensification. We thoroughly studied the optimization advantages of the improved CMSSA using several representative benchmark cases, including unimodal, multimodal, and fixed-dimension multimodal functions, and three well-regarded engineering cases. The obtained experimental results, statistical tests, and comparative simulations indicate that the exploratory and exploitative proclivities of the SSA and its convergence patterns are vividly improved. The results indicate that the proposed CMSSA is a promising algorithm and shows superior efficacy compared with other algorithms.