The tunicate swarm algorithm (TSA) is a recently introduced bio-inspired optimization algorithm motivated by the foraging and swarming behaviour of bioluminescent tunicates. It has gained a lot of attention from the heuristic community because of its superior performance in solving various optimization problems. However, it is also easy to get stuck in the local optima, resulting in premature convergence when dealing with highly challenging optimization problems. To alleviate these shortcomings, this study presents an improved TSA termed random opposition based TSA (ROBTSA), which integrates a novel random opposition based learning (ROBL) technique into the conventional TSA. This proposed approach is implemented with jumping probability, which facilitates the algorithm to jump out of local optimal traps by enhancing the diversity of the tunicates. To test the efficacy of the proposed algorithm, experimentations are conducted on a set of thirteen standard test functions, comprising unimodal and multimodal functions. The proposed ROBTSA is tested against several well-known and advanced algorithms, including PSO, GWO, WOA, SCA, MVO, and STOA. In addition, it has been compared with the original TSA and its variant OBTSA. Further, it has been applied to solve two real-life engineering design problems: pressure vessel and tension/compression spring problems. The experimental outcomes exhibit that ROBTSA outperforms the other competing algorithms in terms of convergence rate, accuracy, and stability. Moreover, the performance of ROBTSA has been proven by statistical measures such as the Friedman test and Wilcoxon rank-sum test, demonstrating its potential in the realms of global optimization and real-life engineering design problems.