A swarm based nature-inspired optimization algorithm namely fruit fly optimization algorithm (FOA) has simple structure and ease of implementation. However, FOA has a low success rate and a slow convergence because FOA generates new positions around the best location using fixed search radius. Several improved FOAs have been proposed. But their exploration ability is questionable. To make the search process to transit from the exploration phase to the exploitation phase smoothly, this paper proposes a new FOA constructed from a cooperation of the multileader and the probabilistic random walk strategies (CPFOA). It has two population types working together. CPFOA's performance is evaluated by 18 well-known standard benchmark, and 30 CEC’2017 functions. The results showed that CPFOA outperforms both the original FOA and its variants in terms of convergence speed and performance accuracy. The results base on CEC’2017 show that CPFOA can achieve a very promising accuracy when compared with the well-known competitive algorithms. CPFOA is applied to optimize two applications; the MLPs classifying real datasets and extracting parameters of T-S fuzzy system for modelling Box and Jenkins gas furnace data set. CPFOA can find parameters having a very high quality compared with the best known competitive algorithms.