Service quality is the key for takeaway platforms to maintain their advantages in the fierce market competition. In this study, we construct a mathematical model to solve the takeaway delivery problem by ant colony algorithm, so as to realize the takeaway delivery path planning based on ant colony algorithm. The grey neural network model is used to predict the order demand in the takeaway platform, and the fruit fly algorithm is used to fine-tune and optimize the parameters in the grey neural network model to avoid the model from falling into the local optimum and to improve the accuracy of the model in predicting the takeaway demand. Through simulation experiments, it is found that the planning algorithm in this paper can successfully realize the reasonable planning of takeaway delivery paths when the initial positions of merchants, users and delivery workers are known. The gray neural network optimized using the fruit fly algorithm is also able to accurately predict the takeout demand of platform users based on the order data provided by the takeout platform. Using the method of this paper for the improvement of the service quality of the takeaway platform can significantly improve the delivery efficiency of takeaway orders and develop personalized service strategies according to user demand, thus enhancing user satisfaction with the takeaway platform.