Fuzzy c-means (FCM) is one of the most frequently used methods for clustering. However, with the increasing amount of data, FCM suffers from slow convergence and a large amount of calculation because all samples are involved in updating the solutions per iteration without considering the current clustering results. In this research, a new membership scaling FCM (MSFCM) is proposed, based on the observation that the samples, whose nearest cluster center is v, aid the convergence of v, whereas the remaining samples prevent the convergence of v. In the new algorithm, many samples whose nearest cluster centers do not change in the next iteration are chosen by using the triangle inequality. A new scheme for scaling the membership degrees of the chosen samples is suggested to boost the effect of the in-cluster samples and weaken the effect of the out-of-cluster samples in the clustering process. The new scheme not only accelerates the convergence of the algorithm but also maintains the high clustering quality. Many experimental results on synthetic and real-world data sets have verified the effectiveness of the proposed algorithm in improving the speed of the convergence of the fuzzy clustering. In particular, compared with FCM, MSFCM saves at least two thirds of total rounds of iterations without significantly increasing the cost per iteration.

For the dynamic takeout delivery vehicle routing problem, which faces fluctuating order demand and time-varying speeds, this study presents a novel approach. We analyze the time distribution of takeout orders and apply a Receding Horizon Control (RHC) strategy to convert the dynamic challenge into a static one. The driving speed of delivery vehicles on different roads at different times is determined based on the subdivision criteria of the urban road network and a traffic congestion measurement method. We propose a dynamic takeout delivery vehicle routing optimization model and a time-varying subdivision road network is established to minimize the total delivery cost. We validated the model through simulation examples. The optimization results show that the total distribution cost is reduced after considering the time-varying subdivision road network, with the penalty cost decreasing by 39%. It is evident that considering the subdivision of the road network can enhance order delivery efficiency and optimize the overall dining experience. The sensitivity analysis of various parameters reveals that the delivery platform must appropriately determine the time domain and allocate the number of delivery personnel based on order scale to avoid escalating delivery costs. These findings provide theoretical guidance for vehicle routing planning in the context of delivery platforms.