Adaptive Cultural Algorithm-Based Cuckoo Search for Time-Dependent Vehicle Routing Problem with Stochastic Customers Using Adaptive Fractional Kalman Speed Prediction

Abstract

For the Time-Dependent Vehicle Routing Problem with Stochastic Customers (TDVRPSC), an adaptive Cultural Algorithm-Based Cuckoo Search (CACS) has been proposed in this paper. The convergence of the new algorithm is proved. An adaptive fractional Kalman filter (AFKF) for traffic speed prediction is proposed. An adaptive mechanism for choosing the covariance of state noise is designed. Its mathematical process is proved. Several benchmark instances with different scales are tested, and new solutions are discovered, which are better than the published solutions. The effects of the parameters on the convergence and the results are studied. According to cargo weight of customers to be delivered, the customers can be divided into large, small, and retail customers. The algorithm is tested with fixed demand probability and also different customer types with stochastic demand. The traffic speeds in different business districts in Xiamen at different times are predicted by AFKF. The results show that AFKF has smaller prediction error and better prediction accuracy than fractional Kalman filter and Kalman filter. The effect of different fractional orders on prediction error is compared. The performance of the new algorithm is compared with that of the cultural algorithm and the Cuckoo Search. The result shows that the new algorithm can efficiently and effectively solve DTVRPSC and improve the accuracy of vehicle routing planning of time-varying actual urban traffic road.