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.
Highlights
With the rapid development of the logistics industry, Vehicle Routing Problem (VRP) gets more and more attention. e traditional VRP uses static road network model and cannot accurately estimate the travelling time based on the actual changing traffic conditions
After finding optimal robust virtual routes for all customers by adopting multiobjective particle swarm optimization in the first phase, static vehicle routes for static customers are formed by removing all dynamic customers from robust virtual routes in phase. e dynamically appearing customers append to be served according to their service time and the vehicles’ statues
To accelerate the convergence speed, this paper adopts the double mechanism in cultural algorithm (CA) [19] and proposed a Cultural Algorithm Based Cuckoo Search (CACS)
Summary
With the rapid development of the logistics industry, Vehicle Routing Problem (VRP) gets more and more attention. e traditional VRP uses static road network model and cannot accurately estimate the travelling time based on the actual changing traffic conditions. Guo studied dynamic multiobjective Vehicle Routing Problem with a corresponding carbon emission model and it was set as an optimization objective [1]. To accelerate the convergence speed, this paper adopts the double mechanism in cultural algorithm (CA) [19] and proposed a Cultural Algorithm Based Cuckoo Search (CACS). An adaptive fractional Kalman filter for traffic speed prediction is proposed to update and estimate the time-varying vehicle speed. (1) An adaptive Cultural Algorithm Based Cuckoo Search is proposed (2) An adaptive fractional Kalman filter for traffic speed prediction is proposed (3) e convergence of CACS and the mathematical process of AFKF are proved (4) New solutions of VRP are discovered, which are better than the published solutions (5) With real-time urban traffic data, vehicle speed is dynamically predicted to adjust the solution scheme of TDVRPSC in time
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