A novel approximation algorithm was proposed for the problem of finding the minimum total cost of all routes in Capacity Vehicle Routing Problem (CVRP). CVRP can be partitioned into three parts: the selection of vehic...A novel approximation algorithm was proposed for the problem of finding the minimum total cost of all routes in Capacity Vehicle Routing Problem (CVRP). CVRP can be partitioned into three parts: the selection of vehicles among the available vehicles, the initial routing of the selected fleet and the routing optimization. Fuzzy C-means (FCM) can group the customers with close Euclidean distance into the same vehicle according to the principle of similar feature partition. Transiently chaotic neural network (TCNN) combines local search and global search, possessing high search efficiency. It will solve the routes to near optimality. A simple tabu search (TS) procedure can improve the routes to more optimality. The computations on benchmark problems and comparisons with other results in literatures show that the proposed algorithm is a viable and effective approach for CVRP.展开更多
Air route network optimization,one of the essential parts of the airspace planning,is an effective way to optimize airspace resources,increase airspace capacity,and alleviate air traffic congestion.However,little has ...Air route network optimization,one of the essential parts of the airspace planning,is an effective way to optimize airspace resources,increase airspace capacity,and alleviate air traffic congestion.However,little has been done on the optimization of air route network in the fragmented airspace caused by prohibited,restricted,and dangerous areas（PRDs）.In this paper,an air route network optimization model is developed with the total operational cost as the objective function while airspace restriction,air route network capacity,and non-straight-line factors（NSLF） are taken as major constraints.A square grid cellular space,Moore neighbors,a fixed boundary,together with a set of rules for solving the route network optimization model are designed based on cellular automata.The empirical traffic of airports with the largest traffic volume in each of the 9 flight information regions in China's Mainland is collected as the origin-destination（OD） airport pair demands.Based on traffic patterns,the model generates 35 air routes which successfully avoids 144 PRDs.Compared with the current air route network structure,the number of nodes decreases by 41.67%,while the total length of flight segments and air routes drop by 32.03% and 5.82% respectively.The NSLF decreases by 5.82% with changes in the total length of the air route network.More importantly,the total operational cost of the whole network decreases by 6.22%.The computational results show the potential benefits of the model and the advantage of the algorithm.Optimization of air route network can significantly reduce operational cost while ensuring operation safety.展开更多
文摘A novel approximation algorithm was proposed for the problem of finding the minimum total cost of all routes in Capacity Vehicle Routing Problem (CVRP). CVRP can be partitioned into three parts: the selection of vehicles among the available vehicles, the initial routing of the selected fleet and the routing optimization. Fuzzy C-means (FCM) can group the customers with close Euclidean distance into the same vehicle according to the principle of similar feature partition. Transiently chaotic neural network (TCNN) combines local search and global search, possessing high search efficiency. It will solve the routes to near optimality. A simple tabu search (TS) procedure can improve the routes to more optimality. The computations on benchmark problems and comparisons with other results in literatures show that the proposed algorithm is a viable and effective approach for CVRP.
基金co-supported by the National Natural Science Foundation of China(No.61304190)the Natural Science Foundation of Jiangsu Province(No.BK20130818)the Fundamental Research Funds for the Central Universities of China(No.NJ20150030)
文摘Air route network optimization,one of the essential parts of the airspace planning,is an effective way to optimize airspace resources,increase airspace capacity,and alleviate air traffic congestion.However,little has been done on the optimization of air route network in the fragmented airspace caused by prohibited,restricted,and dangerous areas（PRDs）.In this paper,an air route network optimization model is developed with the total operational cost as the objective function while airspace restriction,air route network capacity,and non-straight-line factors（NSLF） are taken as major constraints.A square grid cellular space,Moore neighbors,a fixed boundary,together with a set of rules for solving the route network optimization model are designed based on cellular automata.The empirical traffic of airports with the largest traffic volume in each of the 9 flight information regions in China's Mainland is collected as the origin-destination（OD） airport pair demands.Based on traffic patterns,the model generates 35 air routes which successfully avoids 144 PRDs.Compared with the current air route network structure,the number of nodes decreases by 41.67%,while the total length of flight segments and air routes drop by 32.03% and 5.82% respectively.The NSLF decreases by 5.82% with changes in the total length of the air route network.More importantly,the total operational cost of the whole network decreases by 6.22%.The computational results show the potential benefits of the model and the advantage of the algorithm.Optimization of air route network can significantly reduce operational cost while ensuring operation safety.
