Transportation problem has many real world applications, it can be solved by linear programming model, but in most time the model exists more for less paradox, this paper considers the reasons for the paradox and s...Transportation problem has many real world applications, it can be solved by linear programming model, but in most time the model exists more for less paradox, this paper considers the reasons for the paradox and search the way to eliminate the phenomenon. First this paper formulates a loose constrained linear programming model for the transportation problem, and gives the definition of the paradox which exists in it, some preliminary notions and one example is also given. Then it gives a table based algorithm for the loose constrained model, the steps of the algorithm and example will follow. The examples show that: (1) It is not a contradictory that transportation problem exists more for less paradox. (2) The loose constrained model is better used in practice for its less total cost. (3) The algorithm is easy to calculate, to study and highly speed to convergence. Finally, comparied with other ways it shows that the loose constrained model can thoroughly eliminate the paradox.展开更多
Most of the traditional taxi path planning studies assume that the aircraft is in uniform speed,and the optimization goal is the shortest taxi time.Although it is easy to solve,it does not consider the changes in the ...Most of the traditional taxi path planning studies assume that the aircraft is in uniform speed,and the optimization goal is the shortest taxi time.Although it is easy to solve,it does not consider the changes in the speed profile of the aircraft when turning,and the shortest taxi time does not necessarily bring the best taxi fuel consumption.In this paper,the number of turns is considered,and the improved A*algorithm is used to obtain the P static paths with the shortest sum of the straight-line distance and the turning distance of the aircraft as the feasible taxi paths.By balancing taxi time and fuel consumption,a set of Pareto optimal speed profiles are generated for each preselected path to predict the 4-D trajectory of the aircraft.Based on the 4-D trajectory prediction results,the conflict by the occupied time window in the taxiing area is detected.For the conflict aircraft,based on the priority comparison,the waiting or changing path is selected to solve the taxiing conflict.Finally,the conflict free aircraft taxiing path is generated and the area occupation time window on the path is updated.The experimental results show that the total taxi distance and turn time of the aircraft are reduced,and the fuel consumption is reduced.The proposed method has high practical application value and is expected to be applied in real-time air traffic control decision-making in the future.展开更多
Improviag transportation system is essential for all people in each city since transport plays a very important role. Using mathematical programming approach transport problem is an effective way to improve transporta...Improviag transportation system is essential for all people in each city since transport plays a very important role. Using mathematical programming approach transport problem is an effective way to improve transportation system. In this paper, the traffic equilibrium problem （TEP） with a general nonadditive route cost function is studied. We formulate the route cost function for each route as a disutility function, which can evaluate route cost function flexibly and analyze the route toll conveniently. Furthermore, we present the TEP with a nonlinear complementary problem （NCP） formulation. The monotonicity and the existence with the NCP formulation are also given under relative assumptions.展开更多
文摘Transportation problem has many real world applications, it can be solved by linear programming model, but in most time the model exists more for less paradox, this paper considers the reasons for the paradox and search the way to eliminate the phenomenon. First this paper formulates a loose constrained linear programming model for the transportation problem, and gives the definition of the paradox which exists in it, some preliminary notions and one example is also given. Then it gives a table based algorithm for the loose constrained model, the steps of the algorithm and example will follow. The examples show that: (1) It is not a contradictory that transportation problem exists more for less paradox. (2) The loose constrained model is better used in practice for its less total cost. (3) The algorithm is easy to calculate, to study and highly speed to convergence. Finally, comparied with other ways it shows that the loose constrained model can thoroughly eliminate the paradox.
基金supported by the National Key R&D Project(No.2020YFB1600101)National Natural Science Foundations of China(Nos.U1833103,71801215)Civil Aviation Flight Wide Area Surveillance and Safety Control Technology Key Laboratory Open Fund(No.202008)。
文摘Most of the traditional taxi path planning studies assume that the aircraft is in uniform speed,and the optimization goal is the shortest taxi time.Although it is easy to solve,it does not consider the changes in the speed profile of the aircraft when turning,and the shortest taxi time does not necessarily bring the best taxi fuel consumption.In this paper,the number of turns is considered,and the improved A*algorithm is used to obtain the P static paths with the shortest sum of the straight-line distance and the turning distance of the aircraft as the feasible taxi paths.By balancing taxi time and fuel consumption,a set of Pareto optimal speed profiles are generated for each preselected path to predict the 4-D trajectory of the aircraft.Based on the 4-D trajectory prediction results,the conflict by the occupied time window in the taxiing area is detected.For the conflict aircraft,based on the priority comparison,the waiting or changing path is selected to solve the taxiing conflict.Finally,the conflict free aircraft taxiing path is generated and the area occupation time window on the path is updated.The experimental results show that the total taxi distance and turn time of the aircraft are reduced,and the fuel consumption is reduced.The proposed method has high practical application value and is expected to be applied in real-time air traffic control decision-making in the future.
基金supported by the National Natural Science Foundation of China(Grant Nos.71071014,70771005,70631001)the Fundamental Research Funds for Central Universities of China(Grant No. 2009JBM044)
文摘Improviag transportation system is essential for all people in each city since transport plays a very important role. Using mathematical programming approach transport problem is an effective way to improve transportation system. In this paper, the traffic equilibrium problem （TEP） with a general nonadditive route cost function is studied. We formulate the route cost function for each route as a disutility function, which can evaluate route cost function flexibly and analyze the route toll conveniently. Furthermore, we present the TEP with a nonlinear complementary problem （NCP） formulation. The monotonicity and the existence with the NCP formulation are also given under relative assumptions.
