基于ASRank和MMAS的蚁群算法求解飞机指派问题

本文将航班串的飞机指派问题归结为车辆路径问题,考虑连续航班串之间衔接时间、衔接机场的约束、每架飞机的总飞行时间约束,建立了带有飞行时间约束的车辆路径问题的混合整数规划模型。构造了蚁群系统算法,引入基于排序的蚂蚁系统和最大最小蚂蚁系统算法的信息素更新策略。选取某航空公司7组初始航班串集合进行测试,并对算法中的重要参数进行了分析。实验结果表明,本文设计的模型和算法可以有效地减少连续航班串之间的总衔接时间,在可接受的计算时间内获得满意解。

Ant Colony Algorithm based on the ASRank and MMAS for the Aircraft Assigning Problem

The domestic airlines are relatively small in comparison with the international airlines.Airlines used to make the flight plans using simple and rough methods.The competition among the airlines became stronger with the expansion of airlines,and the opening of the air transportation market.Therefore,flight-planning management becomes more important.Aircraft assigning problem(AAP) is to assign planes to the proper flight reasonably in order to make full use of the fleet resources.Good flight planning can not only ensure the safety and punctuality of flights,but also improve the utilization rate of fleets and decrease the cost of operation and maintenance so as to maximize the economic benefits of the airlines. The theoretical research on the flight-assigning problem is in its infancy,and most of the research just considers the next day aircraft assignment.However,in practice the airline engineering personnel generally makes aircraft plans every week.Although conducting aircraft assignment daily simplifies the problem and greatly reduces the constraints involved,the assignment method can hardly capture the actual demand.Based on the process of flight planning of the domestic airlines,we transform the aircraft assignment problem into vehicle routing problem(VRP) and study the weekly flight assignment problem.This problem is a kind of large scale NP-hard combinatorial optimization problem which is difficult to be solved by the accurate algorithms effectively.As a meta-heuristics algorithm,ant colony optimization algorithm(ACO) has strong global search ability and the ability to find a better solution.Thus,we select the ACO as the algorithm for the AAP problem. Considering the link time constraints and link airport constraints between two consecutive flight strings,and considering the total flying time constraints of the aircrafts,we propose the concept of virtual flight string and construct a mixed integer programming model.To solve this model,we propose an ACO algorithm according to the characteristics of the problem.In this algorithm we adopt the pheromone updating strategy of rank-based version of ant system(ASRank) and MAX-MIN ant system(MMAS).The ASRank can make the search space more close to the optimal solution while the MMAS make the algorithm avoid stagnation in the process of searching. For testing the validity of our model and algorithm,we use the practical data of one airline to do the experiments and test some important parameters of the algorithm.The numerical results show that the best goal value obtained by our method is 3.75% less than the best goal value obtained by manual method,the utilization rate of the aircrafts is improved and the total link time is effectively decreased.