Application of Greedy Random Adaptive Search Algorithm (GRASP) in Flight Recovery Problem

With the rapid growth of air transportation, capital is becoming increasingly scarce, and the abnormal situation of flight is becoming more and more serious. Irregular flights have become popular in society, and it is also a great difficulty for airlines. Flight recovery is a classic NP problem. It is of great theoretical significance and practical value to study flight restoration problem. The punctuality of the airline's schedule is a key factor in retaining current customers and attracting new passengers. However, because the civil aviation transportation system is very complex, many reasons will cause the flight plan can not be carried out normally. Weather, air traffic flow control, airport security check, passenger's own reasons and temporary shortage of crew cause the flight can't be executed normally, that is, abnormal flight or flight interruption. Flight interruption will affect the normal operation of airlines. Some flights have to be cancelled or delayed, which will cause huge economic losses to airlines. Besides, the delay or cancellation of flights will cause great inconvenience to passengers and affect the reputation of airlines. The operation control and management level of abnormal flights has attracted more and more attention from domestic airlines. Optimization control and algorithm design have also become a hot topic in the research of abnormal flights in China. Based on the further understanding of the NP problem, this paper verifies the feasibility of the greedy random adaptive search algorithm GRASP algorithm in the NP problem solving process under the flight recovery problem model. According to the analysis, the resource allocation model is established to verify the shortcomings of Lagrange relaxation algorithm (LRS) in flight recovery problem. Meanwhile, the greedy random adaptive search algorithm (GRASP) is used to solve the model, and the new flight schedule is obtained. Through the experimental results, the feasibility of the algorithm is proved in the error range. Keywords-Light Recovery; NP Problem; LRS Algorithm; GRASP Algorithm; Modeling I. THE PROBLEM BACKGROUND As is known to all, there are many interesting problems in computer field, such as salesman problem, packaging problem, partner problem, etc., and they are all belong to NP problem. The flight scheduling problem is also one of the classic NP problems. In the case of simple flight recovery, it's essentially a part of the operational recovery problem. In a broad sense, flight recovery is operation recovery. It includes narrow flight recovery, crew recovery and rescheduling of passenger trips, which are bound together to form an overall super-sized operational optimization problem. The difficulty of flight recovery is mainly due to the immediacy of the recovery programme, except for the complexities involved. After the flight disturbance, the decision and implementation of the recovery plan is the sooner the better. In the case of manual adjustment, operator can only think of some basic factors affecting the flight safety, it is difficult to take into account the global network optimization, not to mention the passenger trip plan or according to the value of passenger flight information to determine the priority of the recovery. In the literature [1], Danzig-Wolfe algorithm was used to solve the multi-commodity flow model of abnormal flight passenger trips. The correctness and validity of the algorithm is verified by a classical example. According to the literature [2], a deep priority algorithm is proposed to construct all feasible trips. By simplex method, the model algorithm can quickly and efficiently restore the passenger flow, and can reduce the loss greatly. In the literature [3],a heuristic method is used to solve the problem and the feasibility is proved. In the literature [4], the timetable recovery model and algorithm of the airline are proposed. Literature [5] proposed a mathematical model for the simultaneous recovery of airline flights and passengers. In the literature [6], Lagrangian relaxation method is used to relax the task constraint and equipment constraint in the model. However, 2018 International Conference on Sensor Network and Computer Engineering (ICSNCE 2018) 40 the LRS algorithm has some shortcomings in solving the problem, which will be explained in detail in the following sections. II. MATHEMATICAL MODEL A. Problems to be solved 1) The maximum delay time of the flight is 5 hours, which means that the flight will be cancelled after more than 5 hours. With a decision unit at 10 minutes interval, then there are 30 delay decisions for one flight. 2) Aircraft replacement is to arrange flights to other planes for execution, which are different from the original plan. Aircraft replacement does not need to be carried out between identical planes, and is generally arranged for any aircraft belonging to the same family or the same aircraft. 3) The minimum interval is 45 minutes. 4) The earliest flight delay cannot be delayed earlier than the original planned departure time. 5) Flight time for each flight is equal to the arrival time in flight data minus departure time in flight data. 6) To make sure that every single plane is connected to the end of the plane, which means that the first flight to the airport has to be the same as the next flight, and that the time between the arrival and the flight of the first flight is 45 minutes. 7) The first flight of all aircraft has to meet the following two conditions: the plane's departure airport is the same as the departure airport of the flight, and the flight time is no longer than the earliest available time of flight. 8) The arrival time of the last flight of all aircraft cannot be later than the latest available time of the aircraft. 9) The decision time interval for flight delay is 10 minutes, regardless of the capacity of the airport. Fellow travelers are passengers who book together and travel in exactly the same way. They share the same passenger number and consider it as a whole, which means they can't take different flights. 10) All flights, including the airport's OVS during the closing time, their delays require consideration. To the greatest possible protection flight, try not to cancel the flight. 11) Due to the impact of the snowstorm, the management decided to close the airport OVS between 18:00 and 21:00 on April 22, 2016.The airport can't take off or land on any flight at the time of the hour, and every flight before that time is in a normal state, and the airport is immediately back to normal after that time period. All flights scheduled to take off between 18:00 and 21:00 (not including 18:00 and 21:00) on that day need to be rescheduled, and their rearrangement may result in rescheduling of other flights after closure. 12) The runway at OVS airport is limited to five aircraft in five minutes, and five planes to land at the same time. Considering the passenger capacity of the aircraft, it is assumed that the cost of adjusting the flight between different types of machines is not only delayed by half an hour but also the cost of the passengers(We still don't think about the passenger's journey, assuming that the passenger's schedule is all right, and assuming that all flights are 100% full).For example, aircraft DIBPV has a capacity of 140 people, and COBPV has 170 passengers. If the aircraft COBPV is distributed to DIBPV, 30 passengers will be unable to board because there are no seats available. However this is not the case if the original planned flight of DIBPV is assigned to the COBPV. Suppose a passenger is unable to board a plane that costs about two hours' delay, how do you reschedule the flight to ensure the shortest amount of delays? B. Question assumptions 1) Assume that each flight is not renamed; 2) Assume that only the minimum cost of the recovery system is considered and all flights are treated equally; 3) Assume that the crew is not equipped; 4) Assume that there is no fault plane flying normally, it will take off and land normally; 5) Assume that the aircraft can be accelerated in the air and should fly at normal speed; 6) Assume that the aircraft will not take the channel during maintenance of the airport, other aircraft can enter the airport normally. 7) Assume that all aircraft of the same model have the same capacity, while there is no cost to adjust the flight, but there are costs to adjust between different models; 8) Assume that the added cost of a flight adjustment on a different aircraft is equivalent to a half-hour delay, and if the displacement and delay might occur at the same time, the cost added; 9) Assume that a passenger cannot board an aircraft equal to the passenger's delay of 2 hours; 10) Regardless of the capacity of the airport, all airports can theoretically work 24 hours a day. C. Meaning of the symbols TABLE 1. NOTATION TABLE