# Multi-Objective Gate Allocation Problem Based on Multi-Commodity Network Flow Model
## 1 Introduction  
Over the past few decades, the rapid development of the civil aviation industry has been witnessed. However, the contradiction between the rapid increase in the demand for civil aviation transportation and the lack of existing resources has become more and more prominent. The contradiction reduces the airport's operational efficiency in the central position, making it easy to cause large-scale delays [1]. The fundamental solution to this problem is to increase the airport's capacity among which the construction of infrastructure is the most direct way. However, this method is challenging due to high costs and long periods. Another way is to increase the airport capacity by improving the operating efficiency, which is also the direction of this paper. As one of the important resources in airport surfaces, the gate is a main factor to ensure the efficient operation of the airport [2]. Under the circumstance of limited gate resources, the allocation of gates will play a key role in the transition and connection of aircraft entering and leaving the airport. An effective gate allocation scheme can help reduce surface conflicts and flight delays, thereby improving service quality and passenger satisfaction. Gate allocation refers to selecting suitable and compatible gates for arrival and departure flights with a fixed occupancy time to complete the corresponding surface tasks [3]. It is essentially a resource scheduling and optimization problem that is ubiquitous in various fields [4, 5, 6, 7, 8]. At the airport planning level, the manager allocates the gate reasonably according to the number, location, and type to meet the expected demand of surface flights. At the airport operation level, based on the flight plan data and appropriate optimization goals,we can predict the assignment of the aircraft in advance. According to the actual operation of the airport surface, the results of gate allocation can have a huge impact on a variety of stakeholders, especially passengers, airlines, and airports. Passengers expect to walk the shortest distance to board the corresponding flight or arrive at the corresponding terminal smoothly. Airlines want to minimize taxi time due to congestion and surface conflicts and maximize the operational efficiency of their resources. The airport hopes to optimize the use of surface resources, thereby ensuring passenger satisfaction and balancing the interests of multiple airlines. Therefore, in order to comprehensively consider the interests of multiple parties and generate an efficient and reasonable gate allocation scheme, this paper builds a multi-objective optimization model of gate allocation based on the multi-commodity network flow theory. To solve it, a regularized linear weighting method converts it into a single-objective optimization model. Furthermore, to analyze and evaluate different weight combinations, cluster analysis is applied. According to the analysis results, different weight combinations may correspond to the same objective function value. Therefore, the gate robustness is introduced as an auxiliary indicator to determine the most suitable weight combination. The proposed model is validated on the real data of Shanghai Pudong International Airport. Overall, our main contributions can be summarized as follows:  
1. A multi-objective optimization model based on multi-commodity network flow is proposed, where the interests of passengers, airports, and airlines are comprehensively considered. 2. A linear weighting method is used to solve the multi-objective optimization model, where cluster analysis and auxiliary metrics are used to determine weight combinations. 3. Extensive experimental analysis is performed on real operational data, and the validity of the allocation results is illustrated from both qualitative and quantitative perspectives, respectively. The rest of this paper is organized as follows. In Section 2, the related work is reviewed, and the research status of gate allocation is introduced from three aspects.