불확실성하에서 항공기 도착 시퀀싱과 스케줄링을 위한 결정론적 및 확률론적 최적화

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 기계항공공학부, 2018. 2. 김유단.As the demand for air transportation increases, air traffic congestion is becoming a critical issue in the current air traffic control system. In particular, many researchers have recognized the need for decision support tools for human air traffic controllers in the terminal area, where incoming arrivals and outgoing departures are concentrated in a limited airspace surrounding airports. Although uncertainty comes from various sources in the terminal area, only a few existing works consider uncertainty with respect to the aircraft sequencing and scheduling problem. In this dissertation, two different robust optimization approaches for aircraft arrival sequencing and scheduling are presented that consider the uncertainty of fight time. First, robust optimization based on deterministic programming is proposed, which has a two-level hierarchical architecture. At the higher level, an extra buffer is introduced in the aircraft safe separation constraint by adopting the typical deterministic programming. The extra buffer size is analytically derived based on a deterministic robust counterpart problem. However, robust solutions obtained at the higher level can only be implemented in restricted situations where the magnitude of uncertainty is less than a predetermined constant value. Therefore, at the lower level, to compensate for the effects of unexpected situations under a dynamic environment, robust solutions obtained at the higher level are adjusted by using a heuristic adjustment with a sliding time window. Second, two-stage stochastic programming based on Particle Swarm Optimization (PSO) is proposed to determine less conservative robust solutions than the robust optimization based on deterministic programming. First and second stage decision problems are defined as aircraft sequencing and scheduling, respectively. PSO is utilized for a randomized search to make the first stage decision under incomplete information about uncertain parameters. A random key representation is adopted to apply PSO to a discrete aircraft sequencing problem because PSO has a continuous nature. Next, the second stage decision is made by solving a mixed integer linear programming problem after the realization of uncertain parameters. The performances of the two proposed robust optimization methodologies are verified through numerical simulations with historical flight data. Monte Carlo simulations are also performed for randomly generated air traffic situations.Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Literature Review 7 1.2.1 Aircraft Sequencing and Scheduling 7 1.2.2 Deterministic Programming under Uncertainty 10 1.2.3 Stochastic Programming under Uncertainty 12 1.3 Contributions 15 1.3.1 Systematic Problem Formulation 15 1.3.2 Robust Optimization: Deterministic Programming 16 1.3.3 Robust Optimization: Stochastic Programming 17 1.4 Dissertation Organization 18 Chapter 2 Mixed Integer Linear Programming for Aircraft Arrival Sequencing and Scheduling 19 2.1 Point Merge System (PMS) 20 2.1.1 Configuration of PMS 20 2.1.2 Arrival Procedure through PMS 20 2.1.3 Characteristic of PMS 21 2.2 Concept of Operation 22 2.3 Problem Formulation 24 2.3.1 Decision Variables 24 2.3.2 Objective Function 24 2.3.3 Constraints 25 2.3.4 Mathematical Formulation 27 Chapter 3 Deterministic Programming for Aircraft Arrival Sequencing and Scheduling under Uncertainty 28 3.1 Hierarchical Architecture 29 3.2 Deterministic Programming 30 3.2.1 Impact of Uncertainty 30 3.2.2 Determination of Extra Buffer Size [15] 30 3.2.3 Mathematical Formulation 33 3.3 Algorithm Enhancements for Dynamic Environments 35 3.3.1 Heuristic Adjustment 35 3.3.2 Sliding Time Window 39 3.4 Algorithm Summary 41 3.5 Historical Data Analysis 44 3.6 Toy Problem 50 3.7 Numerical Simulation 60 Chapter 4 Stochastic Programming for Aircraft Arrival Sequencing and Scheduling under Uncertainty 68 4.1 Two-Stage Stochastic Programming 69 4.1.1 Deterministic Equivalent Programming (DEP) 70 4.1.2 Two-Stage Stochastic Programming based on GA 71 4.2 Two-Stage Stochastic Programming based on PSO 72 4.2.1 Master and Sub-Problems 72 4.2.2 Random Key Representation 74 4.2.3 Algorithm Summary 76 4.3 Toy Problem 79 4.4 Numerical Simulation 83 4.4.1 Numerical Analysis on the Number of Scenarios 84 4.4.2 Comparison with Deterministic Programming 89 4.4.3 Comparison with Other Stochastic Programming 95 Chapter 5 Conclusions 100 5.1 Summary 100 5.2 Future Research Directions 104 5.2.1 Applications of Multi-Objective Optimization 104 5.2.2 Extensions of Airport Surface Traffic Optimization 105 5.2.3 Consideration of Various Uncertainties 105 Bibliography 107 Abstract (in Korean) 121Docto

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