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Real-time optimal delay minimization algorithms for aircraft on a same runway and dual runways

Peng Lin, Haopeng Yang

Abstract

In this paper, scheduling problems of aircraft minimizing the total delays on a same runway and on dual runways are studied. In contrast to the algorithms based on mixed-integer optimization models in existing works, where the optimality and the real-time performance are usually unable to be dealt with at the same time, our work focuses on the interaction mechanism between aircraft coupling with delays and two real-time optimal algorithms are proposed for the four scheduling problems by fully exploiting the combinations of different classes of aircraft based on parallel computing technology. When $100$ aircraft on dual runways is considered, by using the algorithm in this paper, the optimal solution can be obtained within less than $10$ seconds, while by using the CPLEX software to solve the mix-integer optimization model, the optimal solution cannot be obtained within $1$ hour.

Real-time optimal delay minimization algorithms for aircraft on a same runway and dual runways

Abstract

In this paper, scheduling problems of aircraft minimizing the total delays on a same runway and on dual runways are studied. In contrast to the algorithms based on mixed-integer optimization models in existing works, where the optimality and the real-time performance are usually unable to be dealt with at the same time, our work focuses on the interaction mechanism between aircraft coupling with delays and two real-time optimal algorithms are proposed for the four scheduling problems by fully exploiting the combinations of different classes of aircraft based on parallel computing technology. When aircraft on dual runways is considered, by using the algorithm in this paper, the optimal solution can be obtained within less than seconds, while by using the CPLEX software to solve the mix-integer optimization model, the optimal solution cannot be obtained within hour.
Paper Structure (13 sections, 11 theorems, 2 equations, 4 tables)

This paper contains 13 sections, 11 theorems, 2 equations, 4 tables.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Some necessary assumptions and definitions
  4. Landing sequences
  5. Takeoff sequences
  6. Mixed landing and takeoff sequences on a same runway
  7. Mixed landing and takeoff aircraft on dual runways
  8. Some theoretical results
  9. Algorithms
  10. Algorithm 1
  11. Algorithm 2
  12. Simulation
  13. Conclusions

Key Result

Theorem 1

b3b Consider a landing/takeoff sequence $\phi=\langle Tcf_1, Tcf_2, \cdots, Tcf_{n}\rangle$. Suppose that $Tf_k=[t_0, +\infty]$ for all $k$. Under Assumptions ass1.3.1-ass2.3.41, if the aircraft $Tcf_j$ is relevant to $Tcf_i$, then $j=i+1$.

Theorems & Definitions (22)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Theorem 1
  • Theorem 2
  • Remark 1
  • ...and 12 more