A Dynamic Programming Approach for 4D Flight Route Optimization

A Dynamic Programming Approach for 4D Flight Route Optimization Christian Kiss-Tóth, Gábor Takács Széchenyi István University, Győr, Hungary IEEE International Conference on Big Data Oct 27-30, 2014 Washington Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 1 / 19

Overview GE Flight Quest 2 was an optimization contest in 2013/14, organized by Kaggle. The goal was to optimize flight routes w. r. t. to the average of their total costs. Our team Taki & Chris reached fifth place during the final evaluation. Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 2 / 19

Input data I. Flight Data: the data of the flights had to be optimized in the cut off times data was provided for 14 days, 1000 flights per day departure and arrival airport, the current position and altitude, the departure and scheduled arrival time, fuel, delay, turbulence costs, etc. Airport Data: the list of the 63 airports where planes had to land latitude, longitude coordinates and altitude Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 3 / 19

Data visualization I. 2 : 63 airports 2 : 1000 planes in the cut off time Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 4 / 19

Input data II. Restricted Zones: zones where the planes were not allowed the fly in convex polyhedrons in the airspace same on every day 19 zones Turbulent Zones: zones where you got some penalty if you fly in convex polyhedrons in the airspace different on different days 5 9 zones per day Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 5 / 19

Input data III. Weather Data: wind speeds provided as 2D vectors given hourly on eight different altitude levels every level was a 451 337 grid live wind and forecast wind ground conditions for the arrival: temperature, wind, visibility in hourly resolution Some other less important data about the airports for the arrival process of the simulator. Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 6 / 19

Data visualization II. RESTRICTED ZONES TURBULENT ZONES Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 7 / 19

The problem Optimal flight plans for the plains had to be created, with the lowest possible cost Flight plan: list of instructions (max 200 per flight) every instruction is a (latitude, longitude, altitude, airspeed) quadruples FlightID Ordinal Latitude Longitude Altitude AirSpeed 324485334 1 37:0700 109:7300 40000 600 324485334 2 36:8664 110:3550 40000 600 324485334 3 35:2374 115:0335 40000 600 324485334 4 34:4377 117:1485 2000 600 324485334 5 34:4025 117:2391 2000 600... Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 8 / 19

The simulator The objective function (total cost) of FQ2 was calculated by a simulator: the source code was open, written in F# ( 2300 rows) consists of several submodules, including fuel consumption models for ascending, cruising and descending, a landing, weight, atmosphere and aircraft model and an airspeed limiter simulates all flight plans loaded into it in discrete time steps computes a total cost value for the flights outputs one number, the average total cost The cost of a flight can be written in the following form: C total = C fuel + C delay + C oscillation + C turbulence Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 9 / 19

Proposed solution I. creating initial flight plans for the flights =) initial solution set the latitude and longitude coordinates of the waypoints =) 2D optimization process set the altitudes and the airspeed of the flight =) 1D optimization process Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 10 / 19

Proposed solution II. INITIAL SOLUTION: creating initial routes to avoid crashing of the planes connecting two points on a plane avoiding a set of convex polygons DIJKSTRA S ALGORITHM: shortest path from one point to all others in an edge-weighted graph with non-negative weights vertices: current position, destination airport, all the vertices of the restricted zones weights: the distances between the points Figure: Initial paths avoiding restricted zones using Dijkstra s algorithm Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 11 / 19

Proposed solution III. 2D OPTIMIZATION PROCESS: Fuel consumption: function of the airspeed (instruction) Groundspeed: function of airspeed and wind speed Modifying routes to take advantages on the wind Figure: Reducing fuel, delay and turbulence costs using wind-optimal paths Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 12 / 19

Proposed solution IV. Explore the airspace using DYNAMIC PROGRAMMING technique: Refining the routes with various local search procedures: 2D REFINEMENT Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 13 / 19

Proposed solution V. 1D OPTIMIZATION PROCESS: Parameterizing the 1D profiles with two variables descending distance: the distance from the destination airport cruise speed: the airspeed instruction during the cruising phase Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 14 / 19

Proposed solution VI. optimizing the two parameters with exhaustive search: 1D OPTIMIZATION refining the 1D profile of the routes to take advantages on some specialities of the simulator: 1D REFINEMENT Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 15 / 19

Implementation details Bash scripts for automatization Python for data processing MATLAB to rewrote the simulator and for the optimization process We divided the flights on each day into 4 parts, and run the optimization process on 14 4 = 56 cores The hardware we used during the competition was a 64 core Linux server with 1 terabyte memory Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 16 / 19

Numerical results & Time consumption Solution type Average cost Improvement Dijkstra s algorithm 11736:4$ Dynamic programming 11707:4$ 29$ 2D refinement 11702:3$ 5:1$ 1D optimization 11687:2$ 15:1$ 1D refinement 11680:5$ 6:7$ Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 17 / 19

Conclusions & Summarization We presented our solution that reached fifth place in the final phase of the GE Flight Quest 2 competition. The main elements of our route optimization method are the Dijkstra s algorithm, dynamic programming, local and exhaustive search procedures. Our method is able to produce reasonable initial plans in a short time. To improve the initial solution the most effective and time consuming part was the dynamic programming part. Most of our methods can be useful for real life flight route optimization, since the simulator used in FQ2 was quite realistic in many aspects. Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 18 / 19

Acknowledgement This research was supported by the project TÁMOP-4.2.2.A-11/1/KONV-2012-0012: Basic research for the development of hybrid and electric vehicles - The Project is supported by the Hungarian Government and co-financed by the European Social Fund Thank you for your attention! Christian Kiss-Tóth, Gábor Takács (SZE) 4D Flight Route Optimization IEEE BigData 2014 19 / 19