Heuristics for airport operations

Transcription

1 Heuristics for airport operations NATCOR, Nottingham, 2016 Dr Jason Atkin ASAP Research Group The University of Nottingham 1 1

2 Overview Funder: Research funded by NATS and EPSRC Playback of airport movement Part 1: The take-off sequencing problem The basic constraints and objectives Part 2: Sequencing near the runway at Heathrow Issues of re-sequencing close to the runway Part 3: Pushback time allocation Take-off sequencing at the stands Running live at Heathrow Part 4: Other heuristic methods and problems 2

3 London Heathrow Airport An old map! Terminal 5 is here now Problem 1: at the holding area (in green) Problem 2: at the stands (around the white terminals) Red: taxiways Two runways, shown in white 3

4 Part 1 Understanding the basic problem: Take-off sequencing 4

5 Departures Sequence-dependent separations: Wake vortex heavier then lighter aircraft is bad Routes and speed keep in-flight separation and avoid excessive downstream workload 5

6 Consider only weight class Assume three weight classes (heavy, medium, light) Need larger separations when heavier aircraft then lighter aircraft (H then M or L, or M then L) H M H M M H H M L H H Any ideas what we should do? 6 6

7 Consider only weight class Assume three weight classes (heavy, medium, light) Need larger separations when heavier aircraft then lighter aircraft (H then M or L, or M then L) H M H M M H H M L H H L M M M M H H H H H H Group aircraft by weight class, lightest first? Any problems with this? As a pilot or passenger, would you always be happy? 7 7

8 Consider only weight class Assume three weight classes (heavy, medium, light) Need larger separations when heavier aircraft then lighter aircraft (H then M or L, or M then L) H M H M M H H M L H H L M M M M H H H H H H Group aircraft by weight class, lightest first? Can mean a huge delay for heavy aircraft If only weight class matters: Can consider only weight classes and order firstcome-first-served within each weight class Can be considered as interleaving queues problem 8 8

9 More realistically Separations depend upon: Route + speed + weight class 6 x 3 x 4 = 72 options instead of 3 (or 6) 1. Have to look back multiple aircraft Triangle inequality 2. Take-off time windows (for airspace flow control) 15 min windows, some 5 min extensions Must be modelled as soft constraints, non-convex 3. Equity matters, but some aircraft wait a long time! Trade-off: time-slots v delay v equity No longer optimal to order within each weight class Due to timeslots and control problem Control problem is VERY important 9

10 Minimum separations t A t B t C t D t E t F Time A B C D E F Aircraft Separations time Minimum separation applies between any pair of aircraft Reversing the order may change required separation Need to consider separation from multiple previous aircraft Separations can change over time Temporary increases needed, some runway closures, etc 10

11 Small change, big effect Wake vortex heavier then lighter aircraft is bad Routes and speed keep in-flight separation Time Wt. Dir. 0 H N 1 H S 2 3 M N 4 5 H N 6 7 M S 11

12 Small change, big effect Wake vortex heavier then lighter aircraft is bad Routes and speed keep in-flight separation Time Wt. Dir. 0 H N 1 H S 2 3 M N 4 5 H N 6 7 M S 12

13 Small change, big effect Wake vortex heavier then lighter aircraft is bad Routes and speed keep in-flight separation Time Wt. Dir. 0 H N 1 H S 2 H N 3 4 M N 5 M S

14 ATSP A 3 3 C E B D 1 1 Asymmetric Travelling Salesman Problem Defined distances/times/costs between cities Find best sequence to visit the cities Minimum distance/cost/time route to visit all cities 14 14

15 ASP = ATSP? A 3 3 C E B D 1 1 Can Aircraft Sequencing Problem (ASP) be treated as an ATSP? (To use that research) Potentially could be modelled this way: Cities are aircraft Distances between cities are take-off separations Are there any problems with doing this? 15 15

16 ASP ATSP A 3 3 C E Consider the above distances Now consider the take-off sequence A-E-C, where: A and C have a 3 minute minimum separation A and C must be 3 mins apart in sequence A-E-C Example take-off times : A at 0, E at 1min, C at 3 mins Duration of schedule is 3 mins ATSP equivalent says path length A-E-C is 1+1=2 ATSP considers distance only from previous city Would not be a problem if triangle inequality held 16 16

17 1. The triangle inequality t A t B t C t D t E t F Time A B C D E F For each pair of aircraft, i and j, s.t. t i < t j : t j t i RS ij RS ij is a minimum runway separation Not only for adjacent take-offs RS ij depends upon time of day and runway used RS ij can differ from RS ji RS ik RS ij + RS jk for some i,j,k k 17 i j 17

18 Delay and the Cumulative ATSP A B C 2 2 Delay measures the difference between the earliest take-off time and the actual/predicted take-off time Minimising delay is similar to solving Cumulative ATSP Sum of distances from first city to each other city See: L. Bianco, P. Dell Olma, and S. Giordani, Minimizing total completion time subject to release dates and sequence-dependent processing times, 18 Annals of Operations Research, 86: , D E 18

19 2. Time windows t A t B t C t D t E t F Time A B C D E F A B C E D All aircraft have an earliest take-off time How early it can reach the runway When pre-flight checks completed Like the ATSP with time windows Some aircraft have CTOTs F 19 19

20 CTOTs Calculated Time Of Take-off Around 30-40% of daily take-offs from Heathrow in 2004 Clustered around busy times An assigned time, calculated to stagger flights into busy sectors / destinations Can take off up to 5 mins before CTOT Can take off up to 10 mins after CTOT Thus CTOT implies a 15 minute window CTOT extensions Limited number per hour and per day 5 minute extension to latest take-off To avoid re-negotiations Objective: Limit the number of extensions (and misses) 20 20

21 Objectives What actually are the objectives? Keep good long-term throughput How do we do this considering a sub-problem? Make last take-off as early as possible? Reduce duration/makespan/last take-off time Favour all take-off times being earlier? Reduce sum of take-off times? Weighted? We will look at some examples for this Equity also needs to be considered Limiting how unfair the schedule is Inequitable delay distribution? Use non-linear penalty for delay (e.g. squared) Inequitable overtaking/positional displacement Penalise or limit (e.g. a max) position shift in sequence CTOT time-window compliance 21 21

22 Improving throughput Actually want to maximise long-term throughput This is an online problem: Partial (and possible incorrect) knowledge about the future How do we allow for later occurrences? Need a short-term objective for our long-term goals Two obvious options: Minimising schedule duration: Considers take-off time of last aircraft Machine scheduling: Minimise make-span/last completion time Minimising delay: Considers take-off times of all aircraft Machine scheduling: Minimise sum of completion times Most runway sequencing research still considers minimising schedule duration Assumed to equate to maximising throughput The difference can be illustrated by example 22 22

23 Delay or throughput? Example without any CTOTs (take-off time-slots): 3 minute separation on SE-SE (congestion) 2 minute separation on S-S, N-N, SE-S, S-SE 1 minute separation on N-S, S-N Three N, three S, three SE All aircraft available throughout N S SE N S Same earliest take-off times SE SE S SE N S N SE N S Max throughput S SE N S SE N S N SE Identical throughput SE S N SE N S N SE S Better delay SE N S N SE N S SE S Minimum delay 23 23

24 Delay or throughput? Example with a CTOT (delaying a take-off): 3 minute separation on SE-SE (congestion) 2 minute separation on S-S, N-N, SE-S, S-SE 1 minute separation on N-S, S-N Two N, two S, two SE CTOT applies to one N aircraft (red) All aircraft available throughout N S SE N S SE SE S SE S N N Max throughput SE SE S N S N Identical throughput SE SE N S S N Better delay SE N S SE S N Minimum delay 24 24

25 Delay vs Throughput Max short-term throughput (minimise schedule duration) does not necessarily imply max (or good) long-term throughput Short-term delay reduction encourages schedules which are likely to help in the long term Any gaps are moved later in the schedule, where they are more likely to be filled by later arrivals Delay is also important anyway Related to costs/inconvenience 25 25

26 3. Equity matters Many current solution methods ignore equity or put hard limits on inequity Max position shift Latest time? Often ideal time + X Both types of equity matter 1. Equity of delay how long waiting E.g. use non-linear cost for delay (squared?) 2. Equity of positional delay Overtaken by how many? Big position shifts may be needed for time-slots 26 26

27 Objectives Meet timeslots Meeting these is the top priority Keep runway throughput high Measured how? Last take-off time? (Makespan) Reduce delay Need to consider delay for later aircraft too Be as fair as we can Equity of delay? Limit overtaking 27

28 Good Sequences? What does it mean to be a good take-off sequence? What characteristics does it have? 28

29 Part 2 Sequencing within the holding area 29

30 Manual re-sequencing Controllers re-sequence aircraft manually Within the holding area Evaluate sequences in their heads Tight time constraints Up to a take-off a minute And many other things to do (give instructions) Limits to how many aircraft can be considered, e.g. Only those in holding area 30

31 Solution Method Take-off sequence is key But must be achievable easily! Cost is related to the take-off times and fairness Which depend upon sequence Timeslots missed, delay, overtaking, etc Search through take-off sequences Evaluate each sequence for feasibility 31

32 Solution method Tabu search through sequences Make some moves which ones? Accept the best considered Avoid backtracking (& cycling) Need fast method to evaluate each solution Is it achievable? (How?) Heuristic path allocation Deterministic checks for feasibility What are the predicted take-off times? What is the cost? A B C D E F G H I J 32 32

33 Which moves to choose? The moves determine which solutions are adjacent to each other May be advantages from good solutions being close together 33

34 What do good sequences look like? 34

35 Neighbourhood N S N S N S N S N S Neighbourhood design is important The available solution time is VERY small (solve within 1 second) Need moves which allow fast movement to a good solution and between good solutions Handle huge infeasible region problems E.g. Keep departure route alternation Shift up to 5 aircraft, rather than one Swap 2 aircraft, e.g. swap N & N Randomise 2-5 aircraft N S N S S N S N S N S 35

36 Tabu Search Repeat 200 iterations of: Generate 50 random neighbouring solutions Evaluate each solution Is it achievable within holding area? Using sensible paths only Predict take-off times Determine a schedule cost (delay, CTOTs, Equity) Adopt lowest cost non-tabu solution Tabu list: Maintains details of the last ten moves made Rejects moves which reverse moves on list A B C D E F G H I J 36

37 Aircraft queue in a holding area Controller considers the positions and desired sequences to find achievable good take-off sequence 37 37

38 Model of the problem Appropriate level of abstraction? Model turning? Model acceleration speeds? Gaps between queuing aircraft? Instead looked at the higher level What has been done historically? What can be done? What routes do controllers like? What would they accept if necessary? How many aircraft can fit at each position? 38

39 Directed graph model Example good routes: ADIN, CEGJN, BFHKL Slower (but good) routes: ADIMN, BFHKLOP Short-cuts, if necessary: ADI, CEGJI 39

40 Heuristically solving the graph To evaluate sequence we know: Order of arrival at each entrance Order of departure from runway Know the allocated paths! Key to success is shared paths Consider partial paths at each node Path prefix/path suffix Consider only first from each prefix and suffix Consider one at a time can it move without preventing another getting out on time Consider not-shared nodes 40

41 Dynamic Problem Simple simulation: One minute steps, forward through time Build problem to solve Uses historic data Predict aircraft that real system would know of Optionally apply prediction errors Perform a search to find a good schedule Includes the simple simulation, of ground movement Assume the schedule is adopted Update data accordingly Position in holding point, take-offs, taxi paths 41

42 Playback The real movement Vs Movement from the simulation 42

43 Delay for different holding areas Key Results: Delay decreased, so it is worth considering. Holding area structure affects schedule delay

44 CTOT (timeslot) compliance Key Result: CTOT compliance is also good! 44 44

45 Effects of Constraints (relax some) Percentage decrease in delay when constraints are removed: Constraints Removed: (None) W/V W/V + SID SID (None) Overtaking Overtaking + CTOT CTOT

46 Taxi time uncertainty Modelled as (random within percentage) prediction errors in taxi time values Number of CTOTs missed Delay per aircraft (mins:secs) Mean Min Max Mean Min Real results 10 6:59 Max No errors :51 4:50 4:53 10% errors :51 4:50 4:55 30% errors :55 4:50 5:02 50% errors :00 4:51 5:13 70% errors :10 4:53 5:34 90% errors :54 5:18 7:00 46

47 Planning Horizon: taxiing aircraft? 47 47

48 Part 3 Question: Can we sequence back at the stands and hold aircraft on the stands before starting engines? 48 48

49 Aircraft pushing back block each other Too close for simultaneous pushback? Blocked from leaving by another? 49 49

50 Two sequences Time A 5 B A 1 B 1 C 5 D E Taxi time joins the problems C 1 2 E 1 D 1 3 F F Sequencing at the stands Only between aircraft on stands close to each other Tend to be larger separations time to start up Sequencing at the runway Between all aircraft using runway Tend to be smaller separations 50 50

51 Take-off Sequencing Partial sequences now have more value Rolling window through take-off sequences Branch and bound to sequence aircraft within window When aircraft is added, determine cul-de-sac sequence so that it will take-off as early as possible From take-off times, predict a cost Improvements such as: Multi-passes of the window Heuristic pre-sequencing (for CTOT) Small window pre-sequencing A B C D E F G H I J K L M N Fixed take-off times Ignored unless latest CDS time 51

52 52 52

53 53 53

54 A working system System running live at Heathrow Predicts take-off times Provides these to Eurocontrol Allocates appropriate pushback times Significant fuel-burn savings Wait at the stand rather than the runway And take off no later than before Tuning Objectives, stability, avoid unfairness, etc 54

55 Part 4 Other heuristic airport optimisation problems 55 55

56 Arrival Sequencing Obtain good, easily achievable landing sequences Separations depend upon aircraft Limitations of stacks Costly to take from other than bottom Incoming flight paths 56

57 Arrival Stacks Multiple stacks available One flight per level on each Usually take from bottom level Can take from bottom three if worthwhile more workload Descend only when next level is empty Descent speed faster when two levels below are clear 57

58 Taxi Operations Aim: Reduce environment effect of airports Taxi time prediction Multiple Linear Regression Fuzzy Rules Based Systems Consider layout of airport (travel distance, turning angle) Consider congestion (number on surface/starting/ending) Ground movement Sequential Dijkstra-based approach, with time windows Some benefits from altering input order Environmentally friendly version Improved predictions, significant stand holds, fuel savings 58 58

59 Stand Operations Allocate stands to improve environmental effects Integration: consider effects upon ground movement and runway sequencing Stand allocation restrictions for airlines or aircraft size/type Shadowing constraints upon nearby stand occupancy Inter-stand pushback or arrival time constraints scarce taxiway resources 59 59

60 Resource Allocation Other resource allocation projects Baggage sorting station allocation Constructive algorithms Order flights criteria? Choose sorting stations criteria? Look-ahead? Genetic Algorithms Custom operators 60 60

61 Thank you Any questions? Jason Atkin, ASAP Research Group Web: 61