A Rolling Window with Genetic Algorithm Approach to SortingAircraft for Automated Taxi Routing

Alexander E.I. BrownleeDivision of Computing Science and Mathematics

University of StirlingStirling, UK

alexander.brownlee@stir.ac.uk

John R. WoodwardSchool of Electronic Engineering and Computer Science

Queen Mary University of LondonLondon, UK

j.woodward@qmul.ac.uk

Michal WeiszerSchool of Engineering and Materials Science

Queen Mary University of LondonLondon, UK

m.weiszer@qmul.ac.uk

Jun ChenSchool of Engineering and Materials Science

Queen Mary University of LondonLondon, UK

jun.chen@qmul.ac.uk

ABSTRACTWith increasing demand for air travel and overloaded airport facili-ties, inefficient airport taxiing operations are a significant contribu-tor to unnecessary fuel burn and a substantial source of pollution.Although taxiing is only a small part of a flight, aircraft engines arenot optimised for taxiing speed and so contribute disproportion-ately to the overall fuel burn. Delays in taxiing also waste scarceairport resources and frustrate passengers. Consequently, reduc-ing the time spent taxiing is an important investment. An exactalgorithm for finding shortest paths based on A* allocates routesto aircraft that maintains aircraft at a safe distance apart, has beenshown to yield efficient taxi routes. However, this approach dependson the order in which aircraft are chosen for allocating routes. Find-ing the right order in which to allocate routes to the aircraft is acombinatorial optimization problem in itself.

We apply a rolling window approach incorporating a geneticalgorithm for permutations to this problem, for real-world scenariosat three busy airports. This is compared to an exhaustive approachover small rolling windows, and the conventional first-come-first-served ordering. We show that the GA is able to reduce overall taxitime with respect to the other approaches.

CCS CONCEPTS• Computing methodologies→ Search methodologies; • Ap-plied computing → Transportation;

KEYWORDStransportation, aircraft taxiing, routing, permutations, genetic al-gorithm

1 INTRODUCTIONWe need to make better use of existing aviation infrastructure asworldwide air traffic is predicted to increase 1.5 times by 2035 [16].This means fitting more aircraft into the same runways, terminalgates and taxiways. Although taxiing is only a small part of a flight,the inefficient operation of aircraft engines at taxiing speed cancontribute disproportionately to the overall fuel burn. These effectsapply particularly at larger airports, where ground manoeuvres aremore complex, but also for short-haul operations, where taxiing

represents a larger fraction of a flight. It is estimated that fuel burntduring taxiing alone represents up to 6% of fuel consumption forshort-haul flights resulting in 5 m tonnes of fuel burnt per yearglobally, equating to 1.6 billion pounds given today’s fuel prices.This situation is only set to get worse as more aircraft are squeezedin to the existing infrastructure.

Allocating routes to taxiing aircraft can be modelled as find-ing shortest paths across a graph, with the extension of a timedimension. A shortest path algorithm based on the well knownA* algorithm is able to sequentially allocate efficient routes to air-craft, avoiding conflicts by routing around other aircraft, or waitingfor other aircraft to move. However, this approach is affected bythe order in which aircraft are presented for routing. This paperproposes the application of a rolling window approach, based onthe receding horizon concept [6, 7, 21, 22, 37], incorporating apermutation-encoded genetic algorithm (GA), to find the best se-quence in which to allocate routes to the aircraft. This approachis compared with the baseline method, First-Come-First-Served(FCFS), and an exhaustive search within small rolling windows.The approach is applied to three international airports: Doha, HongKong and Beijing Capital. We show that the GA was able to findbetter routings than FCFS and small window exhaustive search, byvirtue of being able to explore much larger windows. The approachis able to reduce the delays by using FCFS by over 70%. This simpleapplication of a GA represents an effective improvement for aircrafttaxi routing that could have substantial impact.

We begin with a summary of related work in Section 2 and in-troduce background concepts including the taxiing problem and A*algorithm in Section 3. We describe our rolling window method-ology and the genetic algorithm in Section 4. Experiments andresults for the three airports considered are given in Sections 5 and6, before we draw our conclusions in Section 7.

2 RELATEDWORKOptimisation of taxi routes (or Ground Movement) is a challengingproblem that has been tackled in a variety of ways. Comprehensivereviews of this area are [2] and [3]. Early approaches [18, 19, 30]used a list of routes that were either human-designed or generated

Published in Proceedings of the Genetic and Evolutionary Computation Conference 2018 by ACM. The original publication is available at: https://doi.org/10.1145/3205455.3205558

before the algorithm was run using a shortest path algorithm. Meta-heuristics were then used to choose an appropriate route and waitpoints for each aircraft. Genetic algorithms have also been used toevolve the routes rather than choosing predefined ones [24]. Alter-native efforts including [13, 17, 20, 36] formulated Ground Move-ment as a mixed-integer linear programming problem. A recentapproach using pre-computed routes formulated Ground Move-ment as a job-shop scheduling problem [1].

An alternative approach [32] generates the routes for aircrafteach time, allowing the route and its timings to be tailored to ac-count for the movements of other aircraft. Ravizza et al. describedthe Quickest Path Problem with Time Windows (QPPTW) algo-rithm, an adaptation of Dijkstra’s shortest path algorithm that addsa time dimension and accounts for the movements of previously-allocated aircraft. The A* algorithm variant for taxiing that we usetackles the problem in much the same way [26]. While the approachwill find the quickest path for an aircraft given existing movements,Ravizza et al. noted that QPPTW was dependent on the order inwhich aircraft were chosen for allocating routes: this also appliesto the A* approach we use. This is the problem we tackle in thepresent paper.

Often the focus is on optimising taxi times, but other objec-tives have attracted some attention, particularly reducing aircraftemissions and fuel consumption due to taxiing [11, 12, 17, 35]. Anadvantage of accurate and efficient taxi routing is that aircraft canbe made to wait at the gate until the last possible minute beforestarting engines and pushing back, saving fuel that would otherwisebe wasted waiting in a queue at the runway [4].

Metaheuristics have been applied to other aviation optimisationproblems including gate assignment [8], runway sequencing [7],and flight path planning [31]. The Rolling Window or RecedingHorizon approach has been demonstrated to be useful in handlingdynamic problems in aviation [6, 7, 13, 21, 22, 37] and a wide varietyof other application domains (e.g. wireless base station planning[38]).

Metaheuristics have also found application in a variety of otherrouting and transportation problems including GPS navigation [33]and railway scheduling [15].

3 BACKGROUND3.1 Taxiing and Ground MovementAllocation of routes for aircraft taxiing or Ground Movement is acombined routing and scheduling problem [3]. Time-efficient routesmust be allocated to aircraft seeking to pass through the taxiwaysbetween the runways and gates or stands. For safety reasons, it iscrucial that two aircraft never conflict with each other throughoutthe taxiing process. All routes have to respect allocated runwaytimes, taxi route restrictions, and safety constraints on the proximityof other aircraft. At airports with low air traffic, with only one ortwo aircraft moving at any one time, routes could be assigned usingshortest path algorithms like Dijkstra’s or A*. However, interactionsbetween moving aircraft mean that a more sophisticated approachis required at busier airports. At busy airports, taxiways almostalways cross each other. In addition, with obstacles such as runwaysaircraft must be carefully timed to cross busy junctions, reducingthe need to change speed or stop. Both reducing speed or stopping

can cause a knock-on effect in terms of delay, and also increasesfuel consumption

3.2 A*The routing algorithm used in this paper is a multi-objective short-est path A* algorithm [26] adapted to the ground movement prob-lem. Although in the present work we only use one objective (taxitime) we intend to extend this to also consider fuel consumption,which has a complex relationship with speed. For each aircraft,routed sequentially, a set of optimal routes is found from the startnode to the end node. Then, the fastest route is reserved. Aircraftare routed on a directed graph, representing the taxiway layout,where nodes represent gates, stands, taxiway intersections, inter-mediate points and runway exits and edges represent taxiways. Inorder to ensure conflict-free routes, each edge can be occupied byonly one aircraft at a time. This also applies to any edges close toone holding an aircraft (within a radius of 60m) that would cause aconflict. Edges are connected together to form straight and turningsegments. The angle between adjacent edges is less than 30 degreesin straight segments. For each straight segment, its taxi time corre-sponds to the fastest speed profile, i.e. maximum acceleration (0.1 g,where g is 9.8ms−2), followed by maximum allowed constant speed(30 knots) phase and braking (0.1 g). For turning segments, constantspeed (10 knots) is assumed. A more detailed description of speedprofile generation is in [12]. In order to accelerate the search, whilenot compromising the optimality of routes, a heuristic function isused. The heuristic function provides estimates of costs from the allnodes to the end node. For taxi time, it is calculated as the length ofthe shortest path to the end node divided by the maximum allowedspeed (30 knots).

The advantage of this approach is that the route of the aircraftis not pre-determined, allowing greater flexibility for solutions.The times of entry/exit at the runway are fixed for departures andarrivals. The sequential approach to allocating taxi routes will thenbe used to minimise the taxi time for each individual aircraft giventhe planned movement for the aircraft which have already beenrouted.

4 METHODOLOGYThe natural order in which to allocate routes to aircraft is first-come-first-served (FCFS). If departing and arriving aircraft requireroutes allocated at the same time, arriving aircraft are allocatedroutes first because the departing aircraft can simply wait at thegate.

Ravizza et al. [32] noted approximately a 1% reduction in totaltaxi time by using a bespoke swap heuristic. This was embeddedwithin their QPPTW algorithm. Wherever an aircraft deviated fromits shortest possible path (either by having to stop, or taking alonger route), the conflicting aircraft causing the delay is identified,and the two aircraft are swapped and re-routed. If this results ina shorter total taxi time for the two aircraft, the new routes arekept, if not, the initial routes are retained. The approach we takeis a separate search over permutations of aircraft, which can beindependent of the specific shortest path algorithm used.

2

Algorithm 1 Procedure for allocating routes to set of AircraftA = a0, . . . ,an−1, for a window. Note, there is a correction for thefinal window where its size is smaller than usual to avoid runningoff the end of the aircraft list: this is omitted for simplicity. Functionreserve(r ,G) reserves the route r on taxiway graph G.1: Inputs: G,A,w ▷ taxiway graph, set of aircraft, windowSize2: s = 0 ▷ window start3: whilewindowStart < n do4: W = as ,. . .,as+w ▷ Aircraft in the current window5: minP = null,minTime = +∞6: for all Permutations p over W do ▷ can be run in parallel7: if s > 0 then ▷ if not on first window8: reserve((ras−w , . . . , ras−1 ),G)

▷ Reserve routes for previous window’s▷ aircraft on taxiways, so the present

▷ windows aircraft avoid them9: end if10: Let time=011: for a inW do12: ra = allocateRoute(a) ▷ Apply A* to find route13: t = length(ra ) ▷ (length in seconds)14: time += t15: reserve(ra , G) ▷ Ensures remaining

▷ aircraft in the present window avoid a16: end for17: if time < minTime then18: minTime = time19: minP = p20: end if21: Clear reservations on G

▷ Allows next permutation to be checked afresh22: end for23: Apply routes found forminP toW24: s +=windowSize25: end while

4.1 Rolling WindowsWe can consider a window containing the nextw waiting aircraft,and assign routes to aircraft for different potential orderings. Asimple approach will examine allw! permutations of aircraft in awindow of sizew . For a given window sizew , all permutations ofAircraft 1 tow will be considered, and the routes allocated to theaircraft in the order specified by each permutation. The quickestrouting is chosen then those aircrafts’ routes are fixed. The windowthen rolls to Aircraftw +1 to 2w , within which all permutations areconsidered, and routes allocated also accounting for the now chosenroutes for Aircraft from the first window. This continues, with thewindow rolling forward w aircraft at a time, allocating routes toaircraft then fixing them so that subsequent aircraft avoid earlierones. This is more formally set out in Algorithm 1 and illustratedin Figure 1.

However, this exhaustive approach is limited by the long runtime of the routing algorithm. For example, around 5 seconds toallocate routes to 10-20 aircraft for Doha Airport, and up to 200seconds for Beijing. These observations suggest a window size of

more than 5 or 6 aircraft is not practical. However, at busy airportsit can be the case that 10–15 aircraft are taxiing at any one time, anyof which may be in conflict, so a larger window size might yieldsome improvement in the routes. This motivates use of a heuristicsearch method.

4.2 Genetic AlgorithmWe now consider a simple implementation of a genetic algorithmto searching the permutations of aircraft within the larger rollingwindows, in place of the exhaustive search described in the previoussection. The GA will be run once for each window to determinethe permutation that results in the shortest overall taxi time onceaircraft routes have been allocated. The window will then move tothe next set of aircraft and the GA will run again.

The GA encodes the aircraft in a window as a list of integers,each being an index into the aircraft list. The encoding is such thateach aircraft is represented once and only once. The populationis initialised with a set of permutations generated uniformly atrandom, with one seed solution in which the aircraft are arrangedin FCFS order. Four elite solutions are carried over from one gener-ation to the next. 2-tournament selection is used to choose parentsfor recombination. Recombination is the order-crossover [14], inwhich a sub-sequence of indices from the first parent is chosen atrandom and copied to the offspring. The offspring is then completedby adding the remaining indices in-order from the second parent.Mutation used two operators, chosen at random with an equal prob-ability. The Swap Mutation operator [29], which takes two indicesin the permutation and swaps them. Displacement mutation [27]takes a random sub-sequence within the permutation and shifts itto another position chosen at random.

5 EXPERIMENTS5.1 Airport ScenariosIn this paper, we use a set of instances of real arrival and departureflights from 3 airports: Doha International Airport (DOH), HongKong International Airport (HKG) and Beijing Capital International(PEK). The complexity of the taxiway layout ranges from simple(DOH), medium (HKG) to complex (PEK). The instances consist offollowing number of aircraft: 180 (DOH) from 16.3.2014, 506 (HKG)from 17.1.2017 and 349 (PEK) from 9.7.2014. The data providedspecifies landing/pushback times, gates/runway exits and weightcategory for each flight. The taxiway graph of Hong Kong Interna-tional Airport is illustrated in Figure 2. The graph specifying theairport layout and movement data were prepared using the GMTools1 [10].

In all of the experiments, the route allocations were run in up to24 parallel threads. This depends on the number of permutationsbeing tested: obviously smaller GA population sizes, and windowsizes 2 and 3 with 2 and 6 permutations respectively, did not use allthese threads).

5.2 Parameter tuningThere is a balance to be made in where the effort of evaluatingpermutations takes place. In the dynamic and rapidly changing

1https://github.com/gm-tools/gm-tools/wiki

3

w1routing forthcoming

w2fixed forthcoming

w3fixed forthcoming

routing

routing

Figure 1: Illustration of a rolling window of size four (aircraft are a mixture of arrivals and departures)

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Figure 2: Layout of taxiways atHongKong InternationalAir-port

environment of the airport, there is only a certain allowable lengthof time that we can take to find a solution for each group of aircraft.This is an important physical constraint if we aim for our approachto be used in real time under operating constrains and conditions.This time limit corresponds to an upper limit on the number ofpermutations that we can sample for a set of aircraft. The followingtwo factors trade-off against each other:

• a larger window size means a larger search space, so poten-tially needing a longer-running GA, but fewer windows willbe required to cover all aircraft

• in common with many other applications, the GA can runfor a fixed length of time, meaning either a larger popula-tion for few generations, or a smaller population for manygenerations

• the run length for the routing algorithm increases with thenumber of aircraft, but due to set up times there is not an easyrule of thumb to determine the optimal number of aircraftto route with respect to running time

The run time for our A* implementation for a permutation of 20aircraft on Hong Kong Airport is approximately 40s (DOH is around5s, PEK is around 200s). Ideally we want the runs to complete inreal time, so at 120s separation between aircraft, we have 2400sper window, so only about 60 evaluations allowed per window: 3per aircraft. We can (and do) improve this situation by runningevaluations of the permutations in parallel: with 24 threads we arelimited 1440 evaluations for windows of 20 aircraft, or 72 evalua-tions per aircraft. Obviously we could add additional cores withinreason to extend this further (at least 5x the number so that wecan achieve the same run times for PEK as for HKG). The abovemight seem like a long-winded way of reaching the average figureof 72s per aircraft: it needs to be thought of from the perspectiveof a reasonable window length (in the range of 10-60) because dueto set-up time, a run of the routing algorithm for a single aircraftis still several seconds, and while not constant is fairly consistentacross this range of window sizes. These run times do not impacton the potential taxi time savings of the approach: the reason welimit the times is to ensure a high enough throughput that aircraftcan have their routes allocated before they are due to start taxiing.

In order to find a good balance between the population size, GAevaluation limit and window size, we ran a preliminary parametertuning experiment on a subset of 120 aircraft at Hong Kong Airport.At 72 evaluations per aircraft this means we have 8640 evaluationsfor all 120 aircraft. Population size and window size were varied,then the GA evaluation limit computed by dividing the total numberof allowed evaluations (8640) by the number of windows requiredto cover the 120 aircraft. The tuning was carried out using theSequential Model-based Algorithm Configuration (SMAC) tool [23],with a limit of 1000 GA runs. The tuning also included the mutationand crossover rates for the GA: these are simply the proportion ofoffspring that crossover and mutation were applied to.

The best parameters found by SMAC were as follows:4

• GA population size: 17• Window size: 56• GA evaluation limit (computed from the above): 4032• Crossover rate: 0.226• Mutation rate: 0.496

At this point we havemade the assumption that the configurationfor HKG will carry over to the other airports. Strictly speaking theparameter tuning should be carried out for each, but in this studywe are more interested in proving the concept rather than ensuringmaximal performance.

6 RESULTSTable 1 summarises the results. The first block of the table gives totaltaxi times in seconds for all routed aircraft at each airport whenusing the different approaches. The lower bound was determinedby running the routing algorithm for each aircraft in isolation,avoiding any waiting times or detours. This is of course may notbe achievable, but gives us some indication of performance. FCFSis the result when using the standard first-come-first-served orderfor allocating routes. “Exhaustive WSx” are the figures for theexhaustive rolling window approach, with window sizes of 2–6.“GA RW” are the average figures from 20 repeat runs of the GArolling window approach with the tuned parameters (including awindow size of 56). “GA all aircraft” was a single run of the GAconducted as a sanity check, working over the permutation of allaircraft, running for 3000 evaluations with a population size of 20(this would be no use in practice as the run time was several hours).

The “gap” values in the lower half of Table 1 are the gap ordelay in seconds between the lower bound and the result found byeach of the methods. The “reduction of gap” values are the relativeimprovement of the GAWS56 approach over FCFS, ExhaustiveWS2and Exhaustive WS3. The exhaustive search over rolling windowsof 6 for HKG and 5 and 6 for PEK is omitted; in these cases the runtimes were prohibitive for practical use.

It is clear that all of the approaches offer an improvement overFCFS, reducing the gap between the routed times and the theoreti-cal lower bound for the situation where no aircraft are in conflictwith each other. In general, increasing the window size means thatpermutations leading to faster routes can be found, although insome cases (e.g. DOH window sizes 5 and 6), increasing the sizeactually causes the delays to increase. This is because the changein window size causes conflicting 2 aircraft to fall on the bound-ary between windows where they previously did not: when thishappens they cannot be swapped to improve the conflict situation.

The GA with rolling window approach (GA RW) was able tofind the permutation leading to the shortest overall taxi times forall three airports. In all, the reduction in the delay (gap) over theminimal times compared to FCFS was between 74 and 85%, withsimilar reductions for the exhaustive rolling window approacheswith small window sizes.

The sanity-check single GA run on the whole permutation foreach airport was not able to improve on the GAwith rollingwindow:we expect that this was due to the large search space involved butthis requires further investigation.

2conflicting in the sense that they are competing for a route rather than risking safety

Table 1: Results: total taxi time at each airport when usingeach method (‘Exhaustive’ abbreviated to ‘Exh.’). For the GAWS56 rolling window results, this is the mean over 20 runs,with standard deviation given in subscript

Total taxi time (s)Method DOH HKG PEKLower bound 32 430 128 763 88 119FCFS 32 685 129 366 88 707Exh. WS2 32 685 129 229 88 703Exh. WS3 32 685 129 274 88 542Exh. WS4 32 515 129 066 88 640Exh. WS5 32 515 128 954Exh. WS6 32 684GA RW 32 435 35 128 852 100 88 246 79GA all aircraft 32 515 129 070 88 192FCFS gap 255 603 588Exh. WS2 gap 255 466 584Exh. WS3 gap 255 511 423Exh. WS4 gap 85 303 521Exh. WS5 gap 85 191Exh. WS6 gap 254GA RW gap 64 89 127GA all aircraftgap

85 2307 1073

% reduction ofgap over FCFS

74.90 85.24 78.40

% reduction ofgap over Ex. WS2

74.90 80.90 78.25

% reduction ofgap over Ex. WS3

74.90 82.58 69.98

The reductions in delay with respect to the total taxi times mayseem insignificant in terms of percentages, but it is important tosee how this translates into financial cost for this real world prob-lem. Given a lower bound of 128 763s for the movements of theaircraft at Hong Kong Airport, reducing the delays by 514s (0.40%)may seem trivial. However, this is for 506 aircraft, part of one dayof movements. For the 421 000 aircraft movements in 2017, thisamounts to a saving of 427 656s. Following the assumption of [9]that a single aisle jet aircraft uses 25 pounds of fuel per minutewhile taxiing, and an assumed $5 US per gallon of fuel (one gallonbeing 6.7lbs), the savings in fuel at Hong Kong Airport alone wouldbe approximately $133k per year. However, it should be noted thatother sources question the actual fuel rate for taxiing, which ispossibly slightly overestimated by ICAO [25, 28].

7 CONCLUSION AND FUTUREWORKGrowing air traffic means heavier demands on existing airport in-frastructure including taxiways. Although taxiing is only a smallpart of an overall flight, ground movement is is responsible for adisproportionate amount of fuel burn. This is because jet engineare very efficient at cruising speed, but relatively inefficient whilemoving on the ground at low speed. Consequently, even small

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improvements in efficiency in taxiing will reduce economic and en-vironmental costs, notwithstanding reduced frustration for delayedpassengers.

An existing method based on A* has proven successful for rout-ing aircraft without conflicts, but its performance is dependent onthe sequence in which aircraft are presented to it for routing. Weproposed the application of a rolling window approach incorpo-rating a permutation-encoded genetic algorithm to find the bestsequence in which to allocate routes to the aircraft. This was com-pared with FCFS, and an exhaustive search within small rollingwindows. When applied to Doha, Hong Kong and Beijing CapitalInternational Airports, the GA based approach was able to find bet-ter routings than FCFS or exhaustive search. Delays added by FCFSwere reduced by over 70%. This simple application of a relativelynaive genetic algorithm represents an effective improvement foraircraft taxi routing that could have substantial impact.

In terms of future directions to explore, rather than moving thecomplete window forward each time, a more continuous rollingwindow could be considered. For window sizeW , the order wouldbe determined, n <W aircraft would be dispatched, the windowmoved on by n, and the next order for the nextW aircraft found(potentially reordering the lastW −n of the first window’s aircraft).This would avoid the anomalous situation we observed where con-flicting aircraft span the boundary of a window and can not bereordered. Additionally, given that one of the key obstacles en-countered in this work was the long running time of the routingalgorithm, we are investigating more advanced search algorithmssuch as model based algorithms (e.g. [5]) and surrogates (one possi-bility for permutations being [34]). Our model of aircraft movementalso incorporates an estimation of fuel consumption for the allo-cated routes and we are particularly interested in exploring whatthe possible multi-objective trade-off between fuel consumptionand taxi time looks like. Understanding this will be an importantpart of tackling the problem of airport congestion as air trafficcontinues to grow.

ACKNOWLEDGEMENTWork funded byUKEPSRC [grants EP/N029577/2 and EP/N029496/2].

DATA ACCESS STATEMENTThe taxiway layout and aircraft movement data cannot be shareddue to licensing restrictions.

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