A Rolling Window with Genetic Algorithm Approach to Sorting
Aircraft for Automated Taxi Routing
Alexander E.I. Brownlee
Division of Computing Science and Mathematics University of Stirling
Stirling, UK
John R. Woodward
School of Electronic Engineering and Computer Science Queen Mary University of London
London, UK [email protected]
Michal Weiszer
School of Engineering and Materials Science Queen Mary University of London
London, UK [email protected]
Jun Chen
School of Engineering and Materials Science Queen Mary University of London
London, UK [email protected]
ABSTRACT
With 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 are not optimised for taxiing speed and so contribute disproportion-ately to the overall fuel burn. Delays in taxiing also waste scarce airport resources and frustrate passengers. Consequently, reduc-ing the time spent taxireduc-ing is an important investment. An exact algorithm for finding shortest paths based on A* allocates routes to aircraft that maintains aircraft at a safe distance apart, has been shown to yield efficient taxi routes. However, this approach depends on the order in which aircraft are chosen for allocating routes. Find-ing the right order in which to allocate routes to the aircraft is a combinatorial optimization problem in itself.
We apply a rolling window approach incorporating a genetic algorithm for permutations to this problem, for real-world scenarios at three busy airports. This is compared to an exhaustive approach over small rolling windows, and the conventional first-come-first-served ordering. We show that the GA is able to reduce overall taxi time with respect to the other approaches.
CCS CONCEPTS
• Computing methodologies → Search methodologies; • Ap-plied computing → Transportation;
KEYWORDS
transportation, aircraft taxiing, routing, permutations, genetic al-gorithm
1
INTRODUCTION
We need to make better use of existing aviation infrastructure as worldwide air traffic is predicted to increase 1.5 times by 2035 [16]. This means fitting more aircraft into the same runways, terminal gates and taxiways. Although taxiing is only a small part of a flight, the inefficient operation of aircraft engines at taxiing speed can contribute disproportionately to the overall fuel burn. These effects apply particularly at larger airports, where ground manoeuvres are more complex, but also for short-haul operations, where taxiing
represents a larger fraction of a flight. It is estimated that fuel burnt during taxiing alone represents up to 6% of fuel consumption for short-haul flights resulting in 5 m tonnes of fuel burnt per year globally, equating to 1.6 billion pounds given today’s fuel prices. This situation is only set to get worse as more aircraft are squeezed in 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 time dimension. A shortest path algorithm based on the well known A* algorithm is able to sequentially allocate efficient routes to air-craft, avoiding conflicts by routing around other airair-craft, or waiting for other aircraft to move. However, this approach is affected by the order in which aircraft are presented for routing. This paper proposes the application of a rolling window approach, based on the receding horizon concept [6, 7, 21, 22, 37], incorporating a permutation-encoded genetic algorithm (GA), to find the best se-quence in which to allocate routes to the aircraft. This approach is 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, Hong Kong and Beijing Capital. We show that the GA was able to find better routings than FCFS and small window exhaustive search, by virtue of being able to explore much larger windows. The approach is able to reduce the delays by using FCFS by over 70%. This simple application of a GA represents an effective improvement for aircraft taxi 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 and results for the three airports considered are given in Sections 5 and 6, before we draw our conclusions in Section 7.
2
RELATED WORK
Optimisation of taxi routes (or Ground Movement) is a challenging problem that has been tackled in a variety of ways. Comprehensive reviews 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 wait points for each aircraft. Genetic algorithms have also been used to evolve 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 recent approach using pre-computed routes formulated Ground Move-ment as a job-shop scheduling problem [1].
An alternative approach [32] generates the routes for aircraft each time, allowing the route and its timings to be tailored to ac-count for the movements of other aircraft. Ravizza et al. described the Quickest Path Problem with Time Windows (QPPTW) algo-rithm, an adaptation of Dijkstra’s shortest path algorithm that adds a time dimension and accounts for the movements of previously-allocated aircraft. The A* algorithm variant for taxiing that we use tackles the problem in much the same way [26]. While the approach will find the quickest path for an aircraft given existing movements, Ravizza et al. noted that QPPTW was dependent on the order in which aircraft were chosen for allocating routes: this also applies to the A* approach we use. This is the problem we tackle in the present paper.
Often the focus is on optimising taxi times, but other objec-tives have attracted some attention, particularly reducing aircraft emissions and fuel consumption due to taxiing [11, 12, 17, 35]. An advantage of accurate and efficient taxi routing is that aircraft can be made to wait at the gate until the last possible minute before starting engines and pushing back, saving fuel that would otherwise be wasted waiting in a queue at the runway [4].
Metaheuristics have been applied to other aviation optimisation problems including gate assignment [8], runway sequencing [7], and flight path planning [31]. The Rolling Window or Receding Horizon approach has been demonstrated to be useful in handling dynamic problems in aviation [6, 7, 13, 21, 22, 37] and a wide variety of other application domains (e.g. wireless base station planning [38]).
Metaheuristics have also found application in a variety of other routing and transportation problems including GPS navigation [33] and railway scheduling [15].
3
BACKGROUND
3.1
Taxiing and Ground Movement
Allocation of routes for aircraft taxiing or Ground Movement is a combined routing and scheduling problem [3]. Time-efficient routes must be allocated to aircraft seeking to pass through the taxiways between the runways and gates or stands. For safety reasons, it is crucial that two aircraft never conflict with each other throughout the taxiing process. All routes have to respect allocated runway times, taxi route restrictions, and safety constraints on the proximity of other aircraft. At airports with low air traffic, with only one or two aircraft moving at any one time, routes could be assigned using shortest path algorithms like Dijkstra’s or A*. However, interactions between moving aircraft mean that a more sophisticated approach is required at busier airports. At busy airports, taxiways almost always cross each other. In addition, with obstacles such as runways aircraft must be carefully timed to cross busy junctions, reducing the need to change speed or stop. Both reducing speed or stopping
can cause a knock-on effect in terms of delay, and also increases fuel 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 (taxi time) 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 start node to the end node. Then, the fastest route is reserved. Aircraft are 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. In order to ensure conflict-free routes, each edge can be occupied by only one aircraft at a time. This also applies to any edges close to one holding an aircraft (within a radius of 60m) that would cause a conflict. Edges are connected together to form straight and turning segments. The angle between adjacent edges is less than 30 degrees in 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 9.8 ms−2), followed by maximum allowed constant speed (30 knots) phase and braking (0.1 g). For turning segments, constant speed (10 knots) is assumed. A more detailed description of speed profile generation is in [12]. In order to accelerate the search, while not compromising the optimality of routes, a heuristic function is used. The heuristic function provides estimates of costs from the all nodes to the end node. For taxi time, it is calculated as the length of the shortest path to the end node divided by the maximum allowed speed (30 knots).
The advantage of this approach is that the route of the aircraft is not pre-determined, allowing greater flexibility for solutions. The times of entry/exit at the runway are fixed for departures and arrivals. The sequential approach to allocating taxi routes will then be used to minimise the taxi time for each individual aircraft given the planned movement for the aircraft which have already been routed.
4
METHODOLOGY
The natural order in which to allocate routes to aircraft is first-come-first-served (FCFS). If departing and arriving aircraft require routes allocated at the same time, arriving aircraft are allocated routes first because the departing aircraft can simply wait at the gate.
Ravizza et al. [32] noted approximately a 1% reduction in total taxi time by using a bespoke swap heuristic. This was embedded within their QPPTW algorithm. Wherever an aircraft deviated from its shortest possible path (either by having to stop, or taking a longer route), the conflicting aircraft causing the delay is identified, and the two aircraft are swapped and re-routed. If this results in a shorter total taxi time for the two aircraft, the new routes are kept, if not, the initial routes are retained. The approach we take is a separate search over permutations of aircraft, which can be independent of the specific shortest path algorithm used.
Algorithm 1 Procedure for allocating routes to set of Aircraft A= a0, . . . , an−1, for a window. Note, there is a correction for the
final window where its size is smaller than usual to avoid running off the end of the aircraft list: this is omitted for simplicity. Function reserve(r ,G) reserves the route r on taxiway graph G.
1: Inputs: G,A,w ▷ taxiway graph, set of aircraft, windowSize
2: s= 0 ▷ window start
3: while windowStart < n do
4: W = as,. . .,as+w ▷ Aircraft in the current window 5: minP = null, minT ime =+∞
6: for all Permutations p over W do ▷ can be run in parallel 7: if s > 0 then ▷ if not on first window
8: reserve((ras −w, . . . , ras −1),G)
▷ Reserve routes for previous window’s ▷ aircraft on taxiways, so the present ▷ windows aircraft avoid them
9: end if
10: Let time=0
11: for a in W do
12: ra= allocateRoute(a) ▷ Apply A* to find route 13: t = length(ra) ▷ (length in seconds) 14: time += t
15: reserve(ra, G) ▷ Ensures remaining
▷ aircraft in the present window avoid a
16: end for
17: if time < minT ime then
18: minT ime= time
19: minP = p
20: end if
21: Clear reservations on G
▷ Allows next permutation to be checked afresh
22: end for
23: Apply routes found for minP to W
24: s += windowSize
25: end while
4.1
Rolling Windows
We can consider a window containing the next w waiting aircraft, and assign routes to aircraft for different potential orderings. A simple approach will examine all w! permutations of aircraft in a window of size w. For a given window size w, all permutations of Aircraft 1 to w will be considered, and the routes allocated to the aircraft in the order specified by each permutation. The quickest routing is chosen then those aircrafts’ routes are fixed. The window then rolls to Aircraft w+1 to 2w, within which all permutations are considered, and routes allocated also accounting for the now chosen routes for Aircraft from the first window. This continues, with the window rolling forward w aircraft at a time, allocating routes to aircraft then fixing them so that subsequent aircraft avoid earlier ones. This is more formally set out in Algorithm 1 and illustrated in Figure 1.
However, this exhaustive approach is limited by the long run time of the routing algorithm. For example, around 5 seconds to allocate routes to 10-20 aircraft for Doha Airport, and up to 200 seconds for Beijing. These observations suggest a window size of
more than 5 or 6 aircraft is not practical. However, at busy airports it can be the case that 10–15 aircraft are taxiing at any one time, any of which may be in conflict, so a larger window size might yield some improvement in the routes. This motivates use of a heuristic search method.
4.2
Genetic Algorithm
We now consider a simple implementation of a genetic algorithm to searching the permutations of aircraft within the larger rolling windows, in place of the exhaustive search described in the previous section. The GA will be run once for each window to determine the permutation that results in the shortest overall taxi time once aircraft routes have been allocated. The window will then move to the 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 that each aircraft is represented once and only once. The population is initialised with a set of permutations generated uniformly at random, with one seed solution in which the aircraft are arranged in FCFS order. Four elite solutions are carried over from one gener-ation to the next. 2-tournament selection is used to choose parents for recombination. Recombination is the order-crossover [14], in which a sub-sequence of indices from the first parent is chosen at random and copied to the offspring. The offspring is then completed by 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 indices in the permutation and swaps them. Displacement mutation [27] takes a random sub-sequence within the permutation and shifts it to another position chosen at random.
5
EXPERIMENTS
5.1
Airport Scenarios
In this paper, we use a set of instances of real arrival and departure flights from 3 airports: Doha International Airport (DOH), Hong Kong 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 of following number of aircraft: 180 (DOH) from 16.3.2014, 506 (HKG) from 17.1.2017 and 349 (PEK) from 9.7.2014. The data provided specifies landing/pushback times, gates/runway exits and weight category for each flight. The taxiway graph of Hong Kong Interna-tional Airport is illustrated in Figure 2. The graph specifying the airport layout and movement data were prepared using the GM Tools1[10].
In all of the experiments, the route allocations were run in up to 24 parallel threads. This depends on the number of permutations being tested: obviously smaller GA population sizes, and window sizes 2 and 3 with 2 and 6 permutations respectively, did not use all these threads).
5.2
Parameter tuning
There is a balance to be made in where the effort of evaluating permutations takes place. In the dynamic and rapidly changing
1https://github.com/gm-tools/gm-tools/wiki 3
w1
routing
forthcoming
w2
fixed
forthcoming
w3
fixed
forthcoming
routing
routing
Figure 1: Illustration of a rolling window of size four (aircraft are a mixture of arrivals and departures)
1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20 21 22 26 2425232728 29303132 3334 35 3637 3839 40 4144 43 42 45 46 47 48 49 53555254 51 50 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 80 838482 87888990858179787692937573 7477869191 94 95 9697 98 99 100 101 102 103 104 105 106 107 108 109 110110 111112 113 113 114 115 116 117 118 119 120 121123 122 124 125127 132133131130129126128 134 135 136 137 138 139 140141 142 143 144 145 146 147 148 149150 151 152 153 154 155162163168169164165166177175176170178179161159160156157174158173167171172 180 181 182199187189186185183184 196193198195192202191194190188197200201 203 217214215 209210213216211212208205206207204 218 220221 219 222223 224 225 226228227 229 230233232 231 234236239237240241 235238 242243 244 245 245246248 247 249 250 251 251269266259 255 261262263264265258260268254253270 271272273257256252267274275276 277278 279 280 281 282 283 284 285 286 287 288289 290 291292293 294 295 296 297 298 299 300 301 302 303304 305306307 308310312314315309311313317316 318 319 320322 323321 324 325 326 327 328 329331330 332 333 334 335 336337 338339 340 341 342 343 344 345 346 347 348 349 350351 352 352353353 354 354355355 356 357 358 359 360 361 361 362 363364365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380381381 382 383 384 385 386 387 388 389 390 391392393394395 396 397 398 399 400405 442439437435416407434433410412413431432402425422428 450449447445446443441440415414411409444452451438427430429426420421408406453454401424423404403418419417436448 455456457458459460 461 462463 464 465468470471 467469466 472473474475476477480485484482483478479481 486487 488 489 490491 492 492 493494 495497 496 498 499 500 501 502506508 504505503 507507 509 510 511512 548543541546545 515516515518522523528544540538532523526 527529530530534535536537539524 525542533520521547531517513519514 549 550551 552553 554555 556558 557 559560561 562 563 566564567 565 568 570 571574572 569573 575587583592 584585580577588590591586582579578576581 589 593 594 595 596 597 598 599600 601 603 602 604 605608614616611612610607609606613 615 617619623628632 620624631627630625618622629 626633621 634 637 636635 638 639 640 641 642 643654 649650645646653655 647651656644648652657 658 661 662660659663 664 665666 667 668 669 670 671 672 673 674 675 676 677 678679 680681 682 683 684 685686 687 688 689690 691692694695696693 697 698701699700 702 703 704 705707706 708709 710 711 712 713715717718714716 719 720 721 722 723 724 725 726727 728729 730 731 732 733 734 735737736 738 739 740 741743742 744 745746747 748 749 750 751 752 753754 755 756 757 758 758 759 760 761 762763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781782 783784 785786 787788789 790791792793 794795 796797798799 800 801 802803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819822 820824825823821 826 827 828829 830 831 832 833 834835 836 837 838 839 840 841 842844926918922848850851 852853854857860861862874870866867864865871847846843863858856915916914910913878879884883909881880907908903896897905906904920891888886887912899900901902927928923898877875876930845869872873895882855894849885859868892889890893 1006963961100210041000995997970969967976987974980 985983984988990991 992989982937979993 994936978940934939968942977975973972971944954955933966965981962986959960947 9489499579649969989319321001953950 951941938935929952946945943925924921919958911956917 1034112610381039104211101046111811221052108310551075106310951066 10671070107110721062107610771080108610941064106510981101110211031104 1105109710961124113111301129106110591128112510561011101211331079111910851087111310911092109311231117106810881089109011201018101910201013105310481014 1015105110571016101711111112102810291041103110321100111510351116103610371023 10241021102210441058104510541078105011081107103010841033100810091005100711061109102710031010999116211621025116410261166116811701172117311741177117811771136117911371175117111761139114611451141 11421147114811431169116711571155114411561149115011511152115311541165114011381069107411351073116310821060116111341132112111141099108111271160104010431047104911591158 1180 1181 1182 1183 11841185 1186118711881189 1190 1191 1192 1193 11941195 1196 1197 1198 1199 1200 1201 120212031204120512061207120812091210121612151211121212131214 1217 1217122212251227122912311233123412351232123012281226122412231218121912201221 1236 1237 12381239124412451240124312411242 124612471247 1248 1249 1250 1251 1252 12521253125412551256 125712581259 1260126312651266126212641261 1267 1268 1269 1270 1271 1272 1273 1274 12751277127912821276 1303130413021300127812801297129812991295130112961283 12841281130512911294129312921290130612891288128612871285 1307 1308 1309 13101311131213131314 1315 1316 1317 1318 1319 13201321 1322 1323 1324 13251326 1327132913301333133413361338133913351337132813311332 134013411342134313441345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 13571358 1359 1360 1361 136213721377137513821364 1365137013731367 13681366137113801381137913761378136913631374 13831384 13851386 1387 13881389 1390 13911392 1393 1394 13951396140013971398 1399142914271403 140414071408140914101416142614231421141914221417141814141413140614121411143114321435 143614341433145014461437 14381440144114481444144514471428142514491424142014151442144314051430143914011402 1451 1452 14531454 1455 1456 1457 145814601459 1461 14631462 1464 1465 1466 14691470147114741475147614771478148615021499149714881489148714851483 148414821480 148114791472 147315031493 14941495149614681491149214671490149815001501 1504 1505 150615071508 1509151115131515151815171516151415121510 1519 1520 1521 1522 1523 15241525 1526 15271528 1529 1530 1531 153215331534153515361536 1537 1538 1539 1540 1541 1542 1543 1544 1545 154615471548 15491550 15511552 1553 1554 1555 15561557 15581559 1560 1561 1562 15631565156715921590156915881587158115861584158215761577157315721574 15751580158315791568157115641578157015661585158915911593 1594 1595 1596 15971598 15991600 1601 1602 16031604160516061607 1608 16091610 1611 1612 1613 1614 1615 1616 1617 1618 16191620 16211622 1623 16241625 1626 162716281629163016311632164416331634163516431637163816391640164116421636 1645 1646 1647 1648 1649 1650165116521653 16541655 1656 1657 1658 1659 1660 1661 1662 1663 16641665 16661667 1668 16691672 167016711673 16741676 1675 1677 1678 167916811682 16801683 16841698172317201714170617251702170117051694168917211719171517221731173517381742174416861751168717531691175616971758171717101711170817071703175917601807180617261808180518031727180117321771 17721770173417811739 17401779177517411773168517781780177417461755176417571752175417491750174817451688169017431700171617091692179918001802180417981795179717871791176617671768176917631762176117471765173717291718172417131777169516961699169317831704171217861789 17901728173317301794179617931736179217821784177617881785 1809 1810 1811 18121813 18141815 181618211818182018171819 1822182318241825 182618271828 1829 18301831 1832 1833 1834 1835 1836 1837 1838 1838 1839 1840 1841 1842 1843184418451846 1847 1848 18491850 18511852 1853 1854 1855 18561857 185818681869186018611862186718591865186318641866 1870 1871 1872 1873 1874 1875 1876 1877 18781879 1880 18811882 1883 18841885 1886 18871888 1889 189018911892189318941895189718981902190419061907190319051900190118991896 19081909 1910 1911 1912 19131914191519161917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1929 1930 1930 1931 1932 1933 1933 1934 1934 1935 1936 1936 1937 1937 1938 1939 1940 1940 1941 1941 1942 1943 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1952 1953 1954 1955 1956 1957 1958 1958 1959 1960 1961 1961 1962 1963 1963 1964 1965 1966 1966 1967 19681968 1969 19701970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1982 1983 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 20162017201820192020 2021 202220232024 2025 2025 2026 202620272027 2028 2028 2029 2029 2030 2031 2032 2033 2034 2035 2036 2037 2038 2039 2040 2041 2042 2043 2043 2044 2044 2045 2045 2046 2047 2047 2048 2048 2049 2049 2050 2050 2051 2051 2052 2052 2053 2054 2055 2056 2057 2058 2059 206020612062 2063 2064 2065 2066 2067 2068 2069 2070 2071 20722073 2074 20752076 2077 2078 2079 2080 2081 20822083 2084 2085 2086 2087 20882089 2090 2091 2092 2093 2094 2095 2096 2097 20982099 21002101 2102 21032104 2105 2106 2107 2108 2109 2110 2111 2112 2113 2114 2115 2116 2117 2118 2119212021212122212321242125212621272128 2129213021312132213321342135 2136 2137 2138 2139 2140 2141 2142 2143 2144 21452146 2147 2148214921502151215421522153 2155 2156 2157 2158 2159 2160 2161 2162 2163 2164 216521662167 2168 2169 2170 217121722173 21742175 2176 2177 2178 2179 2180 2181 21822183 218421852186 2187 21882189219021912192 2193 2194219521962197 2198 N64 2199 N62 2200 2201 N60 2202 2203 N36 2204 2205 N34 2206 N32 2207 2208 N30 2209 2210 N28 2211 2212 N26 2213 2214 N24 2215 2216 N22 2217 N20 2218 2219 E15 2220 2221 E16 2222 E17 2223 2224 E18 2225 2226 E19 2227 N510 2228 2229 N509 2230 2231 N508 2232 2233 N507 2234 N506 2235 2236 N505 2237 2238 N504 2239 2240 N503 2241 2242 N502 2243 2244 N501 2245 2246 W50 2247 W48 2248 2249 W46 2250 2251 2252W44 2253 2254W42 2255 2256W40 2257 W61 2258 2259 W63 2260 W65 2261 2262 W67 2263 2264 W69 2265 2266 W71 2267 2268 N70 2269 2270 N68 2271 2272 2273 N66 2274 2275 S49 2276 2277 S47 2278 2279 S45 2280 2281 S43 2282 2283 S41 2284 2285 S35 2286 S33 2287 2288 S31 2289 2290 S29 2291 2292 S27 2293 2294 S25 2295 2296 S23 2297 2298 2299 S21 2300 E1 2301 E2 2302 2303 2304E3 2305 2306E4 2307 D219 2308 2309 D217 2310 2311 D215 2312 2313 D213 2314 2315 D211 2316 2317 D229 2318 2319 D209 2320 2321 D207 2322 2323 D205 2324 2325 D203 2326 2327 D201 2328 2329 2330 2331 D216 2332 2333 D214 2334 2335 D212 2336 2337 D300 2338 2339 D210 2340 2341 D208 2342 2343 D206 2344 2345 D204 2346 2347 D202 2348 2349 D218 2350 2351 N141 2352 2353 N142 2354 N143 2355 2356 N144 2357 2358 N145 2359 2360 V135 2361 2362 2363 V132 2364 2365 V131 2366 2367 V133 2368 V134 2369 W125 2370 2371 W124 2372 2373 W122 2374 2375 W121 2376 W123 2377 2378 W126 2379 2380 TW2 2381 TW1 2382 2383 S111 2384 2385 S110 2386 23872388S108S1092389 2390 S107 2391 2392 2393S106 S105 2394 2395 S104 2396 2397 2398S102 2399 S101 2400 2401 S103 2402 2403 C23 2404 2405 C22 2406 C21 2407 2408 C20 2409 2410 C19 2411 2412 C18 2413 2414 C17 2415 2416 C16 2417 2418 C15 2419 2420 C14 2421 2422 C13 2423 2424 C12 2425 2426 C11 2427 2428 C10 2429 2430 C9 2431 2432 C35 2433 2434 C34 2435 2436 C33 2437 2438 C31 24392440C30 C29 2441 C28 2442 2443 C27 2444 2445 C26 2446 2447 C25 2448 2449 C24 2450 2451 TC1 2452 C1 2453 2454 C2 2455 2456 C3 2457 2458 C4 2459 2460 C5 2461 2462 C6R 2463 2464 C6 2465 2466 C6L 2467 2468 TB1 2469 2470 C7 2471 C8 2472 2473 M1 2474 2475 2476 M2 2477 M3 2478 2479 M4 2480 2481 M5 2482 2483 M6 2484 2485 M7 2486 2487 M8 2488 2489 M9 2490 2491 M10 2492 2493 M21 2494 2495 M22 2496 M23 2497 2498 2499 2500 2501 2502 2503 2504 2505 2506 2507 2508 2509 2510 2511 2512 2513 2514 2515 2516 2517 2518 2519 2520 2521 2522 2523 2524 2525 2526 2527 2528 2529 2530 2531 2532 2533 2534 2535 2536 2537 2538 25392540 2541 2542 2543 2544 25452546 2547 2548 2549 2550 2551 2552 2553 2554 2555 2556 2557 2558 2559 2560 2561 2562 2563 2564 2565 2566 2567 2568 2569 2570 2571 2572 2573 2574 2575 2576 2577 2578 2579 2580 2581 2582 2583 2584 25852586 2587 2588 2589 25902591 2592 2593 2594 2595 2596 2597 2598 2599 2600 2601 2602 2603 2604 2605 2606 2607 2608 2609 2610 2611 2612 2613 2614 2615 2616 2617 2618 2619 2620 2621 2622 2623 2624 2625 2626 2627 2628 2629 2630 2631 2632 2633 26342635 2636 2637 2638 2639 2640 2641 2642 2643 2644 2645 2646 2647 2648
Figure 2: Layout of taxiways at Hong Kong International Air-port
environment of the airport, there is only a certain allowable length of 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 approach to be used in real time under operating constrains and conditions. This time limit corresponds to an upper limit on the number of permutations that we can sample for a set of aircraft. The following two 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 will be required to cover all aircraft
• in common with many other applications, the GA can run for a fixed length of time, meaning either a larger popula-tion for few generapopula-tions, or a smaller populapopula-tion for many generations
• the run length for the routing algorithm increases with the number of aircraft, but due to set up times there is not an easy rule of thumb to determine the optimal number of aircraft to route with respect to running time
The run time for our A* implementation for a permutation of 20 aircraft on Hong Kong Airport is approximately 40s (DOH is around 5s, PEK is around 200s). Ideally we want the runs to complete in real time, so at 120s separation between aircraft, we have 2400s per window, so only about 60 evaluations allowed per window: 3 per aircraft. We can (and do) improve this situation by running evaluations of the permutations in parallel: with 24 threads we are limited 1440 evaluations for windows of 20 aircraft, or 72 evalua-tions per aircraft. Obviously we could add additional cores within reason to extend this further (at least 5x the number so that we can achieve the same run times for PEK as for HKG). The above might seem like a long-winded way of reaching the average figure of 72s per aircraft: it needs to be thought of from the perspective of a reasonable window length (in the range of 10-60) because due to set-up time, a run of the routing algorithm for a single aircraft is still several seconds, and while not constant is fairly consistent across this range of window sizes. These run times do not impact on the potential taxi time savings of the approach: the reason we limit the times is to ensure a high enough throughput that aircraft can have their routes allocated before they are due to start taxiing. In order to find a good balance between the population size, GA evaluation limit and window size, we ran a preliminary parameter tuning experiment on a subset of 120 aircraft at Hong Kong Airport. At 72 evaluations per aircraft this means we have 8640 evaluations for all 120 aircraft. Population size and window size were varied, then the GA evaluation limit computed by dividing the total number of allowed evaluations (8640) by the number of windows required to cover the 120 aircraft. The tuning was carried out using the Sequential Model-based Algorithm Configuration (SMAC) tool [23], with a limit of 1000 GA runs. The tuning also included the mutation and crossover rates for the GA: these are simply the proportion of offspring 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 have made the assumption that the configuration for HKG will carry over to the other airports. Strictly speaking the parameter tuning should be carried out for each, but in this study we are more interested in proving the concept rather than ensuring maximal performance.
6
RESULTS
Table 1 summarises the results. The first block of the table gives total taxi times in seconds for all routed aircraft at each airport when using the different approaches. The lower bound was determined by running the routing algorithm for each aircraft in isolation, avoiding any waiting times or detours. This is of course may not be achievable, but gives us some indication of performance. FCFS is the result when using the standard first-come-first-served order for allocating routes. “Exhaustive WSx” are the figures for the exhaustive rolling window approach, with window sizes of 2–6. “GA RW” are the average figures from 20 repeat runs of the GA rolling window approach with the tuned parameters (including a window size of 56). “GA all aircraft” was a single run of the GA conducted as a sanity check, working over the permutation of all aircraft, 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 or delay in seconds between the lower bound and the result found by each of the methods. The “reduction of gap” values are the relative improvement of the GA WS56 approach over FCFS, Exhaustive WS2 and Exhaustive WS3. The exhaustive search over rolling windows of 6 for HKG and 5 and 6 for PEK is omitted; in these cases the run times were prohibitive for practical use.
It is clear that all of the approaches offer an improvement over FCFS, reducing the gap between the routed times and the theoreti-cal lower bound for the situation where no aircraft are in conflict with each other. In general, increasing the window size means that permutations leading to faster routes can be found, although in some cases (e.g. DOH window sizes 5 and 6), increasing the size actually causes the delays to increase. This is because the change in window size causes conflicting2aircraft to fall on the bound-ary between windows where they previously did not: when this happens they cannot be swapped to improve the conflict situation. The GA with rolling window approach (GA RW) was able to find the permutation leading to the shortest overall taxi times for all three airports. In all, the reduction in the delay (gap) over the minimal times compared to FCFS was between 74 and 85%, with similar reductions for the exhaustive rolling window approaches with small window sizes.
The sanity-check single GA run on the whole permutation for each airport was not able to improve on the GA with rolling window: we expect that this was due to the large search space involved but this 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 using each method (‘Exhaustive’ abbreviated to ‘Exh.’). For the GA WS56 rolling window results, this is the mean over 20 runs, with standard deviation given in subscript
Total taxi time (s)
Method DOH HKG PEK
Lower bound 32 430 128 763 88 119 FCFS 32 685 129 366 88 707 Exh. WS2 32 685 129 229 88 703 Exh. WS3 32 685 129 274 88 542 Exh. WS4 32 515 129 066 88 640 Exh. WS5 32 515 128 954 Exh. WS6 32 684 GA RW 32 43535 128 852100 88 24679 GA all aircraft 32 515 129 070 88 192 FCFS gap 255 603 588 Exh. WS2 gap 255 466 584 Exh. WS3 gap 255 511 423 Exh. WS4 gap 85 303 521 Exh. WS5 gap 85 191 Exh. WS6 gap 254 GA RW gap 64 89 127 GA all aircraft gap 85 2307 1073 % reduction of gap over FCFS 74.90 85.24 78.40 % reduction of gap over Ex. WS2
74.90 80.90 78.25
% reduction of gap over Ex. WS3
74.90 82.58 69.98
The reductions in delay with respect to the total taxi times may seem insignificant in terms of percentages, but it is important to see how this translates into financial cost for this real world prob-lem. Given a lower bound of 128 763s for the movements of the aircraft at Hong Kong Airport, reducing the delays by 514s (0.40%) may seem trivial. However, this is for 506 aircraft, part of one day of movements. For the 421 000 aircraft movements in 2017, this amounts to a saving of 427 656s. Following the assumption of [9] that a single aisle jet aircraft uses 25 pounds of fuel per minute while taxiing, and an assumed $5 US per gallon of fuel (one gallon being 6.7lbs), the savings in fuel at Hong Kong Airport alone would be approximately $133k per year. However, it should be noted that other sources question the actual fuel rate for taxiing, which is possibly slightly overestimated by ICAO [25, 28].
7
CONCLUSION AND FUTURE WORK
Growing air traffic means heavier demands on existing airport in-frastructure including taxiways. Although taxiing is only a small part of an overall flight, ground movement is is responsible for a disproportionate amount of fuel burn. This is because jet engine are very efficient at cruising speed, but relatively inefficient while moving on the ground at low speed. Consequently, even small 5
improvements in efficiency in taxiing will reduce economic and en-vironmental costs, notwithstanding reduced frustration for delayed passengers.
An existing method based on A* has proven successful for rout-ing aircraft without conflicts, but its performance is dependent on the sequence in which aircraft are presented to it for routing. We proposed the application of a rolling window approach incorpo-rating a permutation-encoded genetic algorithm to find the best sequence in which to allocate routes to the aircraft. This was com-pared with FCFS, and an exhaustive search within small rolling windows. When applied to Doha, Hong Kong and Beijing Capital International Airports, the GA based approach was able to find bet-ter routings than FCFS or exhaustive search. Delays added by FCFS were reduced by over 70%. This simple application of a relatively naive genetic algorithm represents an effective improvement for aircraft taxi routing that could have substantial impact.
In terms of future directions to explore, rather than moving the complete window forward each time, a more continuous rolling window could be considered. For window size W , the order would be determined, n < W aircraft would be dispatched, the window moved on by n, and the next order for the next W aircraft found (potentially reordering the last W − 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 be reordered. Additionally, given that one of the key obstacles en-countered in this work was the long running time of the routing algorithm, we are investigating more advanced search algorithms such as model based algorithms (e.g. [5]) and surrogates (one possi-bility for permutations being [34]). Our model of aircraft movement also incorporates an estimation of fuel consumption for the allo-cated routes and we are particularly interested in exploring what the possible multi-objective trade-off between fuel consumption and taxi time looks like. Understanding this will be an important part of tackling the problem of airport congestion as air traffic continues to grow.
ACKNOWLEDGEMENT
Work funded by UK EPSRC [grants EP/N029577/2 and EP/N029496/2].
DATA ACCESS STATEMENT
The taxiway layout and aircraft movement data cannot be shared due to licensing restrictions.
REFERENCES
[1] L. Adacher, M. Flamini, and E. Romano. 2018. Airport Ground Movement Problem: Minimization of Delay and Pollution Emission. IEEE Trans. on Intelligent Trans-portation Systems PP, 99 (2018), 1–10. https://doi.org/10.1109/TITS.2017.2788798 [2] Jason A.D. Atkin. 2013. Airport Airside Optimisation Problems. In Automated Scheduling and Planning, A. Sima Uyar, Ender Ozcan, and Neil Urquhart (Eds.). Studies in Computational Intelligence, Vol. 505. Springer Berlin Heidelberg, 1–37. https://doi.org/10.1007/978-3-642-39304-4_1
[3] J. A. D. Atkin, E. K. Burke, and S. Ravizza. 2010. The Airport Ground Movement Problem: Past and Current Research and Future Directions. In 4th International Conference on Research in Air Transportation. 131–138.
[4] Jason A. D. Atkin, Geert De Maere, Edmund K. Burke, and John S. Greenwood. 2012. Addressing the Pushback Time Allocation Problem at Heathrow airport. Transport. Science 47, 4 (2012), 584 – 602. https://doi.org/10.1287/trsc.1120.0446 [5] M. Ayodele, J. McCall, O. Regnier-Coudert, and L. Bowie. 2017. A Random
Key based Estimation of Distribution Algorithm for the Permutation Flowshop Scheduling Problem. In 2017 IEEE Congress on Evolutionary Computation (CEC). 2364–2371. https://doi.org/10.1109/CEC.2017.7969591
[6] J. Bellingham, Y. Kuwata, and J. How. 2003. Stable Receding Horizon Trajectory Control for Complex Environments. In AIAA Guidance, Navigation, and Control Conference and Exhibit, AIAA 2003-5635.
[7] Una Benlic, Alexander E. I. Brownlee, and Edmund K. Burke. 2016. Heuris-tic search for the coupled runway sequencing and taxiway routing problem. Transportation Research Part C: Emerging Technologies 71 (October 2016). https: //doi.org/10.1016/j.trc.2016.08.004
[8] U. Benlic, E.K. Burke, and J.R. Woodward. 2014. Breakout Local Search for Gate Allocation Problem. Submitted manuscript (2014).
[9] C Brinton, C Provan, S Lent, T Prevost, and S Passmore. 2011. Collaborative departure queue management: An Example of collaborative decision making in the United States. In 9th USA/Europe Air Traffic Management Research and Development Seminar (ATM2011), Berlin, Germany.
[10] A. E. I. Brownlee, J. A. D. Atkin, J. A. W. Woodward, U. Benlic, and E. K. Burke. 2014. Airport Ground Movement: Real World Data Sets & Approaches to Handling Uncertainty. In Proc. PATAT. York, UK.
[11] J. Chen, M. Weiszer, G. Locatelli, S. Ravizza, J. A. Atkin, P. Stewart, and E. K. Burke. 2016. Toward a More Realistic, Cost-Effective, and Greener Ground Movement Through Active Routing: A Multiobjective Shortest Path Approach. IEEE Trans. on Intell. Transp. Systems 17, 12 (Dec 2016), 3524–3540. https://doi.org/10.1109/ TITS.2016.2587619
[12] J. Chen, M. Weiszer, P. Stewart, and M. Shabani. 2016. Toward a More Realistic, Cost-Effective, and Greener Ground Movement Through Active Routing–Part I: Optimal Speed Profile Generation. IEEE Trans. on Intel. Transp. Systems 17, 5 (2016), 1196–1209. https://doi.org/10.1109/TITS.2015.2477350
[13] G. L. Clare and A. G. Richards. 2011. Optimization of Taxiway Routing & Runway Scheduling. IEEE T Intell Tran Syst 12, 4 (2011), 1000–1013. https://doi.org/10. 1109/TITS.2011.2131650
[14] Lawrence Davis. 1985. Applying Adaptive Algorithms to Epistatic Domains. In Proceedings of the 9th International Joint Conference on Artificial Intelligence -Volume 1 (IJCAI’85). Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 162–164.
[15] J. Eaton, S. Yang, and M. Gongora. 2017. Ant Colony Optimization for Simulated Dynamic Multi-Objective Railway Junction Rescheduling. IEEE Transactions on Intelligent Transportation Systems 18, 11 (Nov 2017), 2980–2992. https://doi.org/ 10.1109/TITS.2017.2665042
[16] Eurocontrol. 2013. Challenges of Growth 2013-Task 4: European Air Traffic in 2035. (2013).
[17] C. Evertse and H.G. Visser. 2017. Real-time airport surface movement plan-ning: Minimizing aircraft emissions. Transportation Research Part C: Emerging Technologies 79 (jun 2017), 224–241. https://doi.org/10.1016/j.trc.2017.03.018 [18] J-B. Gotteland and N. Durand. 2003. Genetic Algorithms Applied to Airport
Ground Traffic Optimization. In Proc. IEEE CEC. Canberra, Australia, 544–551. https://doi.org/10.1109/CEC.2003.1299623
[19] J-B. Gotteland, N. Durand, J-M. Alliot, and E. Page. 2001. Aircraft Ground Traffic Optimization. In Proc. Int’l Air Traf. Mgmnt. R&D Seminar.
[20] J. Guépet, O. Briant, J.P. Gayon, and R. Acuna-Agost. 2016. The aircraft ground routing problem: Analysis of industry punctuality indicators in a sustainable perspective. European Journal of Operational Research 248, 3 (feb 2016), 827–839. https://doi.org/10.1016/j.ejor.2015.08.041
[21] X.B. Hu and W.H. Chen. 2005. Genetic algorithm based on receding horizon con-trol for arrival sequencing and scheduling. Engineering Applications of Artificial Intelligence 18, 5 (2005), 633 – 642.
[22] X.B. Hu and E. Di Paolo. 2008. Binary-Representation-Based Genetic Algorithm for Aircraft Arrival Sequencing and Scheduling. Intelligent Transportation Systems, IEEE Transactions on 9, 2 (June 2008), 301–310.
[23] F. Hutter, H.ËIJH. Hoos, and K. Leyton-Brown. 2011. Sequential Model-Based Optimization for General Algorithm Configuration. In LION-5 (LNCS). 507–523. [24] Y. Jiang, Z. Liao, and H. Zhang. 2013. A Collaborative Optimization Model
for Ground Taxi Based on Aircraft Priority. Math Probl Eng 2013 (2013), 1–9. https://doi.org/10.1155/2013/854364
[25] Brian Kim and Jawad Rachami. 2008. Aircraft emissions modeling under low power conditions. In 101st Air and Waste Management Association Annual Con-ference and Exhibition, Portland, OR, Paper. Citeseer.
[26] Lawrence Mandow and JosÃľ Luis PÃľrez De La Cruz. 2010. Multiobjective A* search with consistent heuristics. Journal of the ACM (JACM) 57, 5 (2010), 27. [27] Zbigniew Michalewicz. 1996. Genetic Algorithms + Data Structures = Evolution
Programs (3rd Ed.). Springer-Verlag, London, UK, UK.
[28] Kevin M Morris. 2005. Results from a number of surveys of power settings used during taxi operations. British Airways. EJT/KMM/1126/14.8 (2005).
[29] I. M. Oliver, D. J. Smith, and J. R. C. Holland. 1987. A Study of Permutation Crossover Operators on the Traveling Salesman Problem. In Proceedings of the Second International Conference on Genetic Algorithms on Genetic Algorithms and Their Application. L. Erlbaum Associates Inc., Hillsdale, NJ, USA, 224–230. [30] B. Pesic, N. Durand, and J-M. Alliot. 2001. Aircraft Ground Traffic Optimisation
using a Genetic Algorithm. In Proc. GECCO.
[31] Vincent R. Ragusa, H. David Mathias, Vera A. Kazakova, and Annie S. Wu. 2017. Enhanced Genetic Path Planning for Autonomous Flight. In Proceedings of the
Genetic and Evolutionary Computation Conference (GECCO ’17). ACM, New York, NY, USA, 1208–1215. https://doi.org/10.1145/3071178.3071293
[32] S. Ravizza, J. A. D. Atkin, and E. K. Burke. 2013. A more realistic approach for airport ground movement optimisation with stand holding. Journal of Scheduling 17, 5 (Oct 2013), 507–520. https://doi.org/10.1007/s10951-013-0323-3 [33] Daniel H. Stolfi and Enrique Alba. 2017. Computing New Optimized Routes for
GPS Navigators Using Evolutionary Algorithms. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO ’17). ACM, New York, NY, USA, 1240–1247. https://doi.org/10.1145/3071178.3071193
[34] J. Swan. 2017. Harmonic analysis and resynthesis of Sliding-Tile Puzzle heuristics. In 2017 IEEE Congress on Evolutionary Computation (CEC). 516–524. https://doi. org/10.1109/CEC.2017.7969355
[35] Michal Weiszer, Jun Chen, and Paul Stewart. 2015. A real-time Active Routing approach via a database for airport surface movement. Transp. Res. Pt. C: Emerg. Tech. 58 (2015), 127 – 145. https://doi.org/10.1016/j.trc.2015.07.011
[36] K. Yin, C. Tian, B. X. Wang, and L. Quadrifoglio. 2012. Analysis of Taxiway Aircraft Traffic at George Bush Intercontinental Airport, Houston, Texas. Transp. Res. Record 2266, 1 (2012), 85–94.
[37] Z.H. Zhan, J. Zhang, Y. Li, O. Liu, S.K. Kwok, W.H. Ip, and O. Kaynak. 2010. An Efficient Ant Colony System Based on Receding Horizon Control for the Aircraft Arrival Sequencing and Scheduling Problem. IEEE Transactions on Intelligent Transportation Systems 11, 2 (2010), 399–412.
[38] Hong-Yuan Zhang, Yu-Geng Xi, and Han-Yu Gu. 2007. A rolling window optimiza-tion method for large-scale WCDMA base staoptimiza-tions planning problem. European journal of operational research 183, 1 (2007), 370–383.
