Algorithms. Application to the French airspace LFEE (Reims) Judicaël Bedouet, Thomas Dubot, Luis Basora

Transcription

1 Towards an Application to the French airspace LFEE (Reims), Thomas Dubot, Luis Basora ONERA,the French Aerospace Lab 6 th SESAR Innovation Days November 10 th 2016, TU Delft 1/28

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4 Towards an problem I'm a FMP. I group elementary sectors (ES) to form control sectors (CS). Judicae l I FMP: Flow Management Position I From Short-Term Planning to Pre-Tactical I Sector configuration = set of CS for a given period of time. 4/28

5 Motivation Tch,gtchg?gThesegsame oldgmanualgmethods fromgtheg20thgcentury... Whatgaboutgflexibleg modulargdynamicgairspace configurationsg? SESAR 5/28

6 Ambitions Hi,RIRhaveRplentyRofRscientific methodsrtorhelpryou. Hmm...ROK,RbutRIRwant conventionalrsectors RstabilityRoverRtime! SESAR 6/28

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8 - Graph G = (V, E) How I see the world LFEEHH LFEEHE LFEEHR LFEEHN LFEEE LFEEKE LFEEKD LFEEKN LFEESE LFEEUE LFEEKF LFEEUB LFEEUF LFEEKH LFEEKR LFEEUN LFEEUH LFEEXE LFEEUR LFEEXH LFEEXR V the set the building blocks E the set of edges (direct trajectories between two blocks) D v (δt) density for vertex v during δt C e (δt) coordination for edge e during δt 8/28

9 Partition constraints LFEE4E LFEEE LFEEHE LFEESE4H LFEEKD2F LFEEKD LFEEHBN LFEEHN LFEEUB LFEE4R LFEEUKBN LFEEKN LFEESE LFEEHH LFEEUE LFEEKE LFEEKF LFEEHR LFEEUN LFEEUH LFEEKH LFEEXH LFEEXE LFEEUF LFEEKR LFEEXR LFEEUR P k (δt) = S 1,..., S k S 1 = LFEEHBN = {LFEEUB, LFEEHN}, S 2 =... i 1,..., k, S i i, j 1,..., k, i j, S i S j = i 1,...,k S i = E i 1,...k, S i satisfies the connectivity constraint 9/28

10 Balance objective LFEE4E (D = 9.7) LFEEE LFEEHE LFEEKD2F (D = 9.8) LFEEKD LFEEHBN (D = 2.5) LFEEUKBN (D = 4.3) LFEEHN LFEEUB LFEEKN LFEESE4H (D = 9.6) LFEE4R (D = 8) LFEESE LFEEHH LFEEUE LFEEKE LFEEKF LFEEHR LFEEUN LFEEUH LFEEKH LFEEXE LFEEUF LFEEKR LFEEUR LFEEXH LFEEXR Definition balance(p k (δt)) = D Si (δt) D i S i (δt) k i where D Si (δt) = D v (δt) v S i D Si (δt) i = 7.3 k balance(p 6 ) = /28

11 Cut objective LFEE4E LFEEKD2F LFEEHBN LFEEE LFEEHE LFEEKD LFEEHN LFEEUB LFEESE4H LFEE4R LFEESE LFEEHH LFEEUE LFEEKE LFEEKF LFEEHR LFEEUKBN LFEEKN LFEEUN LFEEUH LFEEKH LFEEXE LFEEUF LFEEKR LFEEUR LFEEXH LFEEXR Definition cut(p k (δt)) = cut(δt, S i, S j ) i<j where cut(δt, S i, S j ) = C (v1,v 2)(δt) v 1 S i,v 2 S j 11/28

12 Compactness objective Definition compactness(p k (δt)) = compactness(s i ) i volume(j) j prisms of S i where compactness(s i ) = volume(cover(i) ACC) cover(i) is the smallest prism which includes all the prisms of i 12/28

13 Other objectives that may be considered the total number of re-entries the total number of short transits the total number of overloads... 13/28

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15 Determining all conventional solutions Exhaustive search tree Combining conventional sectors Use of cut rules to rapidly explore the tree i, j 1,..., k, S i S j i 1,...,k S i = E Remaining nodes will not ensure i 1,...,k S i = E Applications Reims (LFEE) - 21 ES - 58 CS - 17 positions conventional sector configurations / Brest (LFRR) - 32 ES CS - 18 positions conventional sector configurations / /28

16 configurations - Pareto-optimal solutions cut(a) < cut (C) A C A dominates C B dominates C We keep solutions from the first Pareto fronts. B balance(a) < balance (C) 16/28

17 Now,AcanAIAalsoApropose nonaconventionalasectors? OK,AbutAonlyAifAIAcan decideatoaintegrateathem oranotainamyacatalogue. SESAR 17/28

18 Simulated Annealing optimisation Disorganising ( ) 1 min αcut(p k ) + βbalance(p k ) + compactness 2 (P k ) Reforming min (1/compactness(P k )) such that balance(p k ) balance(p initial k ) cut(p k ) cut(p initial k ) 18/28

19 over time And we favor collapsing / decollapsing operations. 19/28

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21 Towards an Scenario Comparison to the sector configuration plan of a very busy day of traffic (2015, June 26th ). Judicae l 21/28

22 An initial solution its refinement Conventional sector configuration Balance: Cut: Refined sector configuration /28

23 Balance along the day Balance along the day Average gain : 12.9% 23/28

24 Cut along the day Cut along the day Average gain : 3.4% 24/28

25 Cell-based distance along the day Cell-based distance along the day 25/28

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27 perspectives We can improve the workload distribution while keeping compact sectors ensuring stability over time Integrated to a decision support tool Perspectives: Improving objectives such as workload distribution overloads Determining the opening times Increasing the number of blocks Using multi-objective techniques to refine 27/28

28 Questions? 28/28