A Novel MIP-based Airspace Sectorization for TMAs · ATM seminar, June 28, 2017 3 • International...

A Novel MIP-based Airspace Sectorization for TMAs Tobias Andersson Granberg, Tatiana Polishchuk, Valentin Polishchuk, Christiane Schmidt

ATM seminar, June 28, 2017 2

Introduction: Air transportation, Workload/Taskload, Sectorization

Grid-based IP formulation

Experimental Study: Arlanda Airport

Conclusion/Outlook

• International Air Transport Association (IATA) projected that the number of passengers will double to reach 7 billion/year by 2034

• Terminal Maneuvering Area (TMA) is particularly affected by congestion

• Terminal Maneuvering Area (TMA) is particularly affected by congestion• Improve design of arrival and departure procedures ➜ higher throughput

• Terminal Maneuvering Area (TMA) is particularly affected by congestion• Improve design of arrival and departure procedures ➜ higher throughput• In Air Traffic Management (ATM): humans-in-the-loop!

๏ Planes constantly monitored/guided by air traffic controllers (ATCOs)

๏ Planes constantly monitored/guided by air traffic controllers (ATCOs)๏ ATCOs assigned to sectors of the airspace (TMA)

๏ Planes constantly monitored/guided by air traffic controllers (ATCOs)๏ ATCOs assigned to sectors of the airspace (TMA)๏ Workload of the ATCOs should be balanced

• Plus: geometric constraints on the sector shape

Workload?

Workload?Various tasks contribute to airspace’s complexity and drive ATCO’s mental workload

Workload?Various tasks contribute to airspace’s complexity and drive ATCO’s mental workload• Taskload: objective demands of the ATCO’s monitoring task

Workload?Various tasks contribute to airspace’s complexity and drive ATCO’s mental workload• Taskload: objective demands of the ATCO’s monitoring task • We use heat maps of the density of weighted clicks as an input [Zohrevandi et al., 2016].

Workload?Various tasks contribute to airspace’s complexity and drive ATCO’s mental workload• Taskload: objective demands of the ATCO’s monitoring task • We use heat maps of the density of weighted clicks as an input [Zohrevandi et al., 2016].• BUT: we do not depend on specific maps.

A sectorization of a simple polygon P is a partition of P into k disjoint subpolygons S1,…,Sk (Si ∩ Sj = ∅ ∀i≠j), such that .

Si: sectors

Sectorization Problem:

Si: sectors

Sectorization Problem:Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors.

Si: sectors

Sectorization Problem:Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors.Find: A sectorization of P with k = |S| , fulfilling C.

Si: sectors

Sectorization Problem:Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors.Find: A sectorization of P with k = |S| , fulfilling C.(a) Balanced size

Si: sectors

Sectorization Problem:Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors.Find: A sectorization of P with k = |S| , fulfilling C.(a) Balanced size(b) Bounded task load

Si: sectors

Sectorization Problem:Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors.Find: A sectorization of P with k = |S| , fulfilling C.(a) Balanced size(b) Bounded task load(c) Balanced taskload

Si: sectors

Sectorization Problem:Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors.Find: A sectorization of P with k = |S| , fulfilling C.(a) Balanced size(b) Bounded task load(c) Balanced taskload(d) Connected sectors

Si: sectors

Sectorization Problem:Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors.Find: A sectorization of P with k = |S| , fulfilling C.(a) Balanced size(b) Bounded task load(c) Balanced taskload(d) Connected sectors(e) Nice shape (smooth boundary and an easily memorable shape)

Si: sectors

Sectorization Problem:Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors.Find: A sectorization of P with k = |S| , fulfilling C.(a) Balanced size(b) Bounded task load(c) Balanced taskload(d) Connected sectors(e) Nice shape (smooth boundary and an easily memorable shape)(f) Interior conflict points ( Points that require increased attention from ATCOs

should lie in the sector’s interior.)

Si: sectors

Sectorization Problem:Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors.Find: A sectorization of P with k = |S| , fulfilling C.(a) Balanced size(b) Bounded task load(c) Balanced taskload(d) Connected sectors(e) Nice shape (smooth boundary and an easily memorable shape)(f) Interior conflict points ( Points that require increased attention from ATCOs

should lie in the sector’s interior.)(g) Convex sectors ((straight-line) flight cannot enter and leave a convex sector

multiple times)

ATM seminar, June 28, 2017

Mixed Integer Program (MIP):

Mixed Integer Program (MIP):• Not new for sectorization

Mixed Integer Program (MIP):• Not new for sectorization• But so far: synthesis methods

- Variable per elementary airspace piece

- Variable per elementary airspace piece- Glue together pieces to sectors

• We: variable per potential edge of sector boundary

๏ Square grid in the TMA

๏ Square grid in the TMA๏ G = (V,E):

๏ Every grid node connected to its 8 neighbors

๏ Every grid node connected to its 8 neighbors๏ N(i) = set of neighbors of i (including i)

๏ Every grid node connected to its 8 neighbors๏ N(i) = set of neighbors of i (including i)๏ length of an edge (i, j)`i,j

๏ Every grid node connected to its 8 neighbors๏ N(i) = set of neighbors of i (including i)๏ length of an edge (i, j)

Main idea: use an artificial sector, S0, that encompasses the complete boundary of P, using all counterclockwise (ccw) edges.

๏ Every grid node connected to its 8 neighbors๏ N(i) = set of neighbors of i (including i)๏ length of an edge (i, j)

Main idea: use an artificial sector, S0, that encompasses the complete boundary of P, using all counterclockwise (ccw) edges. We use sectors in S* = S ∪ S0 with S = {S1,…,Sk} .

: edge (i,j) used for sector s

All ccw boundary edges in S0

If (i,j) used for some sector, (j, i) has to be used as well.

If (i,j) used for some sector, (j, i) has to be used as well.Sector cannot contain (i,j) and (j,i).

(i,j) in Sl, (j,i)

has to be in

another

sector

No edge in two sectors.

(i,j) in Sl, (j,i)

has to be in

another

sector

Minimum size

(i,j) in Sl, (j,i)

has to be in

another

sector

Minimum size

Indegree=outdegree for all vertices

(i,j) in Sl, (j,i)

has to be in

another

sector

Minimum size

A node has at most one ingoing edge per sector

(i,j) in Sl, (j,i)

has to be in

another

sector

Minimum size

A node has at most one ingoing edge per sector

(i,j) in Sl, (j,i)

has to be in

another

sector

⟹ Union of the |S| sectors completely covers the TMA.

(a) Balanced Size

(a) Balanced SizeWe need to assign area to sector selected by boundary edges!

(a) Balanced SizeWe need to assign area to sector selected by boundary edges!Area of polygon P with rational vertices and can be computed efficiently [Fekete et al., 2015]:

(a) Balanced SizeWe need to assign area to sector selected by boundary edges!Area of polygon P with rational vertices and can be computed efficiently [Fekete et al., 2015]:• We introduce reference point r.

(a) Balanced SizeWe need to assign area to sector selected by boundary edges!Area of polygon P with rational vertices and can be computed efficiently [Fekete et al., 2015]:• We introduce reference point r.• We compute the area of the triangle of each directed edge e of P.

(a) Balanced SizeWe need to assign area to sector selected by boundary edges!Area of polygon P with rational vertices and can be computed efficiently [Fekete et al., 2015]:• We introduce reference point r.• We compute the area of the triangle of each directed edge e of P.• We sum up the triangle area for all edges of P:

- cw triangles contribute positive

- cw triangles contribute positive- ccw triangles contribute negative

• fi,j: signed area of the triangle (i,j) and r

Assigns area of sector s to as

Sum of areas = area of S0

as � aLB 8s 2 S, aLB = c1 · a0/|S|

(b) Bounded Taskload / (c) Balanced Taskload

(b) Bounded Taskload / (c) Balanced TaskloadWe need to associate task load with a sector.

(b) Bounded Taskload / (c) Balanced TaskloadWe need to associate task load with a sector.• Overlay heat map with a grid.

(b) Bounded Taskload / (c) Balanced TaskloadWe need to associate task load with a sector.• Overlay heat map with a grid.• Extract values at the grid points.

(b) Bounded Taskload / (c) Balanced TaskloadWe need to associate task load with a sector.• Overlay heat map with a grid.• Extract values at the grid points.• Use discretized heat map.

(b) Bounded Taskload / (c) Balanced TaskloadWe need to associate task load with a sector.• Overlay heat map with a grid.• Extract values at the grid points.• Use discretized heat map.• Each discrete heat map point q: “heat value” hq

(b) Bounded Taskload / (c) Balanced TaskloadWe need to associate task load with a sector.• Overlay heat map with a grid.• Extract values at the grid points.• Use discretized heat map.• Each discrete heat map point q: “heat value” hq• Let the sign of fi,j be pi,j

Objective Function

Objective Function• Choice not obvious.

Objective Function• Choice not obvious. • Used in literature:

• Taskload imbalance(constraint c)

• Taskload imbalance(constraint c) • Number of sectors (input)

• If we want to balance the area of the sectors, but are not interested in the sector taskload, this objective function ensures that sectors are connected (constraint d)

• With taskload: only connected sectors if c2 allows it:

• With taskload: only connected sectors if c2 allows it:Given the current complexity map: user must allow larger imbalances between controller’s taskload, if having connected sectors is a necessary condition.

• With taskload: only connected sectors if c2 allows it:Given the current complexity map: user must allow larger imbalances between controller’s taskload, if having connected sectors is a necessary condition.• With constraint (f), interior conflict points:

• Points with higher complexity should be in sector’s interior

• Points with higher complexity should be in sector’s interior• In relation to complexity of other points ➜ no absolute threshold

• Points with higher complexity should be in sector’s interior• In relation to complexity of other points ➜ no absolute threshold• Force points of relatively high complexity to be in interior

Si: sectors

Sectorization Problem:Given: The coordinates of the TMA, defining a polygon P , the number of sectors |S|, and a set C of constraints on the resulting sectors. Find: A sectorization of P with k = |S| , fulfilling C.(a) Balanced size(b) Bounded task load(c) Balanced taskload(d) Connected sectors(e) Nice shape (smooth boundary and an easily memorable shape) (f) Interior conflict points ( Points that require increased attention from ATCOs

multiple times)

Si: sectors

multiple times)

Si: sectors

multiple times)

✔✔

Si: sectors

multiple times)

✔✔✔

Si: sectors

multiple times)

✔✔✔✔

Si: sectors

multiple times)

✔✔✔✔ Preprocessing

Si: sectors

multiple times)

Si: sectors

multiple times)

in a publication based on this work [ICNS 2017]

AMPL and CPLEX 12.6 on a single server with 24GB RAM and four kernels running on Linux. Each instance was run until a solution with less than 1% gap had not been found, or for a maximum of one CPU-hour. No instance finished with an optimality gap of more than 6%.

(c)Balanced taskload, (d) Connected sectors, (e) Nice shape

(c)Balanced taskload, (d) Connected sectors, (e) Nice shape, (g) Interior Conflict Points

wi,j = hi +hj. ←𝛾 = 0.9 𝛾= 0.5➞.

5 sectors: (c)Balanced taskload, (d) Connected sectors, (e) Nice shape, (f) Interior conflict points

wi,j = hi +hj, 𝛾= 0.5 c2=0.9

No “c2-balanced” solution

wi,j = hi +hj, 𝛾= 0.5 c2=0.9

5 sectors: (a)Balanced size, (d) Connected sectors, (e) Nice shape, (f) interior conflict points

wi,j = hi +hj, 𝛾= 0.5 c2=0.9

5 sectors: (a)Balanced size, (d) Connected sectors, (e) Nice shape, (f) interior conflict points

c1=0.7

Influence of choosing wi,j :

Influence of choosing wi,j :|S|=2 ➜ One cut through rectangle

(c)Balanced task load, (d) Connected sectors, (e) Nice shape, (g) Interior Conflict Points

𝛾=1 𝛾=0.5 and 𝛾=0.5 and

Conclusion/Outlook

Conclusion

Outlook

Conclusion/Outlook

Conclusion• Sectorization method that balances sector task load

Outlook

Conclusion/Outlook

Conclusion• Sectorization method that balances sector task load• Includes various geometrical constraints

Outlook

Conclusion/Outlook

Conclusion• Sectorization method that balances sector task load• Includes various geometrical constraints• Results for Stockholm TMA

Outlook

Conclusion/Outlook

Conclusion• Sectorization method that balances sector task load• Includes various geometrical constraints• Results for Stockholm TMA• Highly flexible approach

Outlook

Conclusion/Outlook

Conclusion• Sectorization method that balances sector task load• Includes various geometrical constraints• Results for Stockholm TMA• Highly flexible approach• Fine-grained view on the TMA

Outlook

Conclusion/Outlook

Conclusion• Sectorization method that balances sector task load• Includes various geometrical constraints• Results for Stockholm TMA• Highly flexible approach• Fine-grained view on the TMA• Easily integrates SUA etc.

Outlook

Conclusion/Outlook

• We extended with convex sectors (ICNS 2017)Outlook

Conclusion/Outlook

• We extended with convex sectors (ICNS 2017)Outlook

Conclusion/Outlook

• We extended with convex sectors (ICNS 2017)• Allow usage of a few reflex vertices

Outlook

Conclusion/Outlook

• We extended with convex sectors (ICNS 2017)• Allow usage of a few reflex vertices➡limit the total deviation from a maximum interior degree of 180 of reflex

vertices per sector

Outlook

Conclusion/Outlook

vertices per sector• Detailed evaluation by ATCOs

Outlook

Conclusion/Outlook

vertices per sector• Detailed evaluation by ATCOs• Combine with MIP for SIDs and STARs to an integrated design

Outlook

Conclusion/Outlook

• Sectorization method that balances sector task load • Includes various geometrical constraints • Results for Stockholm TMA • Highly flexible approach • Fine-grained view on the TMA • Easily integrates SUA etc.

• We extended with convex sectors (ICNS 2017) • Allow usage of a few reflex vertices ➡limit the total deviation from a maximum interior degree of 180 of reflex

vertices per sector • Detailed evaluation by ATCOs • Combine with MIP for SIDs and STARs to an integrated design

Outlook

THANK YOU.Conclusion

A Novel MIP-based Airspace Sectorization for TMAs · ATM seminar, June 28, 2017 3 • International...

Documents

Transcript of A Novel MIP-based Airspace Sectorization for TMAs · ATM seminar, June 28, 2017 3 • International...

Sectorization macro risk of flooding in the Torbes river ...€¦ · MACROSECTORIZACIÓN DEL RIESGO DE INUNDACIÓN EN LA CUENCA DEL RÍO TORBES Sectorization macro risk of flooding

MIP Brochure

Implementation of WiFiRe PHY Sectorization in OPNETsri/students/sreedhar-slides.pdf · Implementation of WiFiRe PHY Sectorization in OPNET P Sreedhar Reddy Roll No. 06305024 24th

TMAs, Addition of (6) TMAs and addition of associated ...

Welcome to FHWA’s TMAS version 2.0 Demonstration

MIP MELON_DIAPHANIA.pdf

Tmas presentation

Flood Map Modernization 1 1 MIP: SOMA. Flood Map Modernization 2 2 SOMA APPLICATION IN MIP MIP HOME PAGE.

MIP Guidance (MIP-G)

Chris tmas

Manual MIP

Implementation of WiFiRe PHY Sectorization in OPNETsri/students/sreedhar-thesis.pdf · Implementation of WiFiRe PHY Sectorization in ... 1 Introduction and Motivation 1 ... Specialized

MCQs on TMAs and Vasculitis

Submit Mip

Mip 180111

Mip Folder

An Evaluation of Operational Airspace Sectorization ......1 1 An Evaluation of Operational Airspace Sectorization Integrated System (OASIS) Advisory Tool Paul U. Lee1, Richard Mogford

TMAS PIP WEB - Bartley Corp

STATIC SECTORIZATION APPROACH TO DYNAMIC …catsr.ite.gmu.edu/pubs/147kulka.pdf · 1 STATIC SECTORIZATION APPROACH TO DYNAMIC AIRSPACE CONFIGURATION USING APPROXIMATE DYNAMIC PROGRAMMING

Psychiatric sectorization