Post on 22-May-2020
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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
ATM seminar, June 28, 2017 3
• International Air Transport Association (IATA) projected that the number of passengers will double to reach 7 billion/year by 2034
ATM seminar, June 28, 2017 3
• 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
ATM seminar, June 28, 2017 3
• 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• Improve design of arrival and departure procedures ➜ higher throughput
ATM seminar, June 28, 2017 3
• 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• Improve design of arrival and departure procedures ➜ higher throughput• In Air Traffic Management (ATM): humans-in-the-loop!
ATM seminar, June 28, 2017 3
• 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• 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)
ATM seminar, June 28, 2017 3
• 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• 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)๏ ATCOs assigned to sectors of the airspace (TMA)
ATM seminar, June 28, 2017 3
• 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• 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)๏ ATCOs assigned to sectors of the airspace (TMA)๏ Workload of the ATCOs should be balanced
ATM seminar, June 28, 2017 3
• 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• 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)๏ ATCOs assigned to sectors of the airspace (TMA)๏ Workload of the ATCOs should be balanced
• Plus: geometric constraints on the sector shape
ATM seminar, June 28, 2017 3
• 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• 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)๏ ATCOs assigned to sectors of the airspace (TMA)๏ Workload of the ATCOs should be balanced
• Plus: geometric constraints on the sector shape
Workload?
ATM seminar, June 28, 2017 3
• 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• 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)๏ ATCOs assigned to sectors of the airspace (TMA)๏ Workload of the ATCOs should be balanced
• Plus: geometric constraints on the sector shape
Workload?Various tasks contribute to airspace’s complexity and drive ATCO’s mental workload
ATM seminar, June 28, 2017 3
• 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• 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)๏ ATCOs assigned to sectors of the airspace (TMA)๏ Workload of the ATCOs should be balanced
• Plus: geometric constraints on the sector shape
Workload?Various tasks contribute to airspace’s complexity and drive ATCO’s mental workload• Taskload: objective demands of the ATCO’s monitoring task
ATM seminar, June 28, 2017 3
• 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• 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)๏ ATCOs assigned to sectors of the airspace (TMA)๏ Workload of the ATCOs should be balanced
• Plus: geometric constraints on the sector shape
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].
ATM seminar, June 28, 2017 3
• 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• 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)๏ ATCOs assigned to sectors of the airspace (TMA)๏ Workload of the ATCOs should be balanced
• Plus: geometric constraints on the sector shape
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.
ATM seminar, June 28, 2017 4
A sectorization of a simple polygon P is a partition of P into k disjoint subpolygons S1,…,Sk (Si ∩ Sj = ∅ ∀i≠j), such that .
ATM seminar, June 28, 2017 4
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
ATM seminar, June 28, 2017 4
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:
ATM seminar, June 28, 2017 4
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: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.
ATM seminar, June 28, 2017 4
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: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.
ATM seminar, June 28, 2017 4
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: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
ATM seminar, June 28, 2017 4
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: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
ATM seminar, June 28, 2017 4
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: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
ATM seminar, June 28, 2017 4
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: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
ATM seminar, June 28, 2017 4
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: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)
ATM seminar, June 28, 2017 4
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: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.)
ATM seminar, June 28, 2017 4
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: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 5
Grid-based IP formulation
ATM seminar, June 28, 2017
Grid-based IP formulation
6
ATM seminar, June 28, 2017
Grid-based IP formulation
6
Mixed Integer Program (MIP):
ATM seminar, June 28, 2017
Grid-based IP formulation
6
Mixed Integer Program (MIP):• Not new for sectorization
ATM seminar, June 28, 2017
Grid-based IP formulation
6
Mixed Integer Program (MIP):• Not new for sectorization• But so far: synthesis methods
ATM seminar, June 28, 2017
Grid-based IP formulation
6
Mixed Integer Program (MIP):• Not new for sectorization• But so far: synthesis methods
- Variable per elementary airspace piece
ATM seminar, June 28, 2017
Grid-based IP formulation
6
Mixed Integer Program (MIP):• Not new for sectorization• But so far: synthesis methods
- Variable per elementary airspace piece- Glue together pieces to sectors
ATM seminar, June 28, 2017
Grid-based IP formulation
6
Mixed Integer Program (MIP):• Not new for sectorization• But so far: synthesis methods
- Variable per elementary airspace piece- Glue together pieces to sectors
• We: variable per potential edge of sector boundary
ATM seminar, June 28, 2017
Grid-based IP formulation
7
ATM seminar, June 28, 2017
Grid-based IP formulation
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๏ Square grid in the TMA
ATM seminar, June 28, 2017
Grid-based IP formulation
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๏ Square grid in the TMA๏ G = (V,E):
๏ Every grid node connected to its 8 neighbors
ATM seminar, June 28, 2017
Grid-based IP formulation
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๏ Square grid in the TMA๏ G = (V,E):
๏ Every grid node connected to its 8 neighbors๏ N(i) = set of neighbors of i (including i)
ATM seminar, June 28, 2017
Grid-based IP formulation
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๏ Square grid in the TMA๏ G = (V,E):
๏ 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
ATM seminar, June 28, 2017
Grid-based IP formulation
7
๏ Square grid in the TMA๏ G = (V,E):
๏ 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.
`i,j
ATM seminar, June 28, 2017
Grid-based IP formulation
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๏ Square grid in the TMA๏ G = (V,E):
๏ 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} .
`i,j
ATM seminar, June 28, 2017
Grid-based IP formulation
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: edge (i,j) used for sector s
ATM seminar, June 28, 2017
Grid-based IP formulation
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All ccw boundary edges in S0
: edge (i,j) used for sector s
ATM seminar, June 28, 2017
Grid-based IP formulation
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All ccw boundary edges in S0
If (i,j) used for some sector, (j, i) has to be used as well.
: edge (i,j) used for sector s
ATM seminar, June 28, 2017
Grid-based IP formulation
8
All ccw boundary edges in S0
If (i,j) used for some sector, (j, i) has to be used as well.Sector cannot contain (i,j) and (j,i).
: edge (i,j) used for sector s
ATM seminar, June 28, 2017
Grid-based IP formulation
8
All ccw boundary edges in S0
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
: edge (i,j) used for sector s
ATM seminar, June 28, 2017
Grid-based IP formulation
8
All ccw boundary edges in S0
If (i,j) used for some sector, (j, i) has to be used as well.Sector cannot contain (i,j) and (j,i).
No edge in two sectors.
(i,j) in Sl, (j,i)
has to be in
another
sector
: edge (i,j) used for sector s
ATM seminar, June 28, 2017
Grid-based IP formulation
8
All ccw boundary edges in S0
If (i,j) used for some sector, (j, i) has to be used as well.Sector cannot contain (i,j) and (j,i).
No edge in two sectors.
Minimum size
(i,j) in Sl, (j,i)
has to be in
another
sector
: edge (i,j) used for sector s
ATM seminar, June 28, 2017
Grid-based IP formulation
8
All ccw boundary edges in S0
If (i,j) used for some sector, (j, i) has to be used as well.Sector cannot contain (i,j) and (j,i).
No edge in two sectors.
Minimum size
Indegree=outdegree for all vertices
(i,j) in Sl, (j,i)
has to be in
another
sector
: edge (i,j) used for sector s
ATM seminar, June 28, 2017
Grid-based IP formulation
8
All ccw boundary edges in S0
If (i,j) used for some sector, (j, i) has to be used as well.Sector cannot contain (i,j) and (j,i).
No edge in two sectors.
Minimum size
Indegree=outdegree for all vertices
A node has at most one ingoing edge per sector
(i,j) in Sl, (j,i)
has to be in
another
sector
: edge (i,j) used for sector s
ATM seminar, June 28, 2017
Grid-based IP formulation
8
All ccw boundary edges in S0
If (i,j) used for some sector, (j, i) has to be used as well.Sector cannot contain (i,j) and (j,i).
No edge in two sectors.
Minimum size
Indegree=outdegree for all vertices
A node has at most one ingoing edge per sector
(i,j) in Sl, (j,i)
has to be in
another
sector
: edge (i,j) used for sector s
⟹ Union of the |S| sectors completely covers the TMA.
ATM seminar, June 28, 2017
Grid-based IP formulation
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(a) Balanced Size
ATM seminar, June 28, 2017
Grid-based IP formulation
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(a) Balanced SizeWe need to assign area to sector selected by boundary edges!
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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]:
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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.
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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.
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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:
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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- ccw triangles contribute negative
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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- ccw triangles contribute negative
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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- ccw triangles contribute negative
• fi,j: signed area of the triangle (i,j) and r
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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- ccw triangles contribute negative
• fi,j: signed area of the triangle (i,j) and r
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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- ccw triangles contribute negative
• fi,j: signed area of the triangle (i,j) and r
Assigns area of sector s to as
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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- 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
ATM seminar, June 28, 2017
Grid-based IP formulation
9
(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- 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|
ATM seminar, June 28, 2017
Grid-based IP formulation
10
(b) Bounded Taskload / (c) Balanced Taskload
ATM seminar, June 28, 2017
Grid-based IP formulation
10
(b) Bounded Taskload / (c) Balanced TaskloadWe need to associate task load with a sector.
ATM seminar, June 28, 2017
Grid-based IP formulation
10
(b) Bounded Taskload / (c) Balanced TaskloadWe need to associate task load with a sector.• Overlay heat map with a grid.
ATM seminar, June 28, 2017
Grid-based IP formulation
10
(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.
ATM seminar, June 28, 2017
Grid-based IP formulation
10
(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.
ATM seminar, June 28, 2017
Grid-based IP formulation
10
(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
ATM seminar, June 28, 2017
Grid-based IP formulation
10
(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
ATM seminar, June 28, 2017
Grid-based IP formulation
10
(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
ATM seminar, June 28, 2017
Grid-based IP formulation
11
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious.
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
• Taskload imbalance(constraint c)
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
• Taskload imbalance(constraint c) • Number of sectors (input)
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
• Taskload imbalance(constraint c) • Number of sectors (input)
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
• 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)
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
• 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:
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
• 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:Given the current complexity map: user must allow larger imbalances between controller’s taskload, if having connected sectors is a necessary condition.
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
• 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: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:
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
• 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: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
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
• 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: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• In relation to complexity of other points ➜ no absolute threshold
ATM seminar, June 28, 2017
Grid-based IP formulation
11
Objective Function• Choice not obvious. • Used in literature:
• 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: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• In relation to complexity of other points ➜ no absolute threshold• Force points of relatively high complexity to be in interior
ATM seminar, June 28, 2017 12
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: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 12
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: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 12
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: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 12
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: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 12
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: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 12
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: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)
✔✔✔✔ Preprocessing
ATM seminar, June 28, 2017 12
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: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)
✔✔✔✔ Preprocessing
✔
ATM seminar, June 28, 2017 12
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: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)
✔✔✔✔ Preprocessing
✔
in a publication based on this work [ICNS 2017]
ATM seminar, June 28, 2017 13
Experimental Study: Arlanda Airport
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
14
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
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
14
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
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
14
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➞.
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
15
5 sectors: (c)Balanced taskload, (d) Connected sectors, (e) Nice shape, (f) Interior conflict points
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
15
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
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
15
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
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
15
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
5 sectors: (a)Balanced size, (d) Connected sectors, (e) Nice shape, (f) interior conflict points
No “c2-balanced” solution
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
15
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
5 sectors: (a)Balanced size, (d) Connected sectors, (e) Nice shape, (f) interior conflict points
c1=0.7
No “c2-balanced” solution
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
16
Influence of choosing wi,j :
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
16
Influence of choosing wi,j :|S|=2 ➜ One cut through rectangle
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
16
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
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
16
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
ATM seminar, June 28, 2017
Experimental Study: Arlanda Airport
16
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
ATM seminar, June 28, 2017 17
Conclusion/Outlook
ATM seminar, June 28, 2017
Conclusion/Outlook
18
Conclusion
Outlook
ATM seminar, June 28, 2017
Conclusion/Outlook
18
Conclusion• Sectorization method that balances sector task load
Outlook
ATM seminar, June 28, 2017
Conclusion/Outlook
18
Conclusion• Sectorization method that balances sector task load• Includes various geometrical constraints
Outlook
ATM seminar, June 28, 2017
Conclusion/Outlook
18
Conclusion• Sectorization method that balances sector task load• Includes various geometrical constraints• Results for Stockholm TMA
Outlook
ATM seminar, June 28, 2017
Conclusion/Outlook
18
Conclusion• Sectorization method that balances sector task load• Includes various geometrical constraints• Results for Stockholm TMA• Highly flexible approach
Outlook
ATM seminar, June 28, 2017
Conclusion/Outlook
18
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
ATM seminar, June 28, 2017
Conclusion/Outlook
18
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
ATM seminar, June 28, 2017
Conclusion/Outlook
18
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.
• We extended with convex sectors (ICNS 2017)Outlook
ATM seminar, June 28, 2017
Conclusion/Outlook
18
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.
• We extended with convex sectors (ICNS 2017)Outlook
ATM seminar, June 28, 2017
Conclusion/Outlook
18
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.
• We extended with convex sectors (ICNS 2017)• Allow usage of a few reflex vertices
Outlook
ATM seminar, June 28, 2017
Conclusion/Outlook
18
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.
• 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
ATM seminar, June 28, 2017
Conclusion/Outlook
18
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.
• 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
Outlook
ATM seminar, June 28, 2017
Conclusion/Outlook
18
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.
• 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
ATM seminar, June 28, 2017
Conclusion/Outlook
19
• 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