Modeling Swarm Optimization on 4D Arrivals

TransLabDepartament of Computer Science

University of Brasilia

Modeling the Swarm Optimization to Build EffectiveContinuous Descent Arrival Sequences

Vitor Filincowsky Ribeiro, Daniel Alberto Pamplona,Jose A. T. G. Fregnani, Italo Romani de Oliveira, Li Weigang

November 2nd 2016

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Introduction 4D Navigation Optimization theory AMAN 4D

Agenda

1 Introduction

2 4D Navigation

3 Optimization theory

4 AMAN 4D

VF Ribeiro, DA Pamplona, JTG Fregnani, IR Oliveira, W Li

Modeling the Swarm Optimization to Build Effective Continuous Descent Arrival Sequences

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Introduction



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Introduction

Search for a shift in the Air Traffic Control and ManagementMethodology

Flight path of an aircraft through space and time (4D)

Performance Based Navigation procedures (PBN) to optimize andenhance the usage of air space resources

Descent, Climb and Cruise

Predicted an increase of 146% of the commercial fleet only in LatinAmerica



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Motivation

National ATM: establish the strategic evolution of theperformance-based National ATM System

Brazilian Air Force started an effort to implement PBN

Safety and performance needs of the National ATM program

Compliance to international requirements



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Motivation

Operations in Brazilian airports are performed without anycomputational support for decision making

Arrival sequencing is fully performed by the controller

Decision making process is error-prone

Impossible to evaluate the quality of results



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Motivation

Operations in Brazilian airports are performed without anycomputational support for decision making

Arrival sequencing is fully performed by the controller

Decision making process is error-prone

Impossible to evaluate the quality of results



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Objective

Main objective

Study and develop a computational methodology for the efficientmanagement of trajectories for commercial aircraft under 4D navigationparadigm



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4D Navigation



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What is 4D Navigation

Trajectory

Four-dimensional (4D) flight path of an aircraft through space (3D) andtime (1D)



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Trajectory Based Operations (TBO)

Aircraft’s navigation capability in space and time to improve efficiencyand predictability

Specified timing constraints at designated waypoints along the route



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Flight Management System

Aircraft guidance along a pre-specified flight path

Arrival at the approach gate at a time specified by ATC

Flight planning capabilities for cost efficient operation



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Continuous Descent Approach

CDA

Optimum descent profile while arriving at an airport

Continuously descending path, with a minimum of level flightsegments

Arriving aircraft descend from an optimal position with minimumthrust



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Continuous Descent Approach



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Goals of CDA

Enable the execution of a flight profile optimized to the operatingcapability of the aircraft

low engine thrust settingslow drag configuration

Reduce fuel burn and emissions during descent

Maximize operational efficiency while still addressing local airspacerequirements and constraints



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Air Traffic Coordination

Roles of ATC

Landing sequence and traffic flow integration

En-route conflict detection and resolution

Insertion of vertical and horizontal separation

Concerns on safety and overall operation cost



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Optimization task

Arrival coordination: aircraft want to arrive at a time within anoptimum time window

Aircraft sequencing at confluence points which collect incoming trafficfrom several airways

Individual costs as a matter of concern

Efficient operations

Arrival safety effectively ensured with a minimum, fair cost propagationamong the aircraft involved



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Optimization task

Arrival coordination: aircraft want to arrive at a time within anoptimum time window

Aircraft sequencing at confluence points which collect incoming trafficfrom several airways

Individual costs as a matter of concern

Efficient operations

Arrival safety effectively ensured with a minimum, fair cost propagationamong the aircraft involved



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Optimization theory



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Swarm Optimization

Overall efficiency depends on the collective behavior of all agentsinvolved

Particle swarm: entities involved in social interactions can produceintelligence beyond the pure individual cognitive abilities

Particle Swarm Optimization (PSO)

All population members remain active until the end of processing

Iterations improve the quality of problem solutions over time



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Swarm Optimization

Overall efficiency depends on the collective behavior of all agentsinvolved

Particle swarm: entities involved in social interactions can produceintelligence beyond the pure individual cognitive abilities


All population members remain active until the end of processing

Iterations improve the quality of problem solutions over time



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Entities (particles) are placed in the search space

Objective function is evaluated at the current location

Next movement is determined by a combination of personal bestlocations with those of other members of the swarm

Eventually, particles move closer to an optimum of the fitness function



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Swarm Optimization

Typical PSO problem

a search space represented by a set of positions H = x

an application f defined on H constrained to a domainf : H → C = {c}a semiorder {c, c′} : c � c′ in C, meaning that c is better orequivalent to c′

a fitness function φ



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Swarm Optimization

For each particle, three D-dimensional vectors:

Current position

set of coordinates representing a point in the search space

Best position found so far

pbest (personal best) stores the solution value

Velocity

”heading”of the particle

~vi = ω1~vi + ω2~U(0, 1) · (~pi − ~xi) + ω3

~U(0, 1) · (~pg − ~xi)

~xi = ~xi + ~vi



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AMAN 4D



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Modeling 4D systems

FMS time window calculation

Conflict detection at merging points

Aircraft scheduling

AMAN 4D



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Modeling 4D systems

Merge point concept

All arriving aircraft should cross a specific waypoint in order toperform the descent until the approach fix



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Goals

Goals for Aircraft

Minimization of individual cost

Calculation of an optimal descent profile

Calculation of a feasible time window in order to reach the pointwhere CDA should take place

Goals for ATC

Conflict resolution for aircraft with overlapping TW at merging points

Calculate new values for cruise speed and altitude

Minimize total scenario cost by assigning updated TW



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Goals

Goals for Aircraft

Minimization of individual cost

Calculation of an optimal descent profile

Calculation of a feasible time window in order to reach the pointwhere CDA should take place

Goals for ATC

Conflict resolution for aircraft with overlapping TW at merging points

Calculate new values for cruise speed and altitude

Minimize total scenario cost by assigning updated TW



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Aircraft time window calculation

Cost Index evaluation

CI =Ctime

Cfuel

Profile 1: minimum flight time → delay control

Profile 2: minimum fuel burn → fuel cost control



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ATC decision making process

Ensure safety and minimize global costs

1 Receive TW as input from aircraft

2 Enqueue aircraft by arrival time

partial order

3 Check for overlapping time windows

conflict detection

4 Build search space from possible configurations that solves conflicts

5 Select the optimum state and notify aircraft



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Particle Swarm decision making

Each conflicting aircraft will be a variable to compose the particles

Random time windows will be applied to each aircraft

randomization is constrained to the minimum and maximumperformance values

The fitness function φ is the overall cost to the scenario

estimate by ATC that says how good is the position occupied by theparticle

φj = −n∑

i=1

kji



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Particle Swarm decision making



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Aircraft implementation

Aircraft in the prototype act as agents that have their ownperformance standards

Simulated datalink communication between ATC and aircraft



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ATC implementation

Arrival schedules and speeding instructions

Receive TW and schedule aircraft

Cost Index and specific performance parameters are unknown by theATC, but the time parameters are well-known

Particle Swarm optimization algorithm



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ATC - Particle Swarm optimizer

Setup of default parameters

Each dimension in the particle represents an aircraft

Random positions and random velocities are attributed to eachparticle

positions represent arrival scheduleseach variable in the position vector is a time constraint for an aircraft

The fitness function is the shared global objective function to beminimized



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ATC - Particle Swarm optimizer

Each particle will occupy a different position in its immediateneighborhood after each algorithmic iteration

Updating the velocity of a particle changes its motion profile towardbetter positions

The best particle in the swarm is the one that assigns the less costlytime slots for the whole aircraft set

At the end of the processing, the best position found so far is the finalsolution



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Simulations and results

Test scenario: Presidente Juscelino Kubitschek International Airport inBrasılia (SBBR)

(2015) Domestic International Total

Aircraft 180972 5405 186377

PAX 19110040 711756 19821796

Cargo (kg) 37939488 1528177 39467665

No actual implementation of MP

a virtual MP is created by 150 nautical miles at landing runway

All arriving flights are selected at SBBR from 11:00am to 11:30amduring a regular workday

total of 26 flights scheduled



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Objective function is set to minimize the delay costs of each aircraftindividually

Fitness function corresponds to the estimated delay cost of the targettime assigned to aircraft

Every target time is checked in order to detect conflicts and off-limitspeed performances

When the simulation is ended, the best particle found is collected andthe corresponding target times are extracted

Result: 77% of the flights are able to have their desired TWaccomplished



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Conclusions

An AMAN system counting on two solutions of CDA has beendeveloped as a POC

Arrival coordination with PSO algorithm considers air traffic safetyand individual requirements in the extent of possibilities

Flights issued to later periods are more receptive to absorb delays

Coordination with other air traffic services is needed for proper flowcontrol

Individual interests of aircraft were successfully combined withairspace control constraints



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Thank you!



Engineering

Modeling Swarm Optimization on 4D Arrivals