Yves BoussemartAnna Massie
Brian Mekdeci
Optimization of a heterogeneous unmanned
mission
Motivation
2
Unmanned VehiclesWide variety of uses:
SurveillanceSearch & rescueMiningDull, Dirty, DangerousProblem:
Given a missionOptimal # of UVs?Optimal operator
strategies
Problem Formulation
3
Multiple heterogeneous UVs, single humanQueuing problem
Human is serverEvents are when UVs need attentionService is when human interacts
Discrete event simulator
Model Disciplines
4
Cognitive Psychology
UV Operations
Queuing Theory
Optimization
5
Objectives (J)PerformanceCostUtilization
Design vector (x)# of vehicles
MALE, HALE,UUVOperator strategySwitching
PrioritiesRe-plan
• Parameters(p)– Mission
– Scoring methods– Time
– Vehicle Spec– Arrival rates– Service times– Costs
• Constraints (g)• Queuing• Maximum # of
vehicles
Model Diagram
6
Mission
Situational Awarenes
s
Human Server
Performance
Parameters
Design variables
Constraints
OptimizationTarget
Objectives
Single Objective FormulationGradient Based (SQP)
• JScore: 159.39
• X*:– NH=20– NM=12– NU=12– RS=53.0– SS=1 [UAV>UV]
• Time~20 seconds
• JScore: 276.004
• X*:– NH=19– NM=5– NU=1– RS=88.06– SS=1 [UAV > UV]
• Time~220 seconds
Simulated Annealing
Algorithm Tuning – Simulated Annealing
Choose cooling schedule to optimize performance (exp. cooling,To=100, neq=5, nfrozen=3): dT = 0.75
Performance vs dT
175
200
225
250
275
300
0 0.2 0.4 0.6 0.8 1
dT
Sco
re
Sensitivity Analysis
NH NM NU RS SS PERF
Upper Bounds 20 20 20 100.0 -
Lower Bounds 1 1 1 1.0 1 6.0
Initial Vector (x0) 1 1 1 10.58 3 12.27
Basis (x*) 20 12 15 53.0 1 159.39
∆ # of HALEs 22 12 15 53.0 1 171.55
∆ #of MALEs 20 13 15 53.0 1 161.47
∆ #of UUVs 20 12 17 53.0 1 156.2
∆ Re-plan Strategy 20 12 15 59.0 1 161.45
∆ Switching Strategy 20 12 15 53.0 2 67.62
∆ Switching Strategy 20 12 15 53.0 3 101.5
Multi-objective OptimizationPareto Front: Weighted Sum & Gradient Based
Optimization(much faster than heuristic based)
1 s.t.,min 3
1cos
21 i
itscore
mo sf
Cost
sf
ScoreJ SfCost= (276/76500)=3.6E-3
Sfscore= 1.0
Post Optimality AnalysisYerkes-Dodson
Pareto
Cost
Score
Multi-objective optimizationFull Factorial
3061 Total points502 non-
dominated solutions
Post Optimality AnalysisRe-plan strategy and
Switching Strategy7*3 ANOVA to test effect on
score and utilization
Pareto Front Design Points All Design Points
RS SS RS SS
Score F 3.644 6.793 0.132 8.19
p 0.002 0.001 0.992 <0.001
Utilization F 10.937 2.261 35.098 7.119
p <0.001 0.105 <0.001 0.001
Post Optimality AnalysisNumber of HALEs, MALEs, and UUVs
5*5*5 ANOVA to test score, utilization and costAll independent variables significant for all
three dependent variables
All Points Pareto Frontier Points
Design trade offNumber of Vehicles:
Higher number leads to higher score, cost and utilization
Switching strategy:Using a priority strategy of UAVs over UUVs
allows a higher score, while maintaining similar cost and utilization
Replan StrategyHaving a higher replan time of ~20 seconds
does not significantly increase the score, utilization or cost
Lessons Learned1. Neither the gradient based (170) nor the
simulated annealing (276) algorithm was able to find the absolute maximum score (298)
2. Matlab had a finite # of times that it could call our java program – making it the largest constraint on the SA and full factorial analysis
3. Difficulty using interval and categorical data
ConclusionsCan optimize a model for human-system
interaction in the context of unmanned vehicle supervision
Can forecast the capacity of a human given certain mission parametersLarger number of vehicles increased the cost
linearly, but the cognitive capabilities of an operator limited how high utilization and score could increase
Thanks!
Questions?
Number of MALEs
Number of HALEs
Number of UUVs
• Re-plan strategy and Switching Strategy– 7*3 ANOVA to test effect on score and utilization
• Pareto Front– Score: Significant Difference for both RS (F=3.644, p=.002) and SS
(F=6.793, p=.001)– Cost: Significant Difference for both RS (F=3.982, p=.001) and SS
(F=6.668, p=.001)– Utilization: Significant Difference for both RS (F=3.644, p=.002) and
SS (F=6.793, p=.001)• Non-Pareto Front
– Score: Significant Difference for SS (F=8.190, p<.001) but not SS (F=0.132, p=.992)
– Cost: Significant Difference for both RS (F = 6.789, p<.001) and SS (F=149.14, p<.001)
– Utilization: Significant Difference for both RS (F=35.098, p<.001) and SS (F = 7.119, p=.001)
Pareto
Pareto