Optimization of a heterogeneous unmanned mission

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