Multi-Objective Optimization for Selecting and Scheduling - - PowerPoint PPT Presentation

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Multi-Objective Optimization for Selecting and Scheduling - - PowerPoint PPT Presentation

Oct 31, 2022 306 likes •619 views

Multi-Objective Optimization for Selecting and Scheduling Observations of Agile Earth Observing Satellites By Panwadee Tangpattanakul Directors : Pierre Lopez Nicolas Jozefowiez 2 Contents About our work Multi-Objective Optimization

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Multi-Objective Optimization for Selecting and Scheduling Observations

  • f Agile Earth Observing Satellites

By Panwadee Tangpattanakul Directors : Pierre Lopez Nicolas Jozefowiez

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Contents

  • About our work
  • Multi-Objective Optimization
  • Genetic Algorithm for Multi-Objective Optimization
  • Implementation and Results
  • Conclusions and Future Works

2

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About our work

Agile Earth observing satellites (agile EOS)

  • Mission :
  • Acquire photographs on the Earth’s surface, in

response to observation requests from several users

  • Management problem :
  • Select and schedule a subset of photographs

from a set of candidates

  • Maximize profit
  • Minimize the maximum profit difference

between users (ensure fairness)

  • Satisfy imperative constraints
  • Time windows
  • No overlapping images
  • Sufficient transition times
  • Each strip is acquired in only 1 direction
  • Stereoscopic constraint

3 About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Introduction

  • Types of Earth Observing Satellites
  • SPOT 5
  • 3 cameras (Front, Middle, Rear)
  • Agile
  • Single camera
  • 3 degrees of freedom (roll, pitch, yaw)
  • Profit calculation
  • gains
  • partial acquisition
  • piecewise linear function

Ref: Bensana et al. (1999), Lemaître et al. (2002)

4 About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

P(x) x 0.4 0.7 1 0.1 0.4 1

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  • Selecting and scheduling of multi-user requests
  • Fairness measurement is the maximum value of profit difference between users

Introduction

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P1 = 12 P4 = 8 P2 = 3 P3 = 6 P5 = 4 User 1 User 2

Time Requests from

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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SLIDE 6
  • Selecting and scheduling of multi-user requests
  • Fairness measurement is the maximum value of profit difference between users

Introduction

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P1 = 12 P4 = 8 P2 = 3 P3 = 6 P5 = 4 User 1 User 2

Time Requests from Solution 1 : (P1,P2,P3) Total profit = 21 Fairness : 21

Fairness Total profit

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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  • Selecting and scheduling of multi-user requests
  • Fairness measurement is the maximum value of profit difference between users

Introduction

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P1 = 12 P4 = 8 P2 = 3 P3 = 6 P5 = 4 User 1 User 2

Time Requests from Solution 1 : (P1,P2,P3) Total profit = 21 Fairness : 21 Solution 2 : (P4,P2,P3) Total profit = 17 Fairness : 1

Fairness Total profit

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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SLIDE 8
  • Selecting and scheduling of multi-user requests
  • Fairness measurement is the maximum value of profit difference between users

Introduction

8

P1 = 12 P4 = 8 P2 = 3 P3 = 6 P5 = 4 User 1 User 2

Time Requests from Solution 1 : (P1,P2,P3) Total profit = 21 Fairness : 21 Solution 2 : (P4,P2,P3) Total profit = 17 Fairness : 1 Solution 3 : (P1,P2,P5) Total profit = 19 Fairness : 11

Fairness Total profit

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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SLIDE 9
  • Selecting and scheduling of multi-user requests
  • Fairness measurement is the maximum value of profit difference between users

Introduction

9

P1 = 12 P4 = 8 P2 = 3 P3 = 6 P5 = 4 User 1 User 2

Time Requests from Solution 1 : (P1,P2,P3) Total profit = 21 Fairness : 21 Solution 2 : (P4,P2,P3) Total profit = 17 Fairness : 1 Solution 3 : (P1,P2,P5) Total profit = 19 Fairness : 11 Solution 4 : (P4,P2,P5) Total profit = 15 Fairness : 9

Fairness Total profit

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Multi-Objective Optimization

  • Multi-objective optimization problem

10 About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Multi-Objective Optimization

Pareto dominance (maximize

, minimize ) A solution dominates (denoted ) a solution if

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A C E B D

: total profit : maximum profit difference between users

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Genetic Algorithm for Multi-Objective Optimization

12 About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

Initialisation Evaluation Parents Selection Crossover Mutation Evaluation Replacement Stop? Genitors Offspring Generations Pareto front

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Biased random-key genetic algorithm (BRKGA)

Ref: J.F. Gonçalves et al. (2011)

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POPULATION

Population in generation i

Evaluation :

  • All chromosomes in population
  • Calculate fitness value
  • Encoding
  • Decoding

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Biased random-key genetic algorithm (BRKGA)

Ref: J.F. Gonçalves et al. (2011)

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ELITE NON-ELITE

Elite set :

  • Non-dominated solutions

Population in generation i

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Biased random-key genetic algorithm (BRKGA)

Ref: J.F. Gonçalves et al. (2011)

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ELITE NON-ELITE ELITE

Population in generation i Population in generation i+1

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Biased random-key genetic algorithm (BRKGA)

Ref: J.F. Gonçalves et al. (2011)

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ELITE NON-ELITE ELITE MUTANT

Mutant set :

  • Randomly generated
  • (the same method with

initial population)

Population in generation i Population in generation i+1

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Biased random-key genetic algorithm (BRKGA)

Ref: J.F. Gonçalves et al. (2011)

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ELITE NON-ELITE ELITE CROSSOVER OFFSPRING MUTANT

X

Population in generation i Population in generation i+1

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Biased random-key genetic algorithm (BRKGA)

Ref: J.F. Gonçalves et al. (2011)

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ELITE CROSSOVER OFFSPRING MUTANT

Stopping criteria :

  • A fixed number of generations since the generation of

the last solution total profit improvement

Population for new generation

  • Selection
  • Crossover
  • Mutation

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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  • BRKGA with our problem
  • Encoding
  • One chromosome for one solution
  • Number of genes is two times the number of strips
  • Each gene represents one strip acquisition
  • By real values randomly generated in the interval (0,1]
  • Example : 2 strips (strip 0 and strip 1)
  • Each chromosome in population

Genetic Algorithm for Multi-Objective Optimization

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Stp0 Dir0 Index 0 Stp0 Dir1 Index 1 Stp1 Dir0 Index 2 Stp1 Dir1 Index3 0.6984 0.9939 0.6885 0.2509

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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  • BRKGA with our problem
  • Decoding

Genetic Algorithm for Multi-Objective Optimization

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Stp0 Dir0 Index 0 Stp0 Dir1 Index 1 Stp1 Dir0 Index 2 Stp1 Dir1 Index3 0.6984 0.9939 0.6885 0.2509

  • Chromosome

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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  • BRKGA with our problem
  • Decoding

Genetic Algorithm for Multi-Objective Optimization

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Stp0 Dir0 Index 0 Stp0 Dir1 Index 1 Stp1 Dir0 Index 2 Stp1 Dir1 Index3 0.6984 0.9939 0.6885 0.2509

  • Chromosome

Scheduling sequence

1

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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SLIDE 22
  • BRKGA with our problem
  • Decoding

Genetic Algorithm for Multi-Objective Optimization

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Stp0 Dir0 Index 0 Stp0 Dir1 Index 1 Stp1 Dir0 Index 2 Stp1 Dir1 Index3 0.6984 0.9939 0.6885 0.2509

  • Chromosome

Scheduling sequence

1

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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SLIDE 23
  • BRKGA with our problem
  • Decoding

Genetic Algorithm for Multi-Objective Optimization

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Stp0 Dir0 Index 0 Stp0 Dir1 Index 1 Stp1 Dir0 Index 2 Stp1 Dir1 Index3 0.6984 0.9939 0.6885 0.2509

  • Chromosome

Scheduling sequence

1 2

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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SLIDE 24
  • BRKGA with our problem
  • Decoding

Genetic Algorithm for Multi-Objective Optimization

24

Stp0 Dir0 Index 0 Stp0 Dir1 Index 1 Stp1 Dir0 Index 2 Stp1 Dir1 Index3 0.6984 0.9939 0.6885 0.2509

  • Chromosome

Scheduling sequence

1 2

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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SLIDE 25
  • BRKGA with our problem
  • Decoding

Genetic Algorithm for Multi-Objective Optimization

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Stp0 Dir0 Index 0 Stp0 Dir1 Index 1 Stp1 Dir0 Index 2 Stp1 Dir1 Index3 0.6984 0.9939 0.6885 0.2509

  • Chromosome

Scheduling sequence

1 2

Total profit 1.04234 x 107 Maximum difference profit between users 5.21172 x 106

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Implementation and Results

Multi-objective scheduling of required photographs to be assigned to agile EOS :

  • 4-users modified ROADEF 2003 challenge instances (Subset A)
  • Parameters setting :
  • Number of strips
  • Size of population
  • Size of elite set
  • Size of mutant set
  • Probability of elite element inheritance
  • Stopping value
  • C++ language

26 About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Implementation and Results

Modified instance 2_9_170 : 12 requests (2 stereos) from 4 users, 25 strips

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0,0E+00 2,0E+07 4,0E+07 6,0E+07 8,0E+07 1,0E+08 1,2E+08 0,E+00 5,E+07 1,E+08 2,E+08 2,E+08 3,E+08

Total profit Maximum profit difference between users

Computation time : 3 minutes 47 seconds

About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Conclusions and Future works

  • Conclusions
  • Earth observing satellite
  • Obtain the requests to satisfy users requirement
  • Multi-objective optimization
  • Efficient for real problems
  • Objective functions
  • Maximize : total profit
  • Minimize : maximum profit difference between users

(Ensure fairness)

  • Instances
  • Modified instances of ROADEF 2003
  • BRKGA
  • Good performance but computation time is quite high

28 About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Conclusions and Future works

  • Future works
  • BRKGA
  • Decoding
  • The other decoding methods
  • Hypervolume concept
  • Evolutionary Algorithm
  • Indicator-Based Evolutionary Algorithm (IBEA)
  • Local search
  • Indicator-Based Multi-Objective Local Search (IBMOLS)

29 About work > Multi-Obj. Opt. > Genetic Algo. > Results > Conclusions

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Thank you for your attention. Questions and suggestions?

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