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

Multi-Objective Optimization for Selecting and Scheduling Observations by Agile Earth Observing Satellites

Panwadee Tangpattanakul, Nicolas Jozefowiez, Pierre Lopez

13e Congrès de la Société Française de Recherche Opérationnelle et d’Aide à la Décision (ROADEF 2012) Angers, France 11-13 Avril 2012

Contents

• Introduction
• Multi-objective photograph scheduling problem of agile Earth observing

satellites

• Biased random-key genetic algorithm for the multi-user photograph

scheduling

• Computational results
• Conclusions and future works

2

Introduction

Agile Earth observing satellites (agile EOS)

• Mission:
• Acquire photographs of the Earth surface, in

response to observation requests from several users

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

a set of candidates

• Properties:
• Single camera
• 3 degrees of freedom (roll, pitch, yaw)
• Non-fixed starting time of photograph acquisition

3 Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

• Multi-objective
• Maximize profit
• Minimize the maximum profit difference between users
• ensure fairness
• Constraints
• Time windows
• No overlapping images
• Sufficient transition times
• Each strip is acquired in only 1 direction
• Stereoscopic constraint
• Profit calculation
• gains
• partial acquisition
• piecewise linear function

Multi-objective photograph scheduling problem

4

P(x) x 0.4 0.7 1 0.1 0.4 1

Ref: Lemaître et al. (2002)

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

5

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

Time Requests from

Multi-objective photograph scheduling problem

• Selecting and scheduling of multi-user requests
• Considered objective values
• Total profit
• Maximum profit difference between users

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

• Selecting and scheduling of multi-user requests

6

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 Max difference = 21

Fairness Total profit

Multi-objective photograph scheduling problem

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

• Selecting and scheduling of multi-user requests

7

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 Max difference = 21 Solution 2 : (P4,P2,P3) Total profit = 17 Max difference = 1

Fairness Total profit

Multi-objective photograph scheduling problem

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

• Selecting and scheduling of multi-user requests

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 Max difference = 21 Solution 2 : (P4,P2,P3) Total profit = 17 Max difference = 1 Solution 3 : (P1,P2,P5) Total profit = 19 Max difference = 11

Fairness Total profit

Multi-objective photograph scheduling problem

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

• Selecting and scheduling of multi-user requests

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 Max difference = 21 Solution 2 : (P4,P2,P3) Total profit = 17 Max difference = 1 Solution 3 : (P1,P2,P5) Total profit = 19 Max difference = 11 Solution 4 : (P4,P2,P5) Total profit = 15 Max difference = 9

Max difference Total profit

Multi-objective photograph scheduling problem

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

• Multi-objective optimization problem

10

Multi-objective photograph scheduling problem

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

Pareto dominance (maximize

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

11

A C E B D

: total profit : maximum profit difference between users

Multi-objective photograph scheduling problem

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

12

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

BRKGA for the multi-user photograph scheduling

Ref: http://eodev.sourceforge.net/eo/tutorial/html/eoTutorial.html

• Genetic algorithm

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

Ref: Gonçalves et al. (2011)

13

POPULATION

Generation i

BRKGA for the multi-user photograph scheduling

• Biased random-key genetic algorithm (BRKGA)

ELITE CROSSOVER OFFSPRING MUTANT

Generation i+1

ELITE NON-ELITE

X

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

14

• 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

BRKGA for the multi-user photograph scheduling

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

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

15

• Decoding

BRKGA for the multi-user photograph scheduling

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

16

• Two methods for choosing preference chromosomes
• Dominance-based

(Fast nondominated sorting and crowding distance assignment)

• Fast nondominated sorting (find the solution in rank zero)
• Crowding distance assignment (limit the size of elite set)
• Indicator-based

(Indicator based on the hypervolume concept)

• Assign fitness values to the population members
• Select some solutions to become elite set by

BRKGA for the multi-user photograph scheduling

Ref: Deb et al. (2002) and Zitzler et al. (2004) repeat

• removing the worst solution
• updating the fitness values of remaining solutions

until the remaining solution satisfies the elite set size

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

• Instances:

4-users modified ROADEF 2003 challenge instances (Subset A)

• Stopping criterion:

Number of iterations of the last archive set improvement

• Parameters setting:
• Language: C++
• Number of runs/instances: 10

17

Computational results

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

18

Computational results

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

19

Computational results

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

• Compare the results from population size n and 2n:
• Compare the results from dominance-based and indicator based:

20

Computational results

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

• Conclusions
• The multi-objective optimization is applied to solve the problem of selecting

and scheduling the observations of agile Earth observing satellites.

• The instances of ROADEF 2003 challenge are modified to 4 user

requirements.

• Two objective functions are considered:
• Maximize the total profit
• Minimize the maximum profit difference between users (fairness of resource

sharing)

• A biased random-key genetic algorithm (BRKGA) is applied to solve this

problem.

• Two methods are used for selecting the elite set:
• Dominance-based
• Indicator-based
• The approximate solutions are obtained, but the computation time for large

instances are quite high.

21

Conclusions and future works

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

• Future works
• Use the other random-key decoding methods (in order

to reduce the computation times)

• Use an indicator-based multi-objective local search

(IBMOLS)

• Compare the results between BRKGA and IBMOLS

22

Conclusions and future works

Introduction > Multi-Obj. for scheduling > BRKGA > Results > Conclusions

Thank you for your attention. Questions and suggestions?

23