m ulti - objective o ptimization of e arth o bserving s atellite m issions by panwadee...
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MULTI-OBJECTIVE OPTIMIZATION OF EARTH OBSERVING SATELLITE
MISSIONS
By Panwadee
Tangpattanakul
Thesis supervisorsPierre Lopez
Nicolas Jozefowiez
26th September 2013
AGILE EARTH OBSERVING SATELLITE (AGILE EOS)
2
Mission
Obtain photographs of the Earth surface to satisfy users requirements
Satellite direction
Captured photograph
Candidate photographs
Earth surface
WORK OVERVIEW
3
Observation scheduling problem of agile EOS
&Multi-objective optimization
Biased random key genetic algorithm
(BRKGA)
Indicator-based multi-objective
local search(IBMOLS)
OUTLINE
Problem statement
Multi-objective optimization
Biased random key genetic algorithm
Indicator-based multi-objective local search
BRKGA vs. IBMOLS
Conclusions & perspectives
4
PROBLEM STATEMENT
5
6
PROPERTIES OF AGILE EOS
Ex. PLEIADES CNES (French Center for Space Studies)
• One fixed camera on-board
• The whole satellite can move in 3 degrees of freedom
• Problem data’s description was proposed (Verfaillie et al., 2002)
• Several methods were used to solve the problem, e.g. greedy algorithm, dynamic programming, constraint programming, local search (Lemaître et al., 2002)
• ROADEF 2003 challenge• Simulated annealing (Kuipers, 2003)• Tabu search (Cordeau & Laporte, 2005)
Literature of PLEIADES observation scheduling problem
7
MULTI-USER OBSERVATION SCHEDULING PROBLEM FOR AGILE EOS
8
User 1 User 2 User n
Select
Schedule
&
Ground station
Requests
Acquisitions
Satellitecapacitylimitation
Profit
9
MULTI-USER OBSERVATION SCHEDULING PROBLEM FOR AGILE EOS
Bataille et al., 1999Optimize 2 objectives: fairness and efficiency Use 3 strategies:
Give priority to fairness Give priority to efficiencyConsider 2 objectives, but search for 1 solution
Gabrel & Vanderpooten, 2002Optimize 3 objectives: maximize the number of shots,
maximize the total profit, and minimize the satellite use
Select a satisfactory efficient path in a graph without circuit
Literature
10
MULTI-USER OBSERVATION SCHEDULING PROBLEM FOR AGILE EOS
Bianchessi et al., 2007 Multiple satellites, multiple orbits, and multiple users 3 phases
Select users depending on priority Select requests from the subset of users Allocate the remaining capacities of the satellites
between all users A single objective:
Weighted sum of the normalized utilities of the users Tabu search
Literature
MULTI-USER OBSERVATION SCHEDULING PROBLEM FOR AGILE EOS
11
The obtained sequence has to optimize 2 objectives:
Sequence (SA1, SA2,…, SAn)
Maximize the total profit
Minimize the maximum profit difference between users ensure fairness of resource sharing
𝑓 1=∑𝑖=1
𝑛
𝑝𝑖
𝑓 2= max(𝑖 , 𝑗 )∈ ⟦1 ,𝑛𝑢⟧ 2
¿ 𝑖≠ 𝑗
|𝑢𝑖−𝑢 𝑗|
12
Constraints Time windows
No overlapping acquisitions
MULTI-USER OBSERVATION SCHEDULING PROBLEM FOR AGILE EOS
Acquisition
Possible starting time
Duration time
time
time
Acquisition1
Acquisition2
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Constraints Sufficient transition times
MULTI-USER OBSERVATION SCHEDULING PROBLEM FOR AGILE EOS
Earth surface
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Constraints Two acquisitions may be exclusive
Two acquisition may be linked
MULTI-USER OBSERVATION SCHEDULING PROBLEM FOR AGILE EOS
time
Acqusition2E
Acqusition1E
time
Acqusition2L
Acqusition1L
MULTI-USER OBSERVATION SCHEDULING PROBLEM FOR AGILE EOS
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Request from
Time
User 2
User 1
Acq3-1L
Acq4Acq3-2L
Acq2-2E
Acq1 Acq2-1E
P3 = 20
P4 = 10
P1 = 4
P2-1 = 5
P2-2 = 5
Solution 1: (Acq3-1L & Acq3-2L & Acq4)Total profit = 30, Max profit difference = 30Solution 2: (Acq1 & Acq2-1E & Acq4)Total profit = 19, Max profit difference = 1Solution 3: (Acq3-1L & Acq3-2L & Acq2-1E)Total profit = 25, Max profit difference = 15
Max profit difference
Total profit
MULTI-OBJECTIVE OPTIMIZATION
16
MULTI-OBJECTIVE PROBLEM
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with: n ≥ 2: number of objectives
F = (f1, f2,…,fn): vector of functions to optimize
Ω: set of feasible solutions
y = F(Ω): objective space
The considered problem needs to maximize f1 (x), minimize f2
(x)
A solution x dominates a solution y iff
f1 (x) and f2 (x)
or f1 (x) and f2 (x)
PARETO DOMINANCE & HYPERVOLUME
18A
C
E
BD
f1(x)
f2(x) Reference point
A
C
E
f1 (x)
f2 (x)
IMPLEMENTATION
Conduct on realistic instances 4-user modified ROADEF 2003 challenge instances (Subset A) The instance sizes are between 4 to 1,068
acquisitions Implement via C++ language 10 runs/instance are tested Reference point of the hypervolume
The worst values of both objectives19
BIASED RANDOM KEY GENETIC ALGORITHM
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Biased random key genetic algorithm Gonçalves et al. (2002)
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Random key (Bean, 1994)Chromosomes are represented as a vector of
randomly generated real numbers in the interval [0,1].
EncodingDecision variable
Decoding
Chromosome
Solution
ENCODING
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Acq1 Acq2-1E
Acq2-2E
Acq3-1L
Acq3-2L
Acq4
0.6984 0.9939 0.6485 0.2509 0.7593 0.4236Random key chromosome
Request from
Time
User 2
User 1
Acq3-1L
Acq4Acq3-2L
Acq2-2E
Acq1 Acq2-1E
Biased random key genetic algorithm Gonçalves et al. (2002)
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Random key (Bean, 1994)Chromosomes are represented as a vector of
randomly generated real numbers in the interval [0,1].
EncodingDecision variable
Decoding
Chromosome
Solution
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Random keychromosome
Ordered list ofacquisitions
Multi-user observation scheduling problem
Sequence ofselected acquisitions
Priority computation Assign the acquisition, which satisfies all constraints
DECODING
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• Basic decoding (D1)• The priority is equal to its gene value
Priorityj = genej
• The priority to assign each acquisition in the sequenceAcq2-1E, Acq3-2L, Acq1, Acq2-2E, Acq4, Acq3-1L
Acq1 Acq2-1E
Acq2-2E
Acq3-1L
Acq3-2L
Acq4
0.6984 0.9939 0.6485 0.2509 0.7593 0.4236Random key chromosome
Example
PRIORITY COMPUTATION
26
• Decoding of gene value and ideal priority combination (D2)• The priority is
Priorityj = ideal priority * f(genej)
• Concept of ideal priority• The acquisition, which has the earliest possible starting time,
should be selected firstly and be scheduled in the beginning of the solution sequence
PRIORITY COMPUTATION
𝐼𝑑𝑒𝑎𝑙𝑝𝑟𝑖𝑜𝑟𝑖𝑡𝑦 𝑗=𝑇𝑚𝑎𝑥𝐿−𝑇𝑚𝑖𝑛 𝑗
𝑇𝑚𝑎𝑥𝐿
• The ideal priority values of Acq3-1L = Acq3-2L > Acq1 > Acq2-1E > Acq2-2E > Acq4 27
Request from
Time
User 2
User 1
Acq3-1L
Acq4Acq3-2L
Acq2-2E
Acq1 Acq2-1E
Example
PRIORITY COMPUTATION
28
Random keychromosome
Multi-user observation scheduling problem
Sequence ofselected acquisitions
Priority computation Assign the acquisition, which satisfies all constraints
DECODING
Ordered list ofacquisitions
BRKGA GENERATION
29
POPULATION
Generation i
ELITE
CROSSOVEROFFSPRING
MUTANT
Generation i+1
ELITE
NON-ELITE
X
ADAPTATION TO MULTI-OBJECTIVE
Q: How to select the elite set? A: Borrow selection methods from efficient MOEAs, e.g. NSGA-II, SMS-EMOA, IBEA
Q: Could chromosome be associated to several nondominated solutions? A: Use a multiple decoding
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ELITE SET SELECTIONS
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Ref: Deb et al. (2002)
Fast nondominated sorting and crowding distance assignment
f2 (x)
f1 (x)
Rank1
Rank2Rank3
ELITE SET SELECTIONS
32
Ref: Deb et al. (2002)
Fast nondominated sorting and crowding distance assignment
Rank 1 Nondominated solutions
f1 (x)
f2 (x)
i-1
i i+1
solutions in Rank 1
ELITE SET SELECTIONS
33
Ref: Beume et al. (2007)
S-metric selection evolutionary multiobjective optimization algorithm (SMS-EMOA)
Rank 1 Nondominated solutions
solutions in Rank 1
f1 (x)
f2 (x)
ELITE SET SELECTIONS
34
Ref: Zitzler et al. (2004)
Indicator-based evolutionary algorithm based on the hypervolume concept (IBEA)
f1 (x) f1 (x)
f2 (x) f2 (x)
IHD(B,A) > 0
IHD(A,B) > 0
A
B
A
B
IHD(A,B) = - IHD(B,A) > 0
Binary tournament on all individuals in P Compute the fitness
ADAPTATION TO MULTI-OBJECTIVE
Q: How to select the elite set? A: Borrow selection methods from efficient MOEAs, e.g. NSGA-II, SMS-EMOA, IBEA
Q: Could chromosome be associated to several nondominated solutions? A: Use a multiple decoding
35
MULTIPLE DECODING
36
• Hybrid decoding (HD)
Chromosome
Basic decoding(D1)
Decoding of gene value and ideal priority combination
(D2)
Solution 1 Solution 2
?
HYBRID DECODING
37
• Elite set management – Method 1 (M1)
D1
Population
Elite setPreferred
chromosomesD2
chromosome
solution 1 solution 2
Dominance relation
Dominant solution
HYBRID DECODING
38
• Elite set management – Method 1 (M1)
D1
Population
Elite setPreferred
chromosomesD2
chromosome
solution 1 solution 2
Select randomly
Selected solution
HYBRID DECODING
39
• Elite set management – Method 2 (M2)
D1
Population
Elite setPreferred
chromosomes
D2
chromosome
solution 1
solution 2
HYBRID DECODING
40
• Elite set management – Method 3 (M3)
D1
Population
D2
chromosome
solution 1
solution 2
Elite setPreferred
chr.
Preferred chr.
IMPLEMENTATION
In each iteration, Nondominated solutions are stored in an archive
set A If at least one solution from P can dominate some
solutions in the archive set A Update the archive set A 41
Parameter Value
Population size (p) p = n,where n is the length of the chromosome
Elite set size (pe) 0.15p ≤ pe
Mutant set size (pm) pm = 0.30p
Prob. elite inherent (ρe)
ρe = 0.6
Stopping criteria Number of iterations since the last archive
improvement Value = 50
Computation time limitation Depending on the instances size
42
IMPLEMENTATION
COMPARISON OF TWO DECODINGS (D1, D2) AND THREE ELITE SET SELECTIONS (S1, S2, AND S3)
43
For all instances• All methods obtain
similar results• Each method has the
advantage in different instances
S1, S2, and S3
Large-size instances• D1 obtains better median value• D2 can reduce the range
COMPARISON OF TWO DECODINGS (D1, D2) AND THREE ELITE SET SELECTIONS (S1, S2, AND S3)
44
Medium-size instances• D2 obtains better results
• Median value• Std. deviation• Computation time
D1, D2
HYBRID DECODING – COMPARISON OF ELITE SET MANAGEMENT
45
M1 M2 M3
Hypervolume Median O O OStandard deviation O O O
Computation timeO
Time outLarge instances
(S3)
Time outSmall instances
(S1, S2)
Since M1 spends less computation time for all elite set selection methods, its results will be used to compare with the results from the two single decoding
BRKGA – COMPARISON OF TWO SINGLE DECODING AND HYBRID DECODING
46
• HD obtains results close to the best one, when comparing the two single decoding
• HD can preserve the advantages of each single decoding• D1 vs. HD, HD can reduce the range• D2 vs. HD, HD can avoid to entrap in local optima
INDICATOR-BASED MULTI-OBJECTIVE LOCAL SEARCH
47
INDICATOR-BASED MULTI-OBJECTIVE LOCAL SEARCH (BASSEUR AND BURKE, 2007)
48
Basic Local search&
Binary indicator from IBEA
Each iteration
Update the approximate Pareto front
Initial population generation
Fitness computation
Local search step
STRATEGIES
49
Initial population generationFirst iteration Random generation Using data of problem instancesOther iterations Random generation Perturbation
Neighborhood structure and dynamic stopping value Insert, remove, and replace & Stop value = 10 Insert, remove & Stop value = 10 Insert, remove & Stop value = 50
STRATEGIES
50
Feasibility checking Method 1 Method 2
Stopping criterion Dynamic stopping Fixed computation time Fixed number of visited neighbors
INDICATOR-BASED MULTI-OBJECTIVE LOCAL SEARCH
51
Each iteration
Update the approximate Pareto front
Initial population generation
Fitness computation
Local search step
INITIAL POPULATION GENERATION
52
First iteration - Random generation For all candidate acquisitions are considered depending on a random order
Considered acquisition
Check all constraints
Satisfy
Assign to the
sequence
Consider the next acquisition
Yes
No
INITIAL POPULATION GENERATION
53
Other iterations – Perturbation Original individual selection Select randomly Element removing Repeat
Select the removing position Remove the acquisition Check the constraint of linked
acquisitions
Until nmodify ≤ ¾ noriginal
Approximate Pareto front
A B C D
Individualselection
Positionselection
e.g. 2
A C D
B
INDICATOR-BASED MULTI-OBJECTIVE LOCAL SEARCH
54
Each iteration
Update the approximate Pareto front
Initial population generation
Fitness computation
Local search step
FITNESS COMPUTATION
55
Use the indicator based on the hypervolume concept
Perform binary tournaments for all individuals in P
f1 (x) f1 (x)
f2 (x) f2 (x)
IHD(B,A) > 0
IHD(A,B) > 0
A
B
A
B
IHD(A,B) = - IHD(B,A) > 0
FITNESS COMPUTATION
56
Use the indicator based on the hypervolume concept
Perform binary tournaments for all individuals in P
Fitness value is
INDICATOR-BASED MULTI-OBJECTIVE LOCAL SEARCH
57
Each iteration
Update the approximate Pareto front
Initial population generation
Fitness computation
Local search step
bin
For all individuals x in P
LOCAL SEARCH STEP
58
xy*
Population P
Worst solution
4 types of move Insert an acquisition i Remove an acquisition i Insert linked acquisitions i and j Remove linked acquisitions i and j
NEIGHBORHOOD STRUCTURE
59
Feasibility checking – Method 2
FEASIBILITY CHECKING FOR INSERTION
60
sa1 sa2 sa3 sa4 sa5
Insertion position
time
sa1 sa2 sa3 sa4 sa5
time
Acq k
The acquisitions, which stay behind the insertion position, are moved to the back as late as possible
BRKGA VS. IBMOLS
61
BRKGA VS. IBMOLS
62
Medium instances Large instances
IBMOLS obtains better results than BRKGA for all instances • Median value• Standard deviation
BRKGA VS. IBMOLS (IMPROVEMENT)
63
0 2 4 6 8 10 12 14 16 182.0E+172.2E+172.4E+172.6E+172.8E+173.0E+173.2E+173.4E+17
Instance 68_12_106
Time (s)
0 50 100 150 200 250 3002.0E+16
2.5E+16
3.0E+16
3.5E+16
4.0E+16
4.5E+16
Instance 77_40_147
Time (s)
0 50 100 150 200 2502.0E+16
2.2E+17
4.2E+17
6.2E+17
8.2E+17
Instance 218_39_295
Time (s)0 1000 2000 3000 4000
2.0E+16
5.2E+17
1.0E+18
1.5E+18
2.0E+18
Instance 336_55_483
Time (s)
0 1002003004005006007008002.0E+16
5.2E+17
1.0E+18
1.5E+18
2.0E+18
Instance 375_63_534
Time (s)0 500 1000 1500 2000 2500
2.0E+161.2E+172.2E+173.2E+174.2E+175.2E+176.2E+17
Instance 150_87_342
Time (s)
Medium instances Large instances
For medium instances, IBMOLS spends more computation time• From the start, IBMOLS obtains better hypervolume valueFor large instances, IBMOLS spends less computation time
BRKGAIBMOLS
CONCLUSIONS AND PERSPECTIVES
64
CONCLUSIONS
The multi-user observation scheduling problem of an agile EOS is solved in this work.
The obtained sequences have to optimize two objectives and also satisfy all constraints.
BRKGA and IBMOLS are applied to solve the problem.
All parameters of each algorithm are tested with realistic instances.
The results obtained from BRKGA and IBMOLS are compared.
IBMOLS converges faster and gives better results65
PERSPECTIVES
Short term further worksBRKGA Modify the hybrid decoding
Each single objective may be re-defined to mainly consider one objective
Modify the elite set selection Other indicators can be used (e.g. from SPEA2)
IBMOLS Include other strategies for the initial population
generation by using data of the problem instances The number of removed elements in the
perturbation can also be modified.66
PERSPECTIVES
Long term further worksBRKGA Apply more advanced decoding methods
e.g. consider the decoder as a full multi-objective problem
IBMOLS Use other perturbation rules
e.g. insert some feasible acquisitions for replacing the removed elements
Use other neighborhood structuresScheduling problem Other objective functions can be included
67
THANK YOU FOR YOUR ATTENTION
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