Biased Random Key Genetic Algorithm with Hybrid Decoding for Multi-objective Optimization
Panwadee Tangpattanakul, Nicolas Jozefowiez, Pierre LopezLAAS-CNRS
Toulouse, France
6th Workshop on Computational Optimization (WCO'13)Kraków, Poland
8 September 2013
Contents• Introduction• Multi-objective optimization• Biased Random Key Genetic Algorithm • Computational Results• Conclusions and Future Works
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Agile Earth observing satellite (Agile EOS)
• Mission• Obtain photographs of the Earth surface satisfying users
requirements• Properties
• Single camera• Move in 3 degrees of freedom• Non-fixed starting time
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Satellite direction
Captured photograph Candidate photographs
Earth surface
Introduction > Multi-obj optimization > BRKGA > Results > Conclusions
User 1 User 2 User n
Select
Schedule
&
Ground station
Multi-user observation scheduling problem
• The obtained sequence has to optimize 2 objectives:• Maximize the total profit• Minimize the maximum profit difference between users
• ensure fairness of resource sharing
Introduction > Multi-obj optimization > BRKGA > Results > Conclusions 4
Request from
Time
User 2
User 1
Acq3-1L
Acq4Acq3-2L
Acq2-2E
Acq1 Acq2-1E
Constraints• Time windows• No overlapping acquisitions• Sufficient transition times• Acq2.1E and Acq2.2E are exclusive.
• Only one of them can be selected.• Acq3.1L and Acq3.2L are linked.
• If one of them is selected, the other one must also be selected.
is a time window.
is a duration time.
Multi-user observation scheduling problem
Introduction > Multi-obj optimization > BRKGA > Results > Conclusions 5
6Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
Multi-objective problem
• The considered problem needs to maximize f1 (x), minimize f2 (x)A solution x dominates a solution y (denoted by x y ) , if
f1 (x) and f2 (x) or
f1 (x) and f2 (x)
Reference point
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A
C
E
BD
f1 (x)
f2 (x)
A
C
E
f1 (x)
f2 (x)
Pareto dominance & Hypervolume
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
First proposed by Gonçalves et al. (2002)
Random key & Genetic algorithm
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BRKGA Applications
Past• Considered one objective function• Used only one decoding method
This work• Apply to solve the multi-objective
optimization problem• Propose hybrid decoding
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
Biased random key genetic algorithm
Encoding GA operations Decoding
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Encoding
Decision variablesof the problem
Random keychromosome
Candidate acquisitions
Gene values inInterval [0,1]
Multi-user observation scheduling problem
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 9
Request from
Time
User 2
User 1
Acq3-1L
Acq4Acq3-2L
Acq2-2E
Acq1 Acq2-1E
is a time window.
is a duration time.
Multi-user observation scheduling problem
Example
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 10
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Encoding
Decision variablesof the problem
Random keychromosome
Candidate acquisitions
Gene values inInterval [0,1]
Acq1 Acq2-1E Acq2-2E Acq3-1L Acq3-2L Acq40.6984 0.9939 0.6485 0.2509 0.7593 0.4236
Multi-user observation scheduling problem
Candidate Acquisitions
Random key chromosome
Example
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 11
Ref: Gonçalves et al. (2011)
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POPULATION
Generation i
ELITE
CROSSOVEROFFSPRING
MUTANT
Generation i+1
ELITE
NON-ELITE
X
Biased random key genetic algorithm
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 12
Elite set selection methods
• Fast nondominated sorting and crowding distance assignment (NSGA-II)
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Ref: Deb et al. (2002)
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
f2 (x)
f1 (x)
Rank1
Rank2Rank3
Elite set selection methods
• Fast nondominated sorting and crowding distance assignment (NSGA-II)
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Ref: Deb et al. (2002)
Rank 1 Nondominated solutions
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
f1 (x)
f2 (x)
Elite set selection methods
• metric selection evolutionary multiobjective optimization algorithm (SMS-EMOA)
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Ref: Beume et al. (2007)
Rank 1 Nondominated solutions
solutions in rank
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
f1 (x)
f2 (x)
Elite set selection methods
• Indicator-based evolutionary algorithm based on the hypervolume concept (IBEA)
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Ref: Zitzler et al. (2004)
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
f1 (x) f1 (x)
f2 (x) f2 (x)
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Decoding
Random keychromosome
Solution ofthe problem
Random keychromosome
Priority to assigneach acquisitionin the sequence
Multi-user observation scheduling problem
Sequence ofselected acquisitions
Priority computation Assign the acquisition, which satisfies all constraints
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 17
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Decoding
• 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 Acq40.6984 0.9939 0.6485 0.2509 0.7593 0.4236
Random key chromosome
Example
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 18
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Decoding
• 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
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 19
Request from
Time
User 2
User 1
Acq3-1L
Acq4Acq3-2L
Acq2-2E
Acq1 Acq2-1E
Multi-user observation scheduling problem
Example
• The ideal priority values of Acq3-1L = Acq3-2L > Acq1 > Acq2-1E > Acq2-2E > Acq4
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Decoding
• Hybrid decoding (HD)
Chromosome
Basic decoding(D1)
Decoding of gene value and ideal priority combination
(D2)
Solution 1 Solution 2
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 21
?
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Hybrid decoding
• Elite set management – Method 1 (M1)
Decoding 1Population
Elite setPreferred chromosomes
Decoding 2
chromosome
solution 1 solution 2
Dominance relation
Dominant solution
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 22
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Hybrid decoding
• Elite set management – Method 1 (M1)
Decoding 1Population
Elite setPreferred chromosomes
Decoding 2
chromosome
solution 1 solution 2
Select randomly
Selected solution
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 23
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Hybrid decoding
• Elite set management – Method 2 (M2)
Decoding 1
Population
Elite setPreferred chromosomes
Decoding 2
chromosome
solution 1
solution 2
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 24
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Hybrid decoding
• Elite set management – Method 3 (M3)
Decoding 1
Population
Decoding 2
chromosome
solution 1
solution 2
Elite setPreferred
chromosomes
Preferred chromosomes
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 25
26Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
Computational results• Instances 4-users modified ROADEF 2003 challenge instances (Subset A)• Stopping criteria
• Number of iterations of the last archive set improvement• Computation time limitation
• Parameter setting
• Implementation C++, 10 runs/instance
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Computational results• For hybrid decoding Compare 3 methods of elite set management (M1, M2, M3) (Using 3 elite selection methods borrowed from NSGA-II, SMS-EMOA, IBEA)
• 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
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
M1 M2 M3
Hypervolume Average O O OStandard deviation O O O
Computation time
OX
Large instances(IBEA)
XSmall instances
(NSGA-II, SMS-EMOA)
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Comparisons of D1, D2, and HD
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
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Comparisons of D1, D2, and HD
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions
Conclusions• BRKGA applied to the multi-user observation scheduling problem
for agile EOS.
• Hybrid decoding is proposed.
• Elite set management M1 obtains the best results.
• The hybrid decoding is more efficient than the single decoding.
Future works
• Apply Indicator-based multi-objective local search (IBMOLS)
• Compare BRKGA & IBMOLS
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Conclusions and future works
Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 30
Thank you for your attention.
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