Biased Random Key Genetic Algorithm with Hybrid Decoding for Multi-objective Optimization

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

2

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

3

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.


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

7

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

8

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


Biased random key genetic algorithm

Encoding GA operations Decoding

8

9

Encoding

Decision variablesof the problem

Random keychromosome

Candidate acquisitions

Gene values inInterval [0,1]


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.


Example


11

Encoding

Decision variablesof the problem


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


Candidate Acquisitions

Random key chromosome

Example


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


Elite set selection methods

• Fast nondominated sorting and crowding distance assignment (NSGA-II)

13

Ref: Deb et al. (2002)


f2 (x)

f1 (x)

Rank1

Rank2Rank3


• Fast nondominated sorting and crowding distance assignment (NSGA-II)

14

Ref: Deb et al. (2002)

Rank 1 Nondominated solutions


f1 (x)

f2 (x)


• metric selection evolutionary multiobjective optimization algorithm (SMS-EMOA)

15

Ref: Beume et al. (2007)

Rank 1 Nondominated solutions

solutions in rank


f1 (x)

f2 (x)


• Indicator-based evolutionary algorithm based on the hypervolume concept (IBEA)

16

Ref: Zitzler et al. (2004)


f1 (x) f1 (x)

f2 (x) f2 (x)

17

Decoding


Solution ofthe problem


Priority to assigneach acquisitionin the sequence


Sequence ofselected acquisitions

Priority computation Assign the acquisition, which satisfies all constraints


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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


19

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


Request from

Time

User 2

User 1

Acq3-1L

Acq4Acq3-2L

Acq2-2E

Acq1 Acq2-1E


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


?

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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


23

Hybrid decoding


Decoding 1Population


Decoding 2

chromosome

solution 1 solution 2

Select randomly

Selected solution


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Hybrid decoding


Decoding 1

Population


Decoding 2

chromosome

solution 1

solution 2


25

Hybrid decoding


Decoding 1

Population

Decoding 2

chromosome

solution 1

solution 2

Elite setPreferred

chromosomes

Preferred chromosomes


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

2727

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


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


2929

Comparisons of D1, D2, and HD


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


Thank you for your attention.

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Biased Random Key Genetic Algorithm with Hybrid Decoding for Multi-objective Optimization