Panwadee Tangpattanakul Nicolas Jozefowiez Pierre Lopez LAASCNRS Toulouse France 6th Workshop on Computational Optimization WCO13 Kraków Poland 8 September 2013 Contents Introduction ID: 1026468
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1. Biased Random Key Genetic Algorithm with Hybrid Decoding for Multi-objective OptimizationPanwadee Tangpattanakul, Nicolas Jozefowiez, Pierre LopezLAAS-CNRSToulouse, France6th Workshop on Computational Optimization (WCO'13)Kraków, Poland8 September 2013
2. ContentsIntroductionMulti-objective optimizationBiased Random Key Genetic Algorithm Computational ResultsConclusions and Future Works2
3. Agile Earth observing satellite (Agile EOS)MissionObtain photographs of the Earth surface satisfying users requirementsPropertiesSingle cameraMove in 3 degrees of freedomNon-fixed starting time3Satellite directionCaptured photographCandidate photographsEarth surfaceIntroduction > Multi-obj optimization > BRKGA > Results > Conclusions
4. User 1User 2User nSelectSchedule&Ground stationMulti-user observation scheduling problemThe obtained sequence has to optimize 2 objectives:Maximize the total profitMinimize the maximum profit difference between users ensure fairness of resource sharingIntroduction > Multi-obj optimization > BRKGA > Results > Conclusions4
5. Request fromTimeUser 2User 1Acq3-1LAcq4Acq3-2LAcq2-2EAcq1Acq2-1EConstraintsTime windowsNo overlapping acquisitionsSufficient transition timesAcq2.1E 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 problemIntroduction > Multi-obj optimization > BRKGA > Results > Conclusions5
6. 6Introduction > Multi-obj. optimization > BRKGA > Results > ConclusionsMulti-objective problem
7. 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 point7ACEBDf1 (x)f2 (x)ACEf1 (x)f2 (x)Pareto dominance & HypervolumeIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions
8. First proposed by Gonçalves et al. (2002)Random key & Genetic algorithm8BRKGAApplicationsPast Considered one objective function Used only one decoding methodThis work Apply to solve the multi-objective optimization problem Propose hybrid decodingIntroduction > Multi-obj. optimization > BRKGA > Results > ConclusionsBiased random key genetic algorithmEncodingGA operationsDecoding8
9. 9EncodingDecision variablesof the problemRandom keychromosomeCandidate acquisitionsGene values inInterval [0,1]Multi-user observation scheduling problemIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions9
10. Request fromTimeUser 2User 1Acq3-1LAcq4Acq3-2LAcq2-2EAcq1Acq2-1E is a time window. is a duration time.Multi-user observation scheduling problemExampleIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions10
11. 11EncodingDecision variablesof the problemRandom keychromosomeCandidate acquisitionsGene values inInterval [0,1]Acq1Acq2-1EAcq2-2EAcq3-1LAcq3-2LAcq40.69840.99390.64850.25090.75930.4236Multi-user observation scheduling problemCandidate AcquisitionsRandom key chromosomeExampleIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions11
12. Ref: Gonçalves et al. (2011)12POPULATIONGeneration iELITECROSSOVEROFFSPRINGMUTANTGeneration i+1ELITENON-ELITEXBiased random key genetic algorithmIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions12
13. Elite set selection methodsFast nondominated sorting and crowding distance assignment (NSGA-II)13Ref: Deb et al. (2002)Introduction > Multi-obj. optimization > BRKGA > Results > Conclusionsf2 (x)f1 (x)Rank1Rank2Rank3
14. Elite set selection methodsFast nondominated sorting and crowding distance assignment (NSGA-II)14Ref: Deb et al. (2002)Rank 1Nondominated solutionsIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusionsf1 (x)f2 (x)
15. Elite set selection methods metric selection evolutionary multiobjective optimization algorithm (SMS-EMOA)15Ref: Beume et al. (2007)Rank 1Nondominated solutions solutions in rank Introduction > Multi-obj. optimization > BRKGA > Results > Conclusionsf1 (x)f2 (x)
16. Elite set selection methodsIndicator-based evolutionary algorithm based on the hypervolume concept (IBEA)16Ref: Zitzler et al. (2004)Introduction > Multi-obj. optimization > BRKGA > Results > Conclusionsf1 (x)f1 (x)f2 (x)f2 (x)
17. 17DecodingRandom keychromosomeSolution ofthe problemRandom keychromosomePriority to assigneach acquisitionin the sequenceMulti-user observation scheduling problemSequence ofselected acquisitionsPriority computationAssign the acquisition, which satisfies all constraints Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions17
18. 18DecodingBasic decoding (D1)The priority is equal to its gene valuePriorityj = genejThe priority to assign each acquisition in the sequence Acq2-1E, Acq3-2L, Acq1, Acq2-2E, Acq4, Acq3-1LAcq1Acq2-1EAcq2-2EAcq3-1LAcq3-2LAcq40.69840.99390.64850.25090.75930.4236Random key chromosomeExampleIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions18
19. 19DecodingDecoding of gene value and ideal priority combination (D2)The priority isPriorityj = ideal priority * f(genej) Concept of ideal priorityThe acquisition, which has the earliest possible starting time, should be selected firstly and be scheduled in the beginning of the solution sequenceIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions19
20. Request fromTimeUser 2User 1Acq3-1LAcq4Acq3-2LAcq2-2EAcq1Acq2-1EMulti-user observation scheduling problemExampleThe ideal priority values of Acq3-1L = Acq3-2L > Acq1 > Acq2-1E > Acq2-2E > Acq4Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions20
21. 21DecodingHybrid decoding (HD)ChromosomeBasic decoding(D1)Decoding of gene value and ideal priority combination(D2)Solution 1Solution 2Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions21?
22. 22Hybrid decodingElite set management – Method 1 (M1)Decoding 1PopulationElite setPreferred chromosomesDecoding 2chromosomesolution 1solution 2Dominance relationDominant solutionIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions22
23. 23Hybrid decodingElite set management – Method 1 (M1)Decoding 1PopulationElite setPreferred chromosomesDecoding 2chromosomesolution 1solution 2Select randomly Selected solutionIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions23
24. 24Hybrid decodingElite set management – Method 2 (M2)Decoding 1PopulationElite setPreferred chromosomesDecoding 2chromosomesolution 1solution 2Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions24
25. 25Hybrid decodingElite set management – Method 3 (M3)Decoding 1PopulationDecoding 2chromosomesolution 1solution 2Elite setPreferred chromosomesPreferred chromosomesIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions25
26. 26Introduction > Multi-obj. optimization > BRKGA > Results > ConclusionsComputational resultsInstances 4-users modified ROADEF 2003 challenge instances (Subset A)Stopping criteriaNumber of iterations of the last archive set improvementComputation time limitationParameter settingImplementation C++, 10 runs/instance
27. 2727Computational resultsFor 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 decodingIntroduction > Multi-obj. optimization > BRKGA > Results > ConclusionsM1M2M3HypervolumeAverageOOOStandard deviationOOOComputation timeOXLarge instances(IBEA)XSmall instances(NSGA-II, SMS-EMOA)
28. 2828Comparisons of D1, D2, and HDIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions
29. 2929Comparisons of D1, D2, and HDIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions
30. ConclusionsBRKGA 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 worksApply Indicator-based multi-objective local search (IBMOLS)Compare BRKGA & IBMOLS30Conclusions and future worksIntroduction > Multi-obj. optimization > BRKGA > Results > Conclusions30
31. Thank you for your attention.31