1. Biased Random Key Genetic Algorithm with Hybrid Decoding for Multi-objective Optimization Panwadee Tangpattanakul, Nicolas Jozefowiez, Pierre Lopez LAAS-CNRS Toulouse, France 6th Workshop on Computational Optimization (WCO'13) Kraków, Poland 8 September 2013

2. Contents Introduction Multi-objective optimization Biased Random Key Genetic Algorithm Computational Results Conclusions and Future Works 2

3. 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 photographCandidate photographs Earth surface Introduction > Multi-obj optimization > BRKGA > Results > Conclusions

4. User 1User 2User 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

5. Request from Time User 2 User 1 Acq3-1L Acq4 Acq3-2L 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

6. 6 Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions Multi-objective problem

7. Reference point 7 A C E B D f 1 (x) f 2 (x) A C E f 1 (x) f 2 (x) Pareto dominance & Hypervolume Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions

8. 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 Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions Biased random key genetic algorithm EncodingGA operationsDecoding 8

9. 9 Encoding Decision variables of the problem Random key chromosome Candidate acquisitions Gene values in Interval [0,1] Multi-user observation scheduling problem Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 9

10. Request from Time User 2 User 1 Acq3-1L Acq4 Acq3-2L 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

11. 11 Encoding Decision variables of the problem Random key chromosome Candidate acquisitions Gene values in Interval [0,1] Acq1Acq2-1EAcq2-2EAcq3-1LAcq3-2LAcq4 0.69840.99390.64850.25090.75930.4236 Multi-user observation scheduling problem Candidate Acquisitions Random key chromosome Example Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 11

12. Ref: Gonçalves et al. (2011) 12 POPULATION Generation i ELITE CROSSOVER OFFSPRING MUTANT Generation i+1 ELITE NON-ELITE X Biased random key genetic algorithm Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 12

13. Elite set selection methods Fast nondominated sorting and crowding distance assignment (NSGA-II) 13 Ref: Deb et al. (2002) Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions f 2 (x) f 1 (x) Rank1 Rank2 Rank3

14. Elite set selection methods Fast nondominated sorting and crowding distance assignment (NSGA-II) 14 Ref: Deb et al. (2002) Rank 1 Nondominated solutions Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions f 1 (x) f 2 (x)

15. Elite set selection methods metric selection evolutionary multiobjective optimization algorithm (SMS-EMOA) 15 Ref: Beume et al. (2007) Rank 1 Nondominated solutions in rank Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions f 1 (x) f 2 (x)

16. Elite set selection methods Indicator-based evolutionary algorithm based on the hypervolume concept (IBEA) 16 Ref: Zitzler et al. (2004) Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions f 1 (x) f 2 (x)

17. 17 Decoding Random key chromosome Solution of the problem Random key chromosome Priority to assign each acquisition in the sequence Multi-user observation scheduling problem Sequence of selected acquisitions Priority computationAssign the acquisition, which satisfies all constraints Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 17

18. 18 Decoding Basic decoding (D1) The priority is equal to its gene value Priority j = gene j The priority to assign each acquisition in the sequence Acq2-1E, Acq3-2L, Acq1, Acq2-2E, Acq4, Acq3-1L Acq1Acq2-1EAcq2-2EAcq3-1LAcq3-2LAcq4 0.69840.99390.64850.25090.75930.4236 Random key chromosome Example Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 18

19. 19 Decoding Decoding of gene value and ideal priority combination (D2) The priority is Priority j = ideal priority * f(gene j ) 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

20. Request from Time User 2 User 1 Acq3-1L Acq4 Acq3-2L 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 Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 20

21. 21 Decoding Hybrid decoding (HD) Chromosome Basic decoding (D1) Decoding of gene value and ideal priority combination (D2) Solution 1Solution 2 Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 21 ?

22. 22 Hybrid decoding Elite set management – Method 1 (M1) Decoding 1 Population Elite set Preferred chromosomes Decoding 2 chromosome solution 1solution 2 Dominance relation Dominant solution Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 22

23. 23 Hybrid decoding Elite set management – Method 1 (M1) Decoding 1 Population Elite set Preferred chromosomes Decoding 2 chromosome solution 1solution 2 Select randomly Selected solution Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 23

24. 24 Hybrid decoding Elite set management – Method 2 (M2) Decoding 1 Population Elite set Preferred chromosomes Decoding 2 chromosome solution 1 solution 2 Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 24

25. 25 Hybrid decoding Elite set management – Method 3 (M3) Decoding 1 Population Decoding 2 chromosome solution 1 solution 2 Elite set Preferred chromosomes Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 25

26. 26 Introduction > 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

27. 27 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 M1M2M3 HypervolumeAverage OOO Standard deviation OOO Computation time O X Large instances (IBEA) X Small instances (NSGA-II, SMS-EMOA)

28. 28 Comparisons of D1, D2, and HD Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions

29. 29 Comparisons of D1, D2, and HD Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions

30. 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 30 Conclusions and future works Introduction > Multi-obj. optimization > BRKGA > Results > Conclusions 30

31. Thank you for your attention. 31