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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 Lopez LAAS-CNRS Toulouse, France 6th Workshop on Computational Optimization (WCO'13) Kraków, Poland 8 September 2013. Contents. Introduction

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

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  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

  3. Introduction > Multi-obj optimization > BRKGA > Results > Conclusions 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-fixedstarting time Satellitedirection Captured photograph Candidate photographs Earth surface

  4. 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 Multi-user observation scheduling problem User 1 User 2 User n Ground station Select & Schedule

  5. Introduction > Multi-obj optimization > BRKGA > Results > Conclusions Multi-user observation scheduling problem Request from Acq3-1L User 2 Acq3-2L Acq4 Acq2-2E User 1 Acq1 Acq2-1E Time • 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.

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

  7. Introduction> Multi-obj. optimization> BRKGA > Results > Conclusions Pareto dominance & Hypervolume • The considered problem needs to maximizef1 (x), minimizef2(x) A solution x dominates a solution y (denoted by x y) , if f1 (x) and f2(x) or f1 (x) and f2(x) f2(x) f2(x) Reference point E E D B C C A A f1 (x) f1 (x)

  8. 8 First proposed by Gonçalves et al. (2002) Random key & Genetic algorithm Introduction> Multi-obj. optimization> BRKGA> Results > Conclusions Biased random key genetic algorithm 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 Encoding GA operations Decoding

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

  10. Introduction> Multi-obj. optimization> BRKGA> Results > Conclusions Multi-user observation scheduling problem Example Request from Acq3-1L User 2 Acq3-2L Acq4 Acq2-2E User 1 Acq1 Acq2-1E Time is a time window. is a duration time.

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

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

  13. Introduction> Multi-obj. optimization> BRKGA> Results > Conclusions Elite set selection methods • Fast nondominated sorting and crowding distance assignment (NSGA-II) f2(x) Rank1 Rank2 Rank3 f1 (x) Ref: Deb et al. (2002)

  14. Introduction> Multi-obj. optimization> BRKGA> Results > Conclusions Elite set selection methods • Fast nondominated sorting and crowding distance assignment (NSGA-II) Rank 1 Nondominated solutions f2(x) f1 (x) Ref: Deb et al. (2002)

  15. Introduction> Multi-obj. optimization> BRKGA> Results > Conclusions Elite set selection methods • metric selection evolutionary multiobjective optimization algorithm (SMS-EMOA) Rank 1 Nondominated solutions f2(x) solutions in rank f1 (x) Ref: Beume et al. (2007)

  16. Introduction> Multi-obj. optimization> BRKGA> Results > Conclusions Elite set selection methods • Indicator-based evolutionary algorithm based on the hypervolume concept (IBEA) f2(x) f2(x) f1 (x) f1 (x) Ref: Zitzler et al. (2004)

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

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

  19. 19 Introduction> Multi-obj. optimization> BRKGA> Results > Conclusions Decoding • Decoding of gene value and ideal priority combination (D2) • The priority is Priorityj = ideal priority * f(genej) • Concept of ideal priority • Theacquisition, which has the earliest possible starting time, should be selected firstly and be scheduled in the beginning of the solution sequence

  20. Introduction> Multi-obj. optimization> BRKGA> Results > Conclusions Multi-user observation scheduling problem • The ideal priority values of Acq3-1L=Acq3-2L>Acq1>Acq2-1E>Acq2-2E > Acq4 Example Request from Acq3-1L User 2 Acq3-2L Acq4 Acq2-2E User 1 Acq1 Acq2-1E Time

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

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

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

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

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

  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 Introduction> Multi-obj. optimization> BRKGA > Results > Conclusions 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

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

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

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

  31. Thank you for your attention.

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