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Surrogate Model Based Differential Evolution for Multiobjective Optimization (GP - DEMO) Šmarna gora, 20. 9. 2012Miha Mlakar Algoritmi po vzorih iz narave 20. delavnica

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Overview Motivation Surrogate models – Evolution control – Gaussian process Outline of GP - DEMO Comparison of solutions under uncertainty Selection procedure under uncertainty Testing and results Discussion and future work 2

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Motivation MOEA are effective but require numerous fitness function evaluations Solution evaluations can be: – very complex and can take a lot of computational time – expensive – dangerous Our goal is to build an algorithm that will: – return comparable results to other MOEAs – require fewer evaluations than other MOEAs 3

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Surrogate models Surrogate models (also called meta-models) are models that approximate original fitness function Surrogate models can be NN, GP, SVN,... Optimization with surrogate models uses: – solution evaluation (with original function) – solution approximation (with surrogate model) Evolution control balances the use of the surrogate models 4

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Evolution control Three main approaches: – No evolution control – Fixed evolution control Individual-based evolution control Generation-based evolution control – Adaptive evolution control 5

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Individual-based evolution control Just some individuals evaluated 6

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Generation-based evolution control Some generations evaluated some approximated 7

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Adaptive evolution control Solve optimization problem with the model and evaluate best (nondominated) points Evaluate only better points (using the model) Evaluate points with low confidence to get a better model prediction 8

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Gaussian process modeling Gaussian process model is build from previously evaluated solutions Result of solution approximation is normal distribution Solution fitness value = mean value Solution confidence interval (95%) = twice the standard deviation 9

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Gaussian process modeling (2) 10

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GP - DEMO Algorithm for surrogate model optimization with Gaussian process Based on DEMO Adaptive evolution control in two parts of algorithm: a)Comparison of parent and candidate solutions b)Determining set of non-dominated solutions and environmental selection 11

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GP – DEMO pseudocode 1.Randomly create and evaluate initial population 2.Create GP model 3.Until stopping criteria are not met, repeat: – For every solution in generation: Create candidate and aproximate it with GP model If confidence interval is too large, evaluate solution Compare under uncertainty candidate with parent – Do selection procedure under uncertainty – Update model with newly exactly evaluated solutions 12

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Comparison of parent and candidate solutions under uncertainty Three types of comparison: – Evaluated parent compared to approximated candidate – Parent and candidate both approximated – Parent and candidate both evaluated 13

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Comparison of parent and candidate solutions under uncertainty (2) For every objective we need a separate model Approximated solution has for every objective mean (fitness) value and confidence interval Comparing solutions separately for every objective If solutions interval(value +- confidence interval) overlap => incomparable objective 14

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Comparison of parent and candidate solutions under uncertainty (3) 15

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Comparison of parent and candidate solutions under uncertainty (4) 16

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Comparison of parent and candidate solutions under uncertainty (5) 17

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Comparison of parent and candidate solutions under uncertainty (6) 18

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Comparison of parent and candidate solutions under uncertainty (7) 19

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NSGA-II selection procedure NSGA-II environmental selection procedure: – Nondominated sorting – Crowding distance 20

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NSGA-II selection procedure under uncertainty Rank of solutions determined with comparison under uncertainty If, because of the uncertainty, dominance status could not be obtained, we mark this solution as potential for reevaluated After comparison with all other solutions: – If solution is nondominated and marked, than the solution is exactly reevaluated Solutions on the front are nondominated 21

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NSGA-II selection procedure under uncertainty - example Example when to reevaluate solution 22

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Testing environment 9 WFG benchmark problems Continuous steel casting problem Stopping criteria: max number of evaluations Max number of evaluations: 10000 Population size: 100 Comparing results of our algorithm with DEMO

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Average time for solution approximation

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WFG1 AlgorithmAverage number of exact evaluations HypervolumeAverage opti. time Average eval time DEMO100000.93120:00:15 GP-DEMO85020.89613:37:24

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WFG2 AlgorithmAverage number of function evaluations HypervolumeAverage opti. time Average eval time DEMO100000.9643 GP-DEMO61000.96423:21:52

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WFG3 AlgorithmAverage number of function evaluations HypervolumeAverage opti. time Average eval time DEMO100000.9594 GP-DEMO79730. 95942:54:15

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WFG4 AlgorithmAverage number of function evaluations HypervolumeAverage opti. time Average eval time DEMO100000.9346 GP-DEMO76040.93462:55:33

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WFG5 AlgorithmAverage number of function evaluations HypervolumeAverage opti. time Average eval time DEMO100000.9139 GP-DEMO57660.91352:50:12

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WFG6 AlgorithmAverage number of function evaluations HypervolumeAverage opti. time Average eval time DEMO100000.9366 GP-DEMO69670.93572:54:05

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WFG7 AlgorithmAverage number of function evaluations HypervolumeAverage opti. time Average eval time DEMO100000.9368 GP-DEMO76580.93682:58:11

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WFG8 AlgorithmAverage number of function evaluations HypervolumeAverage opti. time Average eval time DEMO100000.8668 GP-DEMO60210.86323:00:48

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WFG9 AlgorithmAverage number of function evaluations HypervolumeAverage opti. time Average eval time DEMO100000.9202 GP-DEMO71200. 919702:15:55

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Continuous steel casting problem Searching for the best quality of casted steel Continuous steel casting simulator – 4 input variables – 3 objectives 3000 solution evaluations 34

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Continuous steel casting problem AlgorithmAverage number of function evaluations HypervolumeAverage opti. time Average eval time DEMO3000 GP-DEMO (3000)9600.513938:20:053s

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Observations Results depend on the problem If the problem is hard to model, than the solutions have high confidence interval and we have to reevaluate almost all solutions If the problem can be modeled efficiently than the GP-DEMO is very effective

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Future work Use of global and local models for approximation Tests on additional problems Comparison with related methods Publication in an SCI journal 37

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