Noisy Optimization Problem u Without noise With noises, Additive min f(x),x=[x1, x2, ,x d x∈X (x)=f(x)+N(0,72) d is the number of dimensions 12. Multiplicative: x is the feasible region of x (x)=(x)XN(12)
Noisy Optimization Problem ◼ Without noise: min 𝑥∈𝑋 𝑓(𝑥) , 𝑥 = [𝑥 1 , 𝑥 2 , … , 𝑥 𝑑 ] 𝑑 is the number of dimensions. 𝑋 is the feasible region of 𝑥. ◼ With noises: 1. Additive: 𝑓 መ + 𝑥 = 𝑓 𝑥 + 𝑁 0,𝜎 2 2. Multiplicative: 𝑓 መ × 𝑥 = 𝑓 𝑥 × 𝑁(1,𝜎 2 )
Benchmark functions 1. Wang, Handing, Yaochu Jin, and John Doherty, A Generic Test Suite for Evolutionary Multifidelity Optimization", IEEE Transactions on Evolutionary Computation, voL 22, 10.6 pp. 836-850, 2018 2. G.H.Wu,RMallipeddi, P. N. Suganthan, " Problem Definitions and Evaluation Criteria for the CEC 2017 Competition and Special Session on Constrained Single Objective Real-parameter Optimization", Techmical RD0n,2016 3. J.J. Liang, B. Y. Qu, P.N. Suganthan, et al, "Problem Definitions and Evaluation Criteria for the CEc 2015 Competition on Learning-based Rea-Parameter Single Objective Optimization", Technical report, 2014 4. J.J. Liang, B. Y. Qu, P.N. Suganthan, Alfredo G. H, "Problem definitions and evaluation criteria for the cec 2013 special session on real-parameter", EEE Congress on Evolutionary Computation(CEC1, 2013 5. K Tang,XLi, P.N. Suganthan, Z. Yang and W. Thomas, "Benchmark functions for the cec'2010 special session ind competition on large-scale global optimization", Technical Report, 2010 6. R Mallipeddi, P N Suganthan, "Problem definitions and evaluation criteria for the cec 2010 competition on constrained real parameter optimization",EEE Congress on Evolutionary Computation(CEC, 2010 7. K Tang, X. Yao, P.N. Suganthan, C MacNish, Y P Chen, C. M. Chen, Z Yang, "Benchmark functions for the CEC2008 special session and competition on large scale global optimization", IEEE Congress on Evolutionary Computation(CEC, 2008 8. P.N. Suganthan, N. Hansen, J.J. Liang, K Deb, Y.-P. Chen, A. Auger, S. Tiwari, "Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization", IEEE Congress_ onl Evolutionary Computation(CEC1, 2005
Benchmark Functions 1. Wang, Handing, Yaochu Jin, and John Doherty,"A Generic Test Suite for Evolutionary Multifidelity Optimization",IEEE Transactions on EvolutionaryComputation,vol.22,no.6,pp. 836-850,2018. 2. G.H.Wu, R.Mallipeddi, P. N. Suganthan,"Problem Definitions and Evaluation Criteria for the CEC 2017 Competition and Special Session on Constrained Single Objective Real-Parameter Optimization", Technical Report, 2016. 3. J. J. Liang, B. Y. Qu, P. N. Suganthan, et al.,"Problem Definitions and Evaluation Criteria for the CEC 2015 Competition on Learning-basedReal-Parameter Single Objective Optimization",TechnicalReport, 2014. 4. J. J. Liang, B. Y. Qu，P. N. Suganthan, Alfredo G. H., "Problem definitions and evaluation criteria for the CEC 2013 specialsessionon real-parameter optimization",IEEE Congress on EvolutionaryComputation(CEC), 2013. 5. K. Tang, X. Li, P. N. Suganthan, Z. Yang and W. Thomas, "Benchmark functions for the cec' 2010 special session and competitionon large-scale global optimization", Technical Report, 2010. 6. R. Mallipeddi, P. N. Suganthan, " Problem definitions and evaluation criteria for the CEC 2010 competition on constrainedreal parameter optimization ",IEEE Congress on EvolutionaryComputation (CEC), 2010. 7. K. Tang, X. Yao, P. N. Suganthan, C. MacNish, Y. P. Chen, C. M. Chen, Z. Yang, "Benchmark functions for the CEC’2008 special session and competition on large scale global optimization", IEEE Congress on Evolutionary Computation(CEC), 2008. 8. P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y. –P. Chen, A. Auger, S. Tiwari, "Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization", IEEE Congress on EvolutionaryComputation (CEC), 2005
Benchmark Functions on Large-Scale Optimization in CEC 2010 Original 他 Additive Multiplicative noisy
8 Benchmark Functions on Large-Scale Optimization in CEC 2010 Original Additive Noisy Multiplicative Noisy
Effects of noisy fitness Evaluation Undesirable selection Behavior a superior candidate may be erroneously believed to be inferior, causing it to be eliminated An inferior candidate may be erroneously believed to be superior, causing it to survive and reproduce. Undesirable effects The system does not retain what it has learnt. Exploitation is limited Fitness does not monotonically improve with generation The learning rate is reduced 1. DiPietro A, While l, Barone l, Applying evolutionary algorithms to problems with noisy, time-consuming fitness functions"EEE Congress on Evolutionar Computation(CEC, pp. 1254-1261, 2004
Effects of Noisy Fitness Evaluation ◼ Undesirable Selection Behavior ◼ A superior candidate may be erroneously believed to be inferior, causing it to be eliminated. ◼ An inferior candidate may be erroneously believed to be superior, causing it to survive and reproduce. ◼ Undesirable effects ◼ The system does not retain what it has learnt. ◼ Exploitation is limited. ◼ Fitness does not monotonically improve with generation. ◼ The learning rate is reduced. 1.Di Pietro A, While L, Barone L, "Applying evolutionary algorithms to problems with noisy, time-consuming fitness functions",IEEE Congress on Evolutionary Computation (CEC), pp. 1254–1261,2004
Learning and Optimization are Both Needed in Noisy Environments Resampling . Fitness value Finite budget Learning Learn Exploitation Swarm Optimize Intelligence e Exploration sy Environment
Learning and Optimization are Both Needed in Noisy Environments 10 • Fitness value • Finite budget Resampling Learning • Exploitation • Exploration Swarm Intelligence Noisy Environment Optimize Learn