M Constraints in GA 16888 ESD.77 Essentially three options Implement implicitely in coding/decoding scheme Penalize objective function for constraint violation Selection operator: only select valid solutions for mating C Massachusetts Institute of Technology -Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
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Mlesd Encoding/Decoding Scheme 16888 E077 Xi-design variable Radius r=2.57[m] 0101111:010 Ensure that only"maximum"and Radius( genotype) “ minimun” variab| e values are captured by coding scheme E.g Works well for implementing 0000000=1.0m(min) bounds Xi.LB <X,<X 1111111=30m(max) but not general constraints such as g(x<0, h(x) =0 C Massachusetts Institute of Technology -Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
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M Penalty Approach( 16888 E077 C Usually some calculation is necessary to verify if a constraint is met or not, e.g. stresses, power output Solution Penalize the fitness of solutions that violate constraints penalty S(r=F()-P(r) valid invalid zone invalid zone zone Fixed Penalty for Constraint Violation C Massachusetts Institute of Technology -Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
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M Penalty Approach(I) 16888 E077 Fixed penalty provides no ranking of the degree of constraint violation -introduce variable penalty penal penalty valid k zone invalid nvalid: zone valid zone zone zone zone Linear variation Stepped penalty Other schemes: polynomial, exponential (close to SA) L Important when constraints are hard to meet o Massachusetts Institute of Technology -Prof de Weck and Prof. Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
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