A core Course on Modeling

1. A core Course on Modeling Introductionto Modeling 0LAB0 0LBB0 0LCB0 0LDB0 c.w.a.m.v.overveld@tue.nl v.a.j.borghuis@tue.nl S.25

2. formulate purpose define identify entities choose relations conceptualize obtain values formalize relations formalize operate model obtain result execute present result interpret result conclude Executionphase: operate model

3. Evolutionarymethodstoapproximate Pareto front Trade-offsand the Pareto front We shouldfind‘good’ or even ‘best’ concepts in cat.-I space. Mathematical optimizationonlyworksfor single-valuedfunctions; Approach: graduallyclimbingupwardto a slopesurface; Thiswouldapplytoa single cat.-II quantity, or allcat.-II quantitieslumped; We seeksomething more generic. http://www.morguefile.com/archive/display/233348

4. Evolutionarymethods Idea (Eckart Zitzler): combine Pareto andEvolution. • Mainfeatures of evolution: • genotypeencodes blueprint of individual (‘cat.-I’); • genotype is passed over tooffspring; • new individual: genotype  phenotype, determiningitsfitness (‘cat.-II’); http://www.clipartlord.com/wp-content/uploads/2013/06/evolution.png

5. Evolutionarymethods • variationsin genotypes (mutation, cross-over) causevariationamongphenotypes; • fitter phenotypes have larger change of surviving, procreating, and passing theirgenotypes on to next generation. http://www.morguefile.com/archive/display/606445

6. Evolutionarymethods Issues toresolve: • How to start  population of random individuals (tuples of valuesfor cat.-I quantities); • How todefine fitness  fitter whendominatedbyfewer; • Next generation  preserve non-dominatedones; complete population with mutationsand crossing-over; • Convergence if Pareto front no longer moves. http://www.morguefile.com/archive/display/672384

7. Evolutionarymethods Caveats: Pareto-Genetic is not perfect http://cdn.morguefile.com/imageData/public/files/j/jusben/preview/fldr_2008_11_17/file000612131406.jpg

8. Evolutionarymethods Caveats: Pareto-Genetic is not perfect QUIZ Whatwould happen ifthere are very few dominatedsolutions in cat.-II space? http://cdn.morguefile.com/imageData/public/files/j/jusben/preview/fldr_2008_11_17/file000612131406.jpg

9. Evolutionarymethods Caveats: Pareto-Genetic is not perfect • If the fraction non-dominatedconcepts is too large, evolutionmakes no progress; • Iftherebroad niches, findingindividuals in a narrow niche maybeproblematic; • Approximationsmayfailto get nearthe theoretical best Pareto front. http://cdn.morguefile.com/imageData/public/files/j/jusben/preview/fldr_2008_11_17/file000612131406.jpg

10. Evolutionarymethods Caveats: Pareto-Genetic is not perfect (No guaranteethatanalyticalalternativesexist) DON’T use Pareto-Genetic ifguaranteeforoptimal solution is required.

11. Evolutionarymethods demo

12. Evolutionarymethods Ifanythingelsefails: • Complementary approach: localoptimization (tobeapplied on allelements of the Pareto-front separately); • Split cat.-I space in sub spacesif model functionbehaves different in different regimes (e.g., toomuch cat.-I freedommay lead to bad evolutionprogress); • Temporarily fix some cat.-IV quantities (pretendthatthey are in category-III). http://www.morguefile.com/archive/display/708871

13. Summary • functionalmodelhelpsdistinguish input (choice) and output (frompurpose); • Building a functional model as a graph shows roles of quantities. These are: • Cat.-I : free tochoose; • Modelsfor (design) decision support: the notion of design space; • Choiceof cat.-I quantities: no dependency-by-anticipation; • Cat.-II : represents the intended output; • The advantagesanddisadvantages of lumpingandpenalty quantities; • The distinctionbetweenrequirements, desires, andwishes; • The notion of dominancetoexpressmulti-criteria comparison; Pareto front; • Cat.-III : represents constraints from context; • Cat.-IV : intermediatequantities; • For optimization: useevolutionary approach; • Approximatethe Pareto front using the SPEA algorithm; • Localsearchcanbeusedfor post-processing.