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Global+Optimization+Algorithms+Theory+and+Application_Part17

# Global+Optimization+Algorithms+Theory+and+Application_Part17...

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20.3 Evaluation 321 runs, we can compute the number # q of experiments that fulfilled the predicates attached to q and the estimators of the minimum hatwide q , mean q , maximum hatwide q , median med( q ), and the standard deviation s [ q ], and so on. Obviously, not all of them are needed or carry a meaning in every experiment. Table 20.5 lists some of these first metrics.

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322 20 Experimental Settings, Measures, and Evaluations Measure Short Description Number of Successful Runs # s The number of runs where successful individuals were discovered. # s = |{ i : ( s τ i negationslash = ) (0 i< # r ) }| (20.1) Success Fraction s / r The fraction of experimental runs that turned out successful. s / r = # s # r (20.2) Minimum Success Evaluation hatwider s τ The number of evaluations τ needed by the fastest (successful) ex- perimental run to find a successful individual. (or if no run was successful) hatwide s τ = braceleftbigg min { s τ i negationslash = ∅} if s τ i negationslash = otherwise (20.3) Mean Success Evaluation s τ The average number of evaluations τ needed by the (successful) experimental runs to find a successful individual. (or if no run was successful) s τ = braceleftBigg s τ i negationslash = s τ i |{ s τ i negationslash = ∅}| if s τ i negationslash = otherwise (20.4) Maximum Success Evaluation hatwider s τ The number of evaluations τ needed by the slowest (successful) experimental run to find a successful individual. (or if no run was successful) hatwide s τ = braceleftbigg max { s τ i negationslash = ∅} if s τ i negationslash = otherwise (20.5) Minimum Success Generation hatwide s t The number of generations/iterations t needed by the fastest (suc- cessful) experimental run to find a successful individual. (or if no run was successful) hatwide s t = braceleftbigg min { s t i negationslash = ∅} if s t i negationslash = otherwise (20.6) Mean Success Generation s t The average number of generations/iterations t needed by the (suc- cessful) experimental runs to find a successful individual. (or if no run was successful) s t = braceleftBigg s t i negationslash = s t i |{ s t i negationslash = ∅}| if s t i negationslash = otherwise (20.7) Maximum Success Generation hatwide s t The number of Generations generations/iterations t needed by the slowest (successful) experimental run to find a successful individual. (or if no run was successful) hatwide s t = braceleftbigg max { s t i negationslash = ∅} if s t i negationslash = otherwise (20.8) Number of Perfect Runs # p The number of runs where perfect individuals were discovered. # p = |{ i : ( p τ i negationslash = ) (0 i< # r ) }| (20.9) Perfection Fraction p / r The fraction of experimental runs that found perfect individuals. p / r = # p # r (20.10) Minimum Perfection Evaluation hatwider p τ The number of evaluations τ needed by the fastest (perfect) exper- imental run to find a perfect individual. (or if no run was found one) hatwider p τ = braceleftbigg min { p τ i negationslash = ∅} if p τ i negationslash = otherwise (20.11) Mean Perfection Evaluation p τ
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