Global+Optimization+Algorithms+Theory+and+Application_Part17

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

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Unformatted text preview: 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. 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....
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Global+Optimization+Algorithms+Theory+and+Application_Part17...

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