### Table 10: Results for binary tournament selection ( order relations (I) till (IV)) and proportionate selection ONEMAX Binary tournament selection does not take the tness values into account; only the order relations are relevant. This leads to the following behavior. The function g(0) = 0; g(1) = ; g(2) = 1 is contained in class (I). The function g(0) = 0; g(1) = 0; g(2) = 1 is contained in class (II). They are mathematically almost identical. Nevertheless, the di erence equations for p are very di erent. From Theorem 16 another important result can be derived. The tness function g(0) = ; g(1) = 0; g(2) = 1 is contained in class (III). If the univariate marginal fre- quency p of the initial population is less than 0:5, then p will converge to p = 0. Now the 35

"... In PAGE 35: ... This value is the root of p2 + p ? 1 = 0. Table10 gives some numerical results. For comparison, results for ONEMAX and proportionate selection are also given.... In PAGE 37: ...endently of the tness values. Only the order relation is used. Proportionate selection selects too weakly when the population approaches the optimum. This can be observed in Table10 . At the beginning, p increases at a much faster rate than for binary tournament selection, giving a faster convergence to the optimum p = 1.... ..."

### Table 10: Results for binary tournament selection ( order relations (I) till (IV)) and proportionate selection ONEMAX Binary tournament selection does not take the tness values into account; only the order relations are relevant. This leads to the following behavior. The function g(0) = 0; g(1) = ; g(2) = 1 is contained in class (I). The function g(0) = 0; g(1) = 0; g(2) = 1 is contained in class (II). They are mathematically almost identical. Nevertheless, the di erence equations for p are very di erent. From Theorem 16 another important result can be derived. The tness function g(0) = ; g(1) = 0; g(2) = 1 is contained in class (III). If the univariate marginal fre- quency p of the initial population is less than 0:5, then p will converge to p = 0. Now the 35

"... In PAGE 35: ... This value is the root of p2 + p ? 1 = 0. Table10 gives some numerical results. For comparison, results for ONEMAX and proportionate selection are also given.... In PAGE 37: ...endently of the tness values. Only the order relation is used. Proportionate selection selects too weakly when the population approaches the optimum. This can be observed in Table10 . At the beginning, p increases at a much faster rate than for binary tournament selection, giving a faster convergence to the optimum p = 1.... ..."

### Table 10: Results for binary tournament selection ( order relations (I) till (IV)) and

in use

"... In PAGE 35: ... This value is the root of p 2 + p ; 1=0. Table10 gives some numerical results. For comparison, results for ONEMAX and proportionate selection are also given.... In PAGE 37: ...endently of the tness values. Only the order relation is used. Proportionate selection selects too weakly when the population approaches the optimum. This can be observed in Table10 . At the beginning, p increases at a much faster rate than for binary tournament selection, giving a faster convergence to the optimum p = 1.... ..."

### Table 12: Correlation between proportionate changes in # of classes and

"... In PAGE 8: ...alues in the JDK versions.......................................................................... 93 Table12 : Correlation between proportionate changes in # of classes and SBSM values in the ANT versions.... In PAGE 102: ... 93 Table 11 and Table12 below show this correlation for the JDK and the ANT versions respectively. Table 11: Correlation between proportionate changes in # of classes and SBSM values in the JDK versions JDK1.... ..."

### Table 15: The incidence of proportionate changes in social incomes

2001

Cited by 2

### Table 1: Network complexities for minimal solutions discovered. The symbols #L, #U, and #W denote the number of layers, units, and weights of the network. The column #g shows the number of generations to obtain the solution. An elitest selection strategy with top 20% truncation was used.

1993

"... In PAGE 5: ... The normalization of the functions does not hinder the probabilistic interpretation of the network learning, because we are using a ranking selection strategy, not proportionate selection: for the survival only the ranking is of importance. The results are summarized in Table1 which shows the complexity of discovered minimal solutions and the required time in generations. The number of weights given in the table is in terms of the num- ber of connections and thresholds with binary val- ues.... ..."

Cited by 27

### Table 1: Network complexities for minimal solutions discovered. The symbols #L, #U, and #W denote the number of layers, units, and weights of the network. The column #g shows the number of generations to obtain the solution. An elitest selection strategy with top 20% truncation was used.

"... In PAGE 5: ... The normalization of the functions does not hinder the probabilistic interpretation of the network learning, because we are using a ranking selection strategy, not proportionate selection: for the survival only the ranking is of importance. The results are summarized in Table1 which shows the complexity of discovered minimal solutions and the required time in generations. The number of weights given in the table is in terms of the num- ber of connections and thresholds with binary val- ues.... ..."

### Table 3 Authors with four or more CI articles (As retrieved from ABI/Inform and LISA for the period January 1975 to December 2004. Co-authorship represented proportionately.) ABI/Inform Complete LISA Author Number of articles* Author Number of articles*

in ABSTRACT

"... In PAGE 4: ...able 2 Articles Retrieved From ABI/Inform and LISA Using Selected Terminology... 28 Table3 Authors with four or more CI articles.... ..."

### Table 3 gathers the time complexity calculations together. The best of the methods are O(n), and it is difficult to imagine how fewer steps can be used since we must select n individuals in some manner. Of the O(n) methods, tournament selection is the easiest to make parallel, and this may be its strongest recommendation, as GAs cry out for parallel implementation, even though most of us have had to make do with serial versions. Whether paying the O( n log n) price of Genitor is worth its somewhat higher later growth ratio is unclear, and the experiments recommended earlier should be performed. Methods with similar early growth ratios and not-too-

1991

"... In PAGE 19: ... Table3 : A Comparison of Selection Algorithm Time Complexity SCHEME TIME COMPLEXITY Roulette wheel proportionate RW proportionate w fbinary search Stochastic remainder proportionate Stochastic universal proportionate Ranking Tournament Selection Genitor w fbinary search O(n2) O(n logn) O(n) O(n) O( n In n)+ time of selection O(n) O(n logn) different late growth ratios should perform similarly. Any such comparisons should be made under controlled conditions where only the selection method is varied, however.... ..."

Cited by 284

### Table 7: Correlation between proportionate changes in number of classes and

"... In PAGE 8: ...alues in the JDK versions.......................................................................... 84 Table7 : Correlation between proportionate changes in number of classes and SSSM values in the ANT versions.... ..."