By Pearl R., Reed. L. J.

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7) and the mean E(z) and 2 and σ 2 of z derived above. 2) of xi,g and yi,g . The pair (xi,g , yi,g ) is generally not independent for different i due to the correlation between yi,g and x j,g (i = j). This is because the indices r0 , r1l and r2l could be equal to j with probability 1/(NP − 1). However, the correlation coefficient is at the order of 1/NP and approaches zero as the population size NP goes to infinity. , independent) for different i. Furthermore, we approximately assume that the identically distributed zi,g ’s are independent, and so are the elements of {z j,i,g }.

JADE is the only algorithm to implement a relatively greedy mutation strategy which utilizes the information of both the high-quality solutions in the current population and the inferior solutions previously explored during the optimization search. It is expected that a greedy mutation strategy and a parameter adaptation scheme can be mutually beneficial, since the former is capable of increasing the convergence rate while the latter is helpful to maintain the reliability of the algorithm at a high level by adapting to appropriate control parameter values.

2 FADE The fuzzy adaptive differential evolution (FADE), introduced by Liu and Lampinen [19], is a new variant of DE, which uses fuzzy logic controllers to adapt the control parameters Fi and CRi for the mutation and crossover operations. A similar 42 4 Parameter Adaptive Differential Evolution method has also been independently proposed for multi-objective DE optimization [20]. Similar to many other adaptive DE algorithms (except DESAP), the population size is assumed to be tuned in advance and kept fixed throughout the evolution process of FADE.

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On the Rate of Growth of the Population of the United States since 1790 and Its Mathematical Representation by Pearl R., Reed. L. J.


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