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Chapter seventhe particle swarmother binary decision

294 Chapter Seven—The Particle Swarm

P x id ( ) = 1 ) = f x id ( t 1 ), v id ( t 1 ), p id , p gd
I P(xid(t)=1) is the probability that individual i will choose 1 (of course the probability of their making the zero choice is 1 − P) for



pid is the best state found so far, for example, it is 1 if the individ-ual’s best success occurred when xid was 1 and 0 if it was 0

pgd is the neighborhood best, again 1 if the best success attained by any member of the neighborhood was when it was in the 1 state

s v ) 1
id = 1 + exp(−v id )

Team LRN

v id ( ) = v id ( t 1 ) + ϕ 1 ( p id x i d ( t 1 )) + ϕ 2 ( p gd x id ( t
if ρid < s v id ( )) then x id ( ) = 1 ; else x id ( ) = 0

where ρid is a vector of random numbers, drawn from a uniform distribu-tion between 0.0 and 1.0. These formulas are iterated repeatedly over each dimension of each individual, testing every time to see if the cur-rent value of xid results in a better evaluation than pid, which will be up-dated if it does. Boyd and Richerson varied the relative weighting of indi-vidual experience and social transmission according to some theoretical suggestions; the current model acknowledges the differential effects of the two forces without preconceptions about their relative importance. Sometimes decisions are based more on an individual’s personal experi-ence and sometimes on their perception of what other people believe, and either kind of information will dominate sometimes.

One more thing: we can limit vid so that s(vid) does not approach too closely to 0.0 or 1.0; this ensures that there is always some chance of a bit flipping (we also don’t want vi moving toward infinity and overloading the exponential function!). A constant parameter Vmax can be set at the

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