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 |
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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 |
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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 |
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s v | ) | 1 | ||||||
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id | = | 1 | + | exp(−v | id | ) |
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v | id | ( ) | = | v | id | ( t | − | 1 ) | + | ϕ 1 | ( | p | id | − | x i | d | ( t | − | 1 )) | + | ϕ | 2 | ( | p | gd | − | x | id | ( t | − | |||||||
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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