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|
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
|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