How to set seed for random simulations with foreach and doMC packages?

Using set.seed(123, kind = "L'Ecuyer-CMRG") also does the trick and does not require an extra package:

set.seed(123, kind = "L'Ecuyer-CMRG")
a <- foreach(i=1:2,.combine=cbind) %dopar% {rnorm(5)}

set.seed(123, kind = "L'Ecuyer-CMRG")
b <- foreach(i=1:2,.combine=cbind) %dopar% {rnorm(5)}

identical(a,b)
# TRUE

My default answer used to be "well then don't do that" (using foreach) as the snow package does this (reliably!) for you.

But as @Spacedman points out, Renaud's new doRNG is what you are looking for if you want to remain with the doFoo / foreach family.

The real key though is a clusterApply-style call to get the seeds set on all nodes. And in a fashion that coordinated across streams. Oh, and did I mention that snow by Tierney, Rossini, Li and Sevcikova has been doing this for you for almost a decade?

Edit: And while you didn't ask about snow, for completeness here is an example from the command-line:

edd@max:~$ r -lsnow -e'cl <- makeSOCKcluster(c("localhost","localhost"));\
         clusterSetupRNG(cl);\
         print(do.call("rbind", clusterApply(cl, 1:4, \
                                             function(x) { stats::rnorm(1) } )))'
Loading required package: utils
Loading required package: utils
Loading required package: rlecuyer
           [,1]
[1,] -1.1406340
[2,]  0.7049582
[3,] -0.4981589
[4,]  0.4821092
edd@max:~$ r -lsnow -e'cl <- makeSOCKcluster(c("localhost","localhost"));\
         clusterSetupRNG(cl);\
         print(do.call("rbind", clusterApply(cl, 1:4, \
                                             function(x) { stats::rnorm(1) } )))'
Loading required package: utils
Loading required package: utils
Loading required package: rlecuyer
           [,1]
[1,] -1.1406340
[2,]  0.7049582
[3,] -0.4981589
[4,]  0.4821092
edd@max:~$ 

Edit: And for completeness, here is your example combined with what is in the docs for doRNG

> library(foreach)
R> library(doMC)
Loading required package: multicore

Attaching package: ‘multicore’

The following object(s) are masked from ‘package:parallel’:

    mclapply, mcparallel, pvec

R> registerDoMC(2)
R> library(doRNG)
R> set.seed(123)
R> a <- foreach(i=1:2,.combine=cbind) %dopar% {rnorm(5)}
R> set.seed(123)
R> b <- foreach(i=1:2,.combine=cbind) %dopar% {rnorm(5)}
R> identical(a,b)
[1] FALSE                     ## ie standard approach not reproducible
R>
R> seed <- doRNGseed()
R> a <- foreach(i=1:2,combine=cbind) %dorng% { rnorm(5) }
R> b <- foreach(i=1:2,combine=cbind) %dorng% { rnorm(5) }
R> doRNGseed(seed)
R> a1 <- foreach(i=1:2,combine=cbind) %dorng% { rnorm(5) }
R> b1 <- foreach(i=1:2,combine=cbind) %dorng% { rnorm(5) }
R> identical(a,a1) && identical(b,b1)
[1] TRUE                      ## all is well now with doRNGseed()
R>